R-process: The Astrophysical Origin Of The Heavy Elements And Related Rare Isotope Accelerator Physics (Proceedings from the Institute for Nuclear Theory)

Proceedings from the Institute for Nuclear Theory - Vol.13

editors

Yong-Zhong Qian Ernst Rehm Hendrik Schatz Friedrich-Karl Thielemann

The r-Process:

The Astrophysical Origin of the Heavy Elements and Related Rare Isotope Accelerator Physics

^ 1 The r-Process:

^ T h e Astrophysical Origin of the Heavy Elements and Related Rare Isotope Accelerator Physics

PROCEEDINGS FROM THE INSTITUTE FOR NUCLEAR THEORY Series Editors: Wick C. Haxton (Univ. of Washington) Ernest M. Henley (Univ. of Washington)

Published Vol. 1:

Nucleon Resonances and Nucleon Structure ed. G. A. Miller

Vol. 2:

Solar Modeling eds. A. B. Balantekin and J. N. Bahcall

Vol. 3:

Phenomenology and Lattice QCD eds. G. Kilcup and S. Sharpe

Vol. 4:

N* Physics eds. T.-S. H. Lee and W. Roberts

Vol. 5:

Tunneling in Complex Systems ed. S. Tomsovic

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Nuclear Physics with Effective Field Theory eds. M. J. Savage, R. Seki and U. van Kolck

Vol. 7:

Quarkonium Production in High-Energy Nuclear Collisions eds. B. Jacak and X.-N. Wang

Vol. 8:

Quark Confinement and the Hadron Spectrum eds. A. Radyushkin and C. Carlson

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Nuclear Physics with Effective Field Theory II eds. P. F. Bedaque, M. J. Savage, R. Seki and U. van Kolck

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Exclusive and Semi-Exclusive Processes at High Momentum Transfer eds. C. Carlson and A. Radyushkin

Vol. 11: Chiral Dynamics: Theory and Experiment III eds. A. M. Bernstein, J. L. Goity and U.-G. MeiBner Vol. 12: The Phenomenology of Large A/c QCD ed. R. F. Lebed Vol. 13:

The r-Process: The Astrophysical Origin of the Heavy Elements and Related Rare Isotope Accelerator Physics eds. Y.-Z. Qian, E. Rehm, H. Schatz and F.-K. Thielemann

National Institute for Nuclear Theory, University of Washington, USA 8-10 January 2004

editors

Yong-Zhong Qian University of Minnesota

Ernst Rehm Argonne National Laboratory

Hendrik Schatz Michigan State University

Friedrich-Karl Thielemann University of Basel

Proceedings of the First Argonne/MSU/JINA/INT RIA Workshop

The r-Process:

The Astrophysical Origin of the Heavy Elements and Related Rare Isotope Accelerator Physics

Y J 5 World Scientific NEWJERSEY

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THE r-PROCESS The Astrophysical Origin of the Heavy Elements and Related Rare Isotope Accelerator Physics Proceedings of the First Argonne/MSU/JINA/INT RIA Workshop Copyright © 2004 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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SERIES PREFACE The National Institute for Nuclear Theory Series

The national Institute for Nuclear Theory (INT) was established by the US Department of Energy in March, 1990. The goals of the INT include: 1. Creating a productive research environment where visiting scientists can focus their energies and exchange ideas on key issues facing the field of nuclear physics, including those crucial to the success of existing and future experimental facilities; 2. Encouraging interdisciplinary research at the intersections of nuclear physics with related subfields, including particle physics, astrophysics, atomic physics, and condensed matter; 3. Furthering the development and advancement of physicists with recent Ph.D.s; 4. Contributing to scientific education through graduate student research, INT summer schools, undergraduate summer research programs, and graduate student participation in INT workshops and programs; 5. Strengthening international cooperation in physics research through exchanges and other interactions. While the INT strives to achieve these goals in a variety of ways, its most important efforts are the three-month programs, workshops, and schools it sponsors. These typically attract 300 visitors to the INT each year. In order to make selected INT workshops and summer schools available to a wider audience, the INT and World Scientific established the series of books to which this volume belongs. In January 2004 the INT and several partners, Argonne National Laboratory, Michigan State University, and the Joint Institute for Nuclear Astrophysics, began a new workshop series to explore physics questions connected with the proposed Rare Isotope Accelerator (RIA). This volume summarizes the inaugural workshop, which focused on the r-process, the mechanism by which many of the heavy elements were synthesized under explosive conditions typical of core-collapse supernovae and neutron star collisions. Organized by Yong-Zhong Qian, Ernst Rehm, Hendrik Schatz, and Friedrich-Karl Thielemann, the workshop sought to connect the astrophysics of this process with the new information on short-lived, neutron-rich isotopes that will become available with RIA.

v

VI

This volume is the 13th in the INT series. Earlier series volumes include the proceedings of the 1991 and 1993 Uehling summer schools on Nucleon Resonances and Nucleon Structure and on Phenomenology and Lattice QCD; the 1994 INT workshop on Solar Modeling; the 1997 Jefferson Lab/INT workshop on Nucleon Resonance Physics; the tutorials of the spring 1997 INT program on Tunneling in Complex Systems; the 1998 and 1999 Caltech/INT workshops on Nuclear Physics with Effective Field Theory; the proceedings of the 1998 RHIC Winter Workshop on Quarkonium Production in Relativistic Nuclear Collisions; and the proceeding of Confinement III, of Exclusive and Semiexclusive Reactions at High Momentum, of Chiral Dynamics 2000, and of the Phenomenology of Large-N QCD, all collaborative efforts with Jefferson Laboratory. We intend to continue publishing those proceedings of INT workshops and schools which we judge to be of broad interest to the physics community.

Wick C. Haxton and Ernest Henley Seattle, Washington, August, 2004

PREFACE The next generation of radioactive beam facilities, such as the Rare Isotope Accelerator (RIA) in the US, promise to open up a wide range of new and exotic nuclei for study within the coming decade. We therefore feel that it is timely to initiate a workshop series on exploring the physics that will be addressed with such a quantum leap in experimental capability. The alternating hosts of the workshops are the National Institute for Nuclear Theory (INT), Argonne National Laboratory (ANL), and Michigan State University (MSU). The first workshop of the series with the title "The r-Process: the Astrophysical Origin of the Heavy Elements and Related Rare Isotope Accelerator Physics" was held on January 8-10, 2004 at the INT and was cosponsored by the Joint Institute for Nuclear Astrophysics (JINA). This volume is the proceedings of the workshop. The site and mechanism of the rapid neutron capture process (r-process) remain one of the big open questions in our understanding of the origin of the elements in nature. This process creates about half the solar abundances of the 60 or so elements heavier than iron and is the main source of the elements such as silver, gold, platinum, and uranium in the universe. But what exactly are the extreme conditions that are required for this process and where in the universe are these conditions realized? Is there only one site for the r-process, or are there many? The workshop brought together over 44 nuclear experimentalists, nuclear theorists, astronomers, and theoretical astrophysicists to assess the status of the field and to identify the open issues. This demonstrates impressively the importance and the great current interest of the r-process problem. Lively discussions and a great variety of ideas provided a very interactive and enjoyable atmosphere for the workshop, but also made it evident that much remains to be done in this field. In particular, a need for new experimental data became apparent. This is where rare isotope/radioactive beam facilities will play a critical role. New observations of stellar abundances, in particular in very metalpoor stars, as well as meteoritic measurements of neutron-capture elements

VII

VIII

provide critical data on the r-process. But without an understanding of the underlying nuclear physics these data cannot serve as quantitative constraints on the r-process. Rare isotope/radioactive beam facilities are expected to finally provide the missing nuclear physics input either directly or by guiding theorists in their quest to better describe extremely unstable nuclei near the drip lines. This strong interplay between nuclear experiments and theory on the one hand and astrophysical observations and theory on the other is nicely illustrated by the cover picture of this volume kindly provided by Peter Moller [see P. Moller, J. R. Nix, and K.-L. Kratz, Atomic Data Nucl. Data Tables 66, 131 (1997) for details]. Our longer-term vision is that rare isotope/radioactive beam facilities will put the nuclear physics of the r-process on a solid basis, such that sitespecific signatures can be extracted and in the end the r-process can be used as a probe of some of the most extreme environments in the universe. This can be compared to the case of the s-process, where decades of experimental studies on neutron-capture cross sections make it possible now to use sprocess nucleosynthesis as a probe of mixing processes deep in the interiors of asymptotic giant branch stars. We thank the Director of INT, Wick Haxton, for his generous financial support of this successful workshop. We are extremely grateful to the INT staff for their hospitality and immaculate logistic support. We also thank ANL, MSU, JINA, and INT for jointly sponsoring the workshop series. Yong-Zhong Qian (University of Minnesota) Ernst Rehm (Argonne National Laboratory) Hendrik Schatz (Michigan State University) Friedrich-Karl Thielemann (University of Basel)

CONTENTS

Series Preface

v

Preface

vii

The r-Process in Supernovae F.-K. Thielemann et al.

1

Precise Mass Measurements of Nuclides Approaching the r-Process J. Clark et al.

11

Fission and the r-Process Path: Recent Experimental Achievements and Future Possibilities J. Benlliure

20

/3-Decay Studies of Neutron Rich Nickel Isotopes P. Hosmer et al.

30

Weak Strength for Astrophysics S. M. Austin and R. Zegers

34

Nuclear Masses and Fission Barriers J. M. Pearson

43

Understanding Beta Decay for the r Process J. Engel

53

Neutron Captures and the r-Process T. Rauscher

63

Supernova Neutrino-Nucleus Physics and the r-Process W. C. Haxton

73

Equation of State and Neutrino Opacity of Dense Stellar Matter S. Reddy

89

IX

X

An Overview of Observations of Neutron-Capture Elements in Metal-Poor Stars J. A. Johnson

99

Efficient Searches for r-Process-Enhanced Metal-Poor Stars T. C. Beers et al.

109

The r-Process Record in Meteorites A. M. Davis

120

Inhomogenous Chemical Evolution and the Source of r-Process Elements D. Argast

129

Go Upstream of the "Milky Way": Origin of Heavy Elements Inferred from Galactic Chemical Evolution Y. Ishimaru et al.

138

The r-Process: Current Understanding and Future Tests Y.-Z. Qian Nuclear Reaction Rates and the Production of Light p-Process Isotopes in Fast Expansions of Proton-Rich Matter G. C. Jordan, IV and B. S. Meyer r-Process Nucleosynthesis in Proto-Magnetar Winds T. A. Thompson r-Process Nucleosynthesis in Neutrino-Driven Winds: Treatment of the Injection Region and Requirements on Neutrino Emission A. W. Steiner and Y.-Z. Qian General Relativity and Neutrino-Driven Supernova Winds C. Y. Cardall

147

157

167

176

186

XI

An Update on the Hot Supernova Bubble r-Process G. J. Mathews et al.

196

Ejecta from Parametrized Prompt Explosion S. Wanajo et al.

204

Are Collapsars Responsible for Some r-Process Elements? How Could We Tell? J. Pruet Neutrino Transport in Core Collapse Supernovae M. Liebendorfer

214

224

Changing the r-Process Paradigm: Multi-Dimensional and Fallback Effects C. L. Fryer and A. Hungerford

234

List of Participants

245

T H E R-PROCESS IN SUPERNOVAE

F.-K. T H I E L E M A N N , D. A R G A S T , D. M O C E L J , T. R A U S C H E R Department

fur Physik und Astronomie, University of Basel, Klingelbergstr. CH-4056 Basel, Switzerland

82,

J O H N J. COWAN Department

of Physics

& Astronomy, University 73019, USA

of Oklahoma,

Norman,

OK

K.-L. KRATZ, B. P F E I F F E R Institut

fur Kernchemie,

Universitat

Mainz, D-S5128 Mainz,

Germany

This introductory review aims at understanding r-process nucleosynthesis by addressing the issues involved, nuclear properties, necessary environment conditions, properties of different suggested r-process sites, observational constraints and Galactic evolution. We summarize the remaining challenges and uncertainties which need to be overcome for a full understanding of the nature and site(s) of the r-process.

1. I n t r o d u c t i o n In nature the formation of the elements beyond iron are almost exclusively due to neutron capture processes, avoiding Coulomb barriers to overcome. The two main processes, the slow neutron capture process (s-process) and rapid neutron capture process (r-process) 2 , are differentiated on the basis of the timescale for neutron captures (r n ) with respect to beta decays ( T ^ ) . In the s-process with r n > > r / 3 , the n-capture path, identifying the isotopes that participate, will remain close to the valley of beta stability (see Figure 1) and the properties of the isotopes involved in s-process nucleosynthesis are in general experimentally determinable. In the r-process with r n < < r / 3 , neutron captures will proceed into the very neutron-rich regions far from the beta-stable valley. Once the neutron flux is exhausted, the unstable nuclei beta-decay back to the valley of stability, forming the stable r-process nuclei. Far from stability, experimental measurements are very difficult, if not impossible at present. The elements that compose solar system material

1

2

contain admixtures from both neutron capture processes with Tn»Tp or rn (Z+l,A) + e~), which produces results similar to /^-transformations10. Site-independent classical analyses - based on neutron number density n„, temperature T, and duration time r, as well as calculations with the parameters entropy S, the average proton to nucleon ratio Ye (measuring the neutron-richness of matter), and the expansion timescale r - have shown that the solar r-process abundances can be fit by a continuous superposition of components with neutron separation energies at freeze-out in the range 4-1 MeV6'14. These are the regions of the nuclear chart where nuclear structure - related to masses far from stability and /3-decay half-lives - has to be investigated. They predominantly include nuclei not currently accessible in laboratory experiments, but maybe in the foreseeable future with facilities such as RIKEN, GSI and RIA in Japan, Germany and the US 14 . In addition, expanding theoretical efforts means will be necessary to provide the improved predictions for nuclear masses, half-lives, neutron-capture reactions, neutrino-induced reactions and fission properties 12,14,10 ' 8 . 3. Abundance Observations in Stars Much of the new knowledge regarding the formation of the heaviest elements has been gained recently from high-resolution spectroscopic observations of stars in our Galaxy. In particular, the halo stars with very low iron abundances as low as [Fe/H] < - 3 a are among the oldest stars, forming early in the history of our Galaxy. The elemental abundance distribution of the most well-studied star CS 22892-052 l r is shown in Figure 2. a

We adopt the usual spectroscopic notations that [A/B] = logio(NA/Ne)star logio(NA/N B )©, and that log e(A) = logio(NA/NH) + 12.0, for elements A and B.

-

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Th\

« Stellar Elemental Abundance Data Solar System r-Process Abundances

30

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>Pb

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O

1"

I. •

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1

60

U" Y

1, ,

70

i,

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. . 1 . . , .

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Atomic Number Figure 2. The neutron-capture elemental abundance pattern in the Galactic halo star CS 22892-052 compared with the (scaled) solar system r-process abundances (solid line) after 1 7 .

For comparison purposes a scaled (for metallicity) solar system r-process elemental abundance curve is superimposed on the stellar data in Figure 2. This line was determined by deconvolving the total solar system abundances into their individual s- and r-process isotopic components, summing them and then obtaining a solar elemental r-process-only curve. 16 ' 15 For the elements from Ba (Z = 56) and above, there is a striking agreement between the abundances in CS 22892-052 and the scaled solar system r-process distribution. This says much about the r-process. First, the presence of these elements in the halo stars demonstrates the operation of the r-process during the earliest Galactic history, presumably related to massive stars that ended their lives fast. The agreement between the heaviest n-capture elements in CS 22892-052 and the Sun also demonstrates the robustness of the r-process, operating in much the same manner over many billions of years. This suggests that however and wherever the r-process operates to form these heaviest elements, it is very well-confined and uniform. That indicates a very narrow range of astrophysical conditions (temperatures,

6

densities, neutron fluxes, etc.) for all of the sites involved, or perhaps, that only a very small minority of supernovae (restricted by mass range) produce r-process elements. While there have not been as much isotopic data available for halo stars, recent observations appear to be in agreement with the elemental abundance trends. In particular it has been found that the two isotopes that compose europium in several old, metal-poor halo stars are in solar system r-process proportions 18 . A recent study 9 , finding also that the Ba isotopes in one metal-poor star are compatible with the solar heavy reprocess pattern further supports the r-only origin for most (all ?) elements - even those made today in the s-process - at early times in the Galaxy. We also see in Figure 2 that the abundances of the lighter n-capture elements from Z = 40-50 are not consistent with (in general fall below) the same r-process curve that fits the heavy n-capture elements. This difference is suggestive and might indicate two separate r-process sites for the lighter and heavier n-capture elements 20 . Further complicating the interpretation, the elements Sr, Y and Zr seem to have a very complex synthesis history, raising the specter of multiple r-processes to explain the entire range of the n-capture elements.

4. The Astrophysical Site(s) of the r-Process The critical parameter that determines whether the r-process occurs or not is the number of neutrons per seed nucleus. To synthesize nuclei with A > 200 requires about 150 neutrons per r-process seed - starting from iron nuclei or somewhat beyond - which can also be translated into the parameters entropy, S, Ye (the total proton to nucleon ratio) and an expansion timescale, r, for a heated blob of material (of nucleons) in astrophysical events. At low entropies the r-process requires a very neutron-rich environment, starting with about Ye = 0.12 - 0.3, which is close to the values found in neutron stars 6,7 . High entropies (oc T3/p in radiation-dominated matter) leave an increasing He mass fraction in comparison to heavy nuclei after explosive burning. A well known case is the Big Bang, where under extreme entropies essentially only 4He is left as the heaviest nucleus. Somewhat lower entropies in stellar explosions will permit the production of (still small) amounts of heavy seed nuclei. In that case, even moderate values of Fe=0.4-0.5 can lead to high ratios of neutrons to heavy nuclei. For entropies in excess of 200 ks per baryon neutron captures can proceed to form the heaviest

7 r-process nuclei. 6 ' 21 The fundamental question then is where in nature are such conditions realized, either high entropies with moderately neutron-rich material or low entropies with very neutron-rich material. To determine if r-process conditions can occur inside of supernovae requires an understanding of supernova explosions. The apparently most promising mechanism is based on energy deposition by neutrinos i>e+n-+ p + e~ and ve + p —> n + e+. streaming out from the hot proto-neutron star (PNS) formed from the central iron-core collapse of a massive star. The explosion mechanism, however, is still uncertain and depends on Fe-core sizes from stellar evolution, electron capture rates of pf-shell nuclei, the supranuclear equation of state, the details of neutrino transport and opacities, Newtonian vs. general relativistic calculations, as well as multi-dimensional effects. 10 ' 21 ' 19 The present situation in supernova modeling is that selfconsistent, spherically-symmetric calculations (with the presently known microphysics) have not produced successful explosions. Solving the full Boltzmann transport equation for all neutrino flavors and a fully generalrelativistic treatment have so far not changed this situation. There is hope, however, that the neutrino-driven explosion mechanism could still succeed. First, the effects of rotation and magnetic fields are likely to be important, and have not yet been included in the current multi-D calculations. In addition there are still more uncertainties in our understanding of neutrino luminosities, neutrino opacities with nucleons and nuclei, convection in the hot PNS and the efficiency of neutrino energy deposition. The lack of understanding of the explosion mechanism also means that we do not know the exact r-process yields for SNe II via the "neutrino wind" - a wind of matter from the PNS surface caused by neutrinos (within seconds after a successful supernova explosion). 2 1 ' 1 9 If SNe II - given their rate in our Galaxy - are responsible for the solar system r-process abundances, they would need to eject about 1 0 - 5 M Q of r-process elements per event - if all SNe II contribute equally. This high-entropy neutrino wind in SNe is expected to lead to a superposition of ejecta with varying entropies. If a sufficiently high entropy range is available, the solar system r-process pattern shown in Figures 1 and 2 can be obtained 6 ' 2 1 . However, whether the very high entropies necessary for reproducing the heavy r-process nuclei can really be attained in supernova explosions still his to be verified. 19 Do only (unrealistically?) large or compact neutron stars with masses in excess of 2 M© provide the high entropies required? It remains to be seen whether the inclusion of non-standard neutrino properties or the role of magnetic fields can cure

8 these difficulties in the neutrino-wind models. So-called prompt supernova explosion models - based on the shock propagation from the core bounce (due to the nuclear equation of state) that do not need to wait for neutrinos to power an explosion - have also been explored. These models, however, still have to lead to an explosion in self-consistent calculations. An alternative (non-supernova) site for the heavy r-process nuclei are neutron-star (NS) ejecta, which are very neutron-rich and do not require high entropies 7 . This material could emerge from jets 4 forming in supernova explosions in environments with strong rotation and magnetic fields or from mergers of two neutron stars in a binary system after energy loss through the emission of gravitational waves 7 . The rate of NS mergers in our Galaxy is small 7 - estimated to be ~ 1 0 - 6 — 1 0 _ 4 y _ 1 . The ejected mass of neutron-rich material depends on Newtonian versus relativistic calculations 13 . While the decompression of cold neutron-star matter has been studied 1 1 , a full realistic calculation has not yet been undertaken. The large amount of free neutrons (up to n n cz 10 32 c m - 3 ) available in such a scenario leads to the build-up of the heaviest elements and also to fission within very short timescales. This, in turn, leads to a recycling of fission products back to the heaviest nuclei via subsequent neutron captures. However, the predicted composition, dependent on fission product distributions, could be void of abundances below mass numbers A~130 7 . Type II supernovae and NS mergers occur at different rates and will, in addition, eject different amounts of r-process material. Both of these parameters enter into the enrichment pattern of r-process elements in Galactic chemical evolution to be compared to observational evidence.

5. Clues from C h e m i c a l E v o l u t i o n Additional clues to the nature of the r-process and the identification of the site are coming from recent studies of chemical evolution, typically shown as elemental abundance trends as a function of metallicity ([Fe/H]). These stellar iron abundances can be thought of very roughly as a timeline, but at very early times mixing of ejected matter with the interstellar medium is not very efficient yet and a (large) scatter can occur. This scatter diminishes dramatically at higher metallicities. The amount of scatter at a given metallicity could also be interpreted as a measure for the frequency of the responsible nucleosynthesis events. Observations indicate that for the r-process production of (Ge,) Zr and Eu we might be witnessing decreasing event statistics, i.e., a smaller number of sites, which create these elements.

-i—i—i—|—i—r

-i—i—i—i—|—i—i—i—i—|—i—r

1.5 CS 22892-052

CD

1

0.5

LLI

_

r

_ i ^ i _ ^ ^

f

-0.5 - HD 122563-

-4

-3

-2

[Fe/H] Figure 3. Abundance scatter of [Eu/Fe] versus metallicity for samples of halo and disk stars. The solid (red) line is a least-square-fit to the data, the dotted line indicates a solar value for the abundance ratio and the two dashed lines are illustrative to indicate the range of the abundance data. The average behavior is very similar to typical Type II supernova products like e.g., O or Si. The larger scatter indicates rarer r-process events.

Figure 3 shows a least-square-fit to the [Eu/Fe] abundance data. The solid line has several interesting features. First, there is a downward trend (lower ratios of Eu/Fe) at higher metallicities, being mostly a result of increasing amounts of iron being deposited in the Galaxy at late times by Type la supernovae. The average Eu/Fe ratio behaves very similar to other elements from SNe II explosions (like O, Si, Ca etc.), but the scatter implies a much lower r-process frequency than typical for those elements. Fitting the Eu/Fe abundance data has been examined by a number of research groups. Neutron star mergers (with a much lower frequency than SNe II) would produce a large scatter in [Eu/Fe] as observed, but only enter at too high metallcities when already too much Fe is produced by SNe II 1 . Thus, while not necessarily excluding other sites, the abundance fit to these data has been satisfactorily reproduced with chemical evolution

10 models assuming core collapse supernovae as the primary site for the reprocess 1 , but with a smaller frequency (possibly limited progenitor mass range) for the supernovae involved in r-process production, in order to explain the larger scatter than for typical SNe II products. Despite of the progress, it is still necessary to improve all ingredients of the r-process puzzle. In nuclear theory as well as the simulation of astrophysical sites it remains to develop more sophisticated models to improve the reliability of predictions and fully understand the objects responsible for r-process conditions. Experiments and observations need to provide tighter constraints via exploring new territory (nuclei further away from stability and the search for r-process-rich stars at lowest metallicities below -3). References 1. D. Argast, et al., Astron. & Astrophys. 416, 997 (2004). 2. E. M. Burbidge, G. R. Burbidge, W. A. Fowler, F. Hoyle, Rev. Mod. Phys. 29, 547 (1957); A. G. W. Cameron, Chalk River Report CRL-41 (1957). 3. M. Busso, R. Gallino, G. J. Wasserburg, Ann. Rev. Astron. Astrophys. 37, 239 (1999). 4. A.G.W. Cameron, Astrophys. J. 587, 327 (2003). 5. J. J. Cowan, F.-K. Thielemann, J. W. Truran, Phys. Rep. 208, 267 (1991). 6. C. Freiburghaus et al., Astrophys. J. 516, 381 (1999). 7. C. Freiburghaus et al., Astrophys. J. 525, L121 (1999). 8. S. Goriely, Nucl. Phys. A 718, 287 (2003). 9. D. L. Lambert, C. Allende Prieto, 2002, Mon. Not. Roy. Astron. Soc. 335, 325 (2002). 10. K. Langanke, G. Martinez-Pinedo, Rev. Mod. Phys. 75, 819 (2003). 11. B.S. Meyer, Astrophys. J. 343, 254 (1989). 12. P. Moller et al., At. Data Nucl. Data Tables 66, 131 (1997). 13. R. Oechslin et al., Phys. Rev. D 65, 3005 (2002). 14. B. Pfeiffer et al., Nucl. Phys. A 693, 282 (2001). 15. C. Sneden, J. J. Cowan, Science 299, 70 (2003). 16. J. W. Truran, J. J. Cowan, C. A. Pilachowski, C. Sneden, PASP 114, 1293 (2002). 17. C. Sneden et a l , Astrophys. J. 591, 936 (2003). 18. C. Sneden et al., Astrophys. J. 566, L25 (2002); W. Aoki, S. Honda, T. C. Beers, C. Sneden, 2003, Astrophys. J. 586, 506 (2003). 19. T. A. Thompson, Astrophys. J. 585, L33 (2003). 20. G. J. Wasserburg, M. Busso, R. Gallino, Astrophys. J. 466, L109 (1996); Y.-Z. Qian, G.J. Wasserburg Astrophys. J. 588, 1099 (2003). 21. S. E. Woosley, et a l , Astrophys. J. 433, 229 (1994); K. Takahashi et al., Astron. & Astrophys. 286, 857 (1994).

P R E C I S E M A S S M E A S U R E M E N T S OF NUCLIDES A P P R O A C H I N G T H E R-PROCESS

J. A. CLARK, 1 ' 2 R. C. BARBER, 2 C. BOUDREAU, 1 ' 3 F. BUCHINGER, 3 J. E. CRAWFORD, 3 J. P. GREENE, 1 S. GULICK, 3 A. HEINZ, 1 ' 4 J. K. P. LEE, 3 A. F. LEVAND, 1 G. SAVARD,1 N. SCIELZO, 1 K. S. SHARMA, 2 G. D. SPROUSE, 5 W. TRIMBLE, 1 J. VAZ, 1 ' 2 J. C. WANG, 1 ' 2 Y. WANG, 1 ' 2 B. Z. ZABRANSKY, 1 AND Z. ZHOU 1 Physics Division, Argonne National Laboratory, Argonne, IL 60439 USA Dept. of Physics & Astronomy, Univ. of Manitoba, Winnipeg, MB R3T 2N2 Canada Department of Physics, McGill University, Montreal, QC H3A 2T8 Canada Wright Nuclear Structure Laboratory, Yale Univ., New Haven, CT 06520 USA 5 Physics Department, SUNY, Stony Brook Univ., Stony Brook, NY 11794 USA 2

The astrophysical r-process is thought to be responsible for the creation of more than half of the elements heavier than iron. An explanation of the nuclide abundances requires information on masses, which are best obtained through direct measurements. The Canadian Penning Trap (CPT) mass spectrometer at Argonne National Laboratory has completed the measurement of 26 neutron-rich Ba, La, Ce, and Pr isotopes approaching the r-process path. The results of these measurements and their potential impact on the r-process are presented in this paper.

One component of our understanding of n a t u r e requires an explanation of how the elements are created in the universe. T h e r-process is one of the processes thought to be responsible for the creation of elements, by which more t h a n half of the elements heavier t h a n iron are created by a series of rapid neutron-capture reactions. T h e process requires an a b u n d a n t supply of neutrons such as t h a t found in supernovae or merging neutron stars as discussed in this workshop. W i t h t h e appropriate n e u t r o n density and t e m p e r a t u r e conditions, neutron-capture and photodisintegration reactions occur on a much faster timescale t h a n do /3-decay. Starting with a seed nucleus, neutron-rich nuclides are produced via a series of neutroncaptures until a point is reached where an equilibrium is established between t h e neutron-capture and photodisintegration reactions. Here, t h e

11

12 r-process essentially stalls until the subsequent (3 decay of this "waitingpoint" nucleus, after which the capture of neutrons can then continue until another equilibrium is established. Once neutron-capture ceases because of the changing environmental conditions, the waiting-point nuclides /3 decay towards stability and 'hopefully' reproduce the observed abundance distribution. Determining which nuclides are waiting-point nuclides in the first place requires knowledge of the neutron separation energies of the nuclides involved, and hence their masses. In the waiting-point approximation, the abundances of the elements along an isotopic chain can be described as 1 : Y(Z,A + 1) Y(Z,A)

n

G(Z,A + 1) A + l 2-Kh2 2G{Z,A) A mukT

3/2

exp

tSn(Z,A + l) kT

(1)

where the abundances Y of the isotopes depend on the neutron number density nn and temperature T of the environment, in addition to the nuclear partition functions G and most importantly the neutron separation energy Sn (due to its exponential influence). The abundance maxima, and hence the waiting-point nuclides, along each isotopic chain may be found by locating the zeroes of the derivative of the isotopic abundance with respect to neutron number. The neutron separation energy is then given by: Sn = kT\n

_2_ nn

/mukT\3/2 V 2TT/1 2 J

(2)

which is only a function of the neutron number density and temperature of the environment, and in this approximation, no information about neutron capture cross sections is needed. Assuming that these quantities are constant during the waiting-point approximation, the abundance maxima along each isotopic chain is determined by the neutron separation energy. Mass measurements are therefore important to determine these points. For temperatures of 1.5 GK and a neutron number density of 1024 c m - 3 , the abundance maxima will occur where the neutron separation energy along the isotopic chain is reduced to approximately 3 MeV. If we examine the neutron separation energies as a function of neutron number, we immediately notice the pairing effect of the neutrons and can conclude the abundance maxima will occur for isotopes with an even number of neutrons. The waiting-point nuclides can also be determined by observing the smoother trend of the 2-neutron separation energy, S(2n). In this case, the position of the abundance maxima is determined by finding the 2-neutron

13 separation energy which is equivalent to 2 times the neutron separation energy2 required which, for the quantities given above, would be 6 MeV. Clearly, atomic masses are required to determine the neutron-separation energies used to establish the nuclides involved in the r-process. Mass models, such as the finite range droplet model (FRDM) 3 and the HFBCS-1 model 4 (which is based on the Hartree-Fock-BCS method with a Skyrmetype force), do a good job in areas where mass measurements have been made, but diverge in regions where no measured masses exist. Therefore, to constrain the present models, which are used in current r-process calculations, more masses need to be measured of neutron-rich nuclides approaching the r-process path. Our investigation of neutron-rich nuclides was achieved by using a 252 Cf source placed just outside the entrance window of a gas catcher 5 containing approximately 200 mbar of purified He gas. (See Fig. 1.) Fission fragments from the source pass through the entrance window and enter the He gas where they are thermalized. The neutron-rich nuclides are then extracted from the gas catcher via a combination of electric fields and gas flow. The ions then proceed through a differentially pumped ion guide 6 and enter an isobar separator 7 where molecular contamination is reduced. From here, the ions are transferred to a radio-frequency quadrupole (RFQ) ion trap where ion bunches are accumulated before finally being transferred to the precision Penning trap where the precise mass measurements are performed. The Penning trap is able to confine ions by a superposition of electric and magnetic fields. Ions are confined radially by the magnetic field provided by a 5.9 T superconducting magnet. Axial confinement is realized by the addition of a harmonic electric field which is constructed by applying appropriate voltages onto the electrodes of the Penning trap. The motion of the ions 8 resulting from the superposition of magnetic and electric fields can be described by three eigenfrequencies of motion: an axial motion at frequency u>z, and two radial motions at frequency u>+ and a>_. Precise mass measurements are obtained by determining the true cyclotron frequency, wc = qB/m, of an ion of mass m and charge q. The ring electrode of the Penning trap is divided into quadrants to enable the application of an azimuthally oscillating quadrupole potential superimposed on the static trapping potential. The influence of a quadrupole excitation 9,10 results in a resonance at uic and since uic depends only on the highly stable, homogeneous magnetic field in the Penning trap, precise mass measurements can be obtained by a determination of the cyclotron frequency. If the ions are driven resonantly at their cyclotron frequency, they will

14

ATLAS beam Figure 1. A bird's eye view of the C P T apparatus used to measure masses either online using the ATLAS facility at ANL or offline using a 2 5 2 Cf source placed just outside the entrance window of the gas cell. In either case, the isotopes thermalized in the cell are extracted and transferred to the precision Penning trap.

gain radial or orbital energy. Once they are ejected from the trap, the orbital energy will be converted into axial or linear energy due to the magnetic field gradient outside the Penning trap. The effect of the resonant excitation can be seen by observing the time-of-flight (TOF) 1 1 of the ions to reach a microchannel plate detector after they are ejected from the trap. Ions which were driven at their resonant cyclotron frequency will have gained energy, and will therefore reach the detector sooner than ions which were not resonantly excited, resulting in a minimum in the TOF spectrum. The resonant cyclotron frequency is therefore determined by fitting a function to the observed TOF distribution which extracts the frequency at which the minimum occurs. Periodically, we perform a calibration of the Penning trap by determining the cyclotron frequency of a known mass, such as C5H8. The cyclotron frequency of an unknown mass is then measured and its mass is determined

15

from the ratio of the measured cyclotron frequencies. Figure 2 shows the distribution of fission fragments expected from the 252 Cf source. Also shown are TOF spectra of two fission fragments, namely

Frequency applied -1214508.01 Hz

Frequency applied -1214488.23 Hz

Figure 2. Distribution of the fission fragments from the 2 5 2 Cf source. Also shown are two T O F spectra obtained for 1 4 9 P r 2 + (left) and 1 4 9 C e 2 + (right). The curves shown represent the theoretical lineshapes expected.

149pr a n c j 149Qe> j n e a c j 1 c a s e ? fae | o n s captured in the Penning trap were subjected to an excitation frequency for a duration of 500 ms which provides a FWHM of 2 Hz, or 250 keV, which is consistent with the Fourier limit. Of course, the precision of the measurement can be measured to better than just the FWHM, since it is the uncertainty in finding the minimum of the TOF spectrum, not the FWHM, which determines the precision of the measurement. A total of 26 neutron-rich nuclides have been investigated so far, concentrating on the heavier mass peak of the fission fragment distribution. A more detailed description of this experiment and its results are in preparation 12 . The deviations of our measurements from the 2003 atomic

16 mass evaluation (AME03) 13 are shown in Fig. 3 where the differences in mass are plotted as a function of mass number for the Ba, La, Ce, and Pr isotopes. Very good agreement was obtained for 1 4 1 _ 1 4 4 Ba, which were measured previously by ISOLTRAP 14 . The perfect agreement between our measured masses and those by ISOLTRAP, obtained with very different production and injection techniques and different trapping systems, indicates the unlikelihood that either the ISOLTRAP or the CPT measurements suffer from unaccounted systematic errors. Of the total of 26 nuclides we measured in this region, 16 agree with AME03 with 13 of those measured to higher precision. That leaves 10 isotopes which disagree with AME03. Most of the deviations, however, are for the extreme neutron-rich region where few, if any, measurements have been performed previously. 600

oBa • La • Ce • Pr

154

Figure 3. Plotted are the differences between the masses as measured by the C P T and those quoted in the latest 2003 atomic mass evaluation.

The difference between our mass measurements and the masses predicted by the FRDM mass model are shown in Fig. 4. It appears that the FRDM differs in mass by about 200 keV per neutron with an over-estimate for nuclides with neutron number N < 87 and an under-estimate for N > 87. The consequence of this trend, if it were to continue, would be a neutron drip-line and r-process path which are less neutron-rich than predicted by

17

the FRDM.

1000

88

90

92

96

Neutron number

Figure 4. The differences between the masses measured by the C P T and those of the FRDM. The lines shown are to guide the eye only.

Plotted in Fig. 5 are the S(2n) values for the Ba isotopes as determined by various models and measurements. Indicated are the values obtained from the latest atomic mass evaluation, the FRDM, the HFBCS-1 model, in addition to our measurements. Although deviations do exist between our measurements and those of the mass models, the general systematic trend of the 2-neutron separation energies is about the same. The most significant differences arise between our measurements and that of the FRDM near the magic number at N = 82. Similar deviations are present for the La, Ce, and Pr isotopes with less of an effect for the Ce and Pr isotopes as our measurements of these isotopes are further from the magic number at N = 82 than the Ba and La isotopes. Our present set of measurements are still far away from the S(2n) = 6 MeV region which is thought to define the r-process path, but ongoing improvements to the CPT system will soon permit the CPT to access more neutron-rich regions. In summary, mass measurements are important to constrain the current models which are used to describe the r-process. The Canadian Penning

18

Trap mass spectrometer has completed the measurement of 26 nuclides approaching the r-process path. Although many measurements are in agreement with the latest atomic mass evaluation (AME03), some deviations do exist. More measurements are required in this region to improve current mass models which are used to determine the r-process path and its outcome. The mass measurement program of the CPT is ongoing, with measurements currently being made of isotopes from the lighter peak of the 252 Cf fission source. More neutron-rich isotopes will be accessible to the CPT mass spectrometer soon.

19000

- AM E 2003 -FRDM -CPT -HFBCS-1

7000 77

82

87

92

97

N Figure 5. A comparison of the S(2n) values for the Ba isotopes obtained from either the AME03, FRDM, HFBCS-1 models or our measurements.

Acknowledgements This work was supported by the U. S. Department of Energy, Nuclear Physics Division, under Contract W-31-109-ENG-38, and by the Natural Sciences and Engineering Research Council of Canada.

19

References 1. Y.-Z. Qian, Prog. Part. Nucl. Phys. 50, 153 (2003). 2. S. Goriely and M. Arnould, Astron. Astrophys. 262, 73 (1992). 3. P. Moller, J. R. Nix, W. D. Myers and W. J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995). 4. S. Goriely, F. Tondeur and J. M. Pearson, At. Data Nucl. Data Tables 77, 311 (2001). 5. G. Savard et. al, Nucl. Instrum. Methods Phys. Res. B204, 582 (2003). 6. M. Maier et. al., Hyperfine Interact. 132, 521 (2001). 7. G. Savard et. al., Phys. Lett. A 158, 247 (1991). 8. L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986). 9. G. Bollen, R. B. Moore, G. Savard and H. Stolzenberg, J. Appl. Phys. 68, 4355 (1990). 10. M. K6nig et. al, Int. J. Mass Spectrom. Ion Processes 142, 95 (1995). 11. G. Graff, H. Kalinowsky and J. Traut, Z. Phys. A 297, 35 (1980). 12. J. C. Wang et. al., (to be published). 13. G. Audi, A.H. Wapstra and C. Thibault, Nucl. Phys. A729, 337 (2003). 14. F. Ames et. al., Nucl. Phys. A651, 3 (1999).

FISSION A N D T H E R-PROCESS PATH: R E C E N T EXPERIMENTAL ACHIEVEMENTS A N D FUTURE POSSIBILITIES

J. BENLLIURE Universidad

de Santiago

de Compostela,

15706 Santiago

de Compostela,

Spain

In this paper we review the main results obtained recently concerning the investigation of fission and their implications in the observed r-process abundances. In particular we focus on experiments where charge and isotopic distributions of residues produced in fission reactions of exotic nuclei were measured. These results allow to validate model calculations providing reliable descriptions of the isotopic distributions of residues produced in fission reactions of heavy neutron-rich nuclei involved in the r-process which are not accessible experimentally.

1. Introduction The role of fission in the observed abundances of the heaviest nuclei was already proposed in the first papers describing the r-process 1 ' 2 . Fission determines the upper end of the r-process cycle and was proposed to lead to a cycling r-process 3 where the residues produced in the fission of heavy neutron-rich isotopes would feed a new rapid neutron capture sequence. In addition, the progenitor distribution of heavy neutron-rich nuclei (260 < A < 320) produced by the r-process may also undergo spontaneous fission during its /3-decay towards stability after freeze-out4, r-process progenitors in the 190 < A < 260 region are not expected to undergo spontaneous fission during its /?-decay towards stability, however, for some scenarios neutrino-induced fission may play a crucial role in this mass region 5 . In order to evaluate the impact of fission in the observed r-process abundances complex calculations including reliable nuclear physics inputs are required. In particular nuclear masses, level densities and fission barriers should be provided to the nucleosynthesis models. However, the nuclei involved in these processes are out of the experimental accessibility and extensive extrapolations of nuclear data close to stability in the direction of larger neutron-excesses and higher mass numbers are required. During the last years, important progress was achieved in modelling 20

21

fission barriers of neutron-rich and superheavy nuclei6 and measuring nuclear masses 7 and isotopic distributions of fission residues 8,9 . In addition, in a pioneer experiment at GSI fission barriers 10 and charge distributions of residues 12 in electromagnetic induced fission of nuclei far from stability were measured. In this paper we will review the most outstanding results concerning the investigations of fission far from stability during the last years, in particular at GSI, and the main attempts to extend this experimental investigations to heavy neutron-rich fissioning systems together with the new possibilities offered by next-generation radioactive beam facilities like RIA 11 . 2. Fission fragment distributions Although fission was discovered more than 50 years ago, the experimental information we have on this process is still rather restricted. In fact, only few nuclei have been intensively investigated because of their application to energy production. The main reason for this lack of experimental information is that nature provides only four fissile stable nuclides and few more long-lived ones decay spontaneously by fission. In this context, radioactive nuclear beams (RNB) offer a new access to fission that overcomes the previous limitations. A clear example is the successful experiment performed few years ago at GSI to investigate the fission properties of actinides and preactinides far from stability 12 . 2.1. Fission

experiments

with

RNB

The secondary-beam facility at GSI was used to produce more than 70 different neutron-deficient actinides and preactinides by fragmentation of a 238 U beam at 1 A GeV in a 657 g/cm 2 Be target as shown in Fig. 1. The fragmentation residues were separated and identified using the fragment separator FRS 1 3 . The acceptance of the separator allowed to produce multiisotopic secondary beams and consequently to investigate simultaneously the fission properties of more than 20 different nuclides. These secondary beams were guided to a specific experimental set up to investigate the low energy induced fission by Coulomb excitation in a high-Z second target (Pb). In this dedicated setup, the charge and the kinetic energy of the fission residues were determined from the measurement of their energy loss and time-of-flight. The energy loss was measured in a vertically subdivided multi-sampling ionisation chamber (twin MUSIC). The velocities of both

22

Figure 1. Nuclei investigated in low-energy fission with RNB at GSI.

fission residues were provided by the time-of-flight measurement between a plastic scintillator placed in front of the target and a plastic-scintillator wall located 5 meters behind. This measurement was used to correct the velocity dependence of the energy loss measured with the MUSIC and to determine the kinetic energy of the fission residues. All the detectors were designed in order to accept all the fission fragments produced in the target. In this experiment, the elemental yields and the total kinetic energies of fission residues produced by Coulomb excitation of long isotopic chains of secondary projectiles from 2 0 5 At to 234 U were determined. In the upper part of Fig. 2, we report in a chart of the nuclides the elemental distributions of fission residues in the range Z=24 to Z=65 after fission of 28 secondary beams between 221 Ac and 234 U. These data allowed for the first time to systematically investigate the fission properties of nuclei in a continuously covered region of the chart of the nuclides. Two main features can be observed in the elemental charge distributions: a coarse structure which corresponds to the fission modes and a fine odd-even effect. Fig. 2 shows that the transition from symmetric fission in the lighter elements to asymmetric fission in the heavier ones is systematically covered by these data. In the transitional region, around 226 Th, triple-humped distributions appear with comparable intensities for symmetric and asymmetric fission. A clear even-odd effect is observed for the even fissioning elements U and Th.

23

92

e si ZJ

c

1 90 o

89

MM MIMM AAAiAA MM MA A A A A A M MM A A A AAA 135

136

137

138

139

U0

U1

Pa Th Ac

U2

Neutron number i

i_ 92 (-1

i

i

i

i

s

i

MMM M A 0 n MMMMM A MM i-AIA AA AA 0A M W

§ 91 c o 90

-t-i

£ 89

Pa

-

132

133

134

135

136

137

u

i

i

i

i

i

138

139

HO

141

142

Th

Neutron number Figure 2. Measured fission-fragment nuclear-charge distributions in the range Z=24 to Z=65 after electromagnetic excitation of 28 secondary projectiles in a lead target between 221 Ac and 2 3 4 U shown in a chart of the nuclides.

The analysis of these data allowed to obtain important conclusion about the role of shell effects and pairing correlations in the fission process. One of the most outstanding results is the unexpected influence of proton shells on the measured charge distributions of fission residues. The whole experimental information together with the main results obtained in this experiment are described in Ref.12. 2.2. Model

description

The interpretation of the observed evolution of the fission residue distributions and their extrapolation to heavy neutron-rich fissile nuclei would require a full theoretical description of the fission process. A realistic model should include not only a description of the potential-energy surface but also the dynamics of the collective motion from saddle to scission. Some recent work concentrates in the description of the potential-energy surface including structure effects 14,15 . Recently, two-dimensional fission-fragment mass-

24

energy distributions were obtained from most advanced multi-dimensional Langevin calculations (e.g. 16 ) on the basis of the liquid-drop model with finite range of the nuclear forces and a modified one-body mechanism for nuclear dissipation. However, to our knowledge a complete dynamical description of low-energy fission which includes the influence of shell effects and pairing correlations is not yet available. Since theory cannot yet provide a full realistic description of the process, we tried to understand the data with a semi-empirical approach 17 . In our description the population of the fission channels is assumed to be basically determined by the statistical weight of transition states above the potentialenergy landscape near the fission barrier. Several properties, however, are finally determined at scission. The barrier as a function of mass asymmetry is defined by three components. The first is the symmetric component Vid defined by the liquid-drop potential by means of a parabolic function with a curvature obtained from experimental data 1 8 . This parabola is assumed to be modulated by two neutron shells, located at mass asymmetries corresponding to neutron numbers N=82 (spherical neutron shell) and N«90 (deformed neutron shell). We assume that the mass-asymmetric degree of freedom at the fission barrier is on average uniquely related to the neutron number of the fragments. The shells are represented by Gaussian functions. The population of the fission channels is proportional to the level density around the corresponding dips in potential at a given excitation energy. Shells are supposed to wash out with excitation energy 19 . The heights of these Gaussians are the only parameters in the model which were adjusted to describe the measured yields for 2 2 7 Th. Other parameters, like the widths of these Gaussians and additional fluctuations in mass asymmetry acquired from saddle to scission are derived from independent data 1 7 . Fluctuations in the neutron-to-proton ratio are also considered by describing the potential in this degree of freedom by a parabolic function. Assuming that the equilibration in this variable is fast compared to the saddle-to-scission time, the curvature of this potential was calculated in a touching-sphere configuration. In the lower panel of Fig.2 we show the predictions of our model for the measured data in the GSI experiment. As can be seen, the model provides a quite good description of the measured charged distributions of fission residues and in particular, of the transition from symmetric to asymmetric fission. These results give us confidence on this calculations that we can use to investigate the isotopic distributions of r-process nuclei

25 A

A

A

A

s

A

A

A

A

A

A

A

A

A

A

Figure 3. Two-dimensional cluster plot of the isotopic distributions of residual fragments produced in the low-energy fission of three r-process representatives nuclei 3 0 0 D b , 250 T h and 2 1 0 H g . We also include the well known distribution of fission residues from 238 U for benchmarking.

26

undergoing low-energy fission. To illustrate the possibilities of this code in Fig. 3 we present on top of different charts of the nuclides the calculated isotopic distributions of residues produced in the low-energy fission of three representative r-process nuclei, 3 0 0 Db, 2 5 0 Th and 210 Hg. For comparison we also include the isotopic distribution of residues produced in the low-energy fission of 238 U. 3. Fission probability The experiments with RNBs and other dedicated ones have been used to investigate fission probabilities and in particular the role of shell effects and collective excitations. A complete discussion of this topic can be found in Ref.20-21

115 120 125 130 135 140 145 150

Neutron number Figure 4. Production cross sections of Ra isotopes produced in the reaction 2 3 8 U ( 1 A GeV)+d compared with model calculations using a Fermi gas level density (dotted line), a level density including ground state shell effects (dashed line) and ground state shell effects and collective excitations (solid line).

In principle, one would expect an enhancement of the survival probability against fission for nuclei across closed shells, in particular Z=82 and N=126. However, different experiments do not show any enhancement of the survival probability against fission as illustrated in Fig. 4. In this figure we report the measured production cross sections of Th isotopes in the reaction 238 U(1 A GeV)+d 22 . The production cross section of these isotopes is directly related to the survival probability against fission. As can be seen, this distribution does not show an enhanced production of residues

27

around N=126 as predicted by a calculation including shell effects (dashed line). This result has been explained as due to a cancellation between shell stabilisation and the increase of collective excitations at saddle 20 , as shown with the different calculations in Fig. 4. Consequently, the description of fission probabilities requires not only precise fission barriers but a proper description of level densities including both shell and collective effects. 4. Future perspectives The experiments performed during the last years clearly show the outstanding role of radioactive nuclear beams in the investigation of fission. However, present RNB facilities still have limited possibilities to produced heavy neutron-rich isotopes involved in the r-process path. Nevertheless, some exploratory experiments have shown that next-generation RNB facilities will be able to produced such extremely neutron-rich nuclei. 4.1. Production

of heavy neutron-rich

nuclei

Recently it has been shown that fragmentation reactions at relativistic energies present large fluctuations in the N/Z and excitation-energy distribution of the final residues. In particular, the proton-removal channels have been investigated in cold-fragmentation reactions 23 where only protons are abraded from the projectile, while the induced excitation energy is below the particle-emission threshold. These reactions can lead to the production of heavy neutron-rich nuclei beyond the present limit of the chart of the nuclides. This reaction mechanism can be described in terms of the abrasionablation model as a two-step process. First, the interaction between projectile and target leads to a projectile-like residue with a given excitation energy which statistically de-excitates by particle evaporation or fission. A new analytical formulation of the abrasion-ablation model, the code COFRA, has been developed 23 in order to calculate the expected low production cross sections of extremely neutron-rich nuclei which are not reachable with Monte Carlo codes. The results of these calculations have been benchmarked with the new available data showing the reliability of the model predictions. Moreover, they have been used to estimate the expected production of heavy neutronrich nuclei in future rare-beam facilities. The results of these calculations are shown in Fig. 5. In this figure we report the expected production cross sections of heavy neutron-rich nuclei that can be obtained in the frag-

28

Figure 5. Estimated production of heavy neutron-rich residues in cold-fragmentation reactions induced by 2 3 8 U , 2 0 8 P b and 1 7 4 W projectiles at 1 A GeV impinging in .a Be target, on top of a chart of the nuclides. The grey scale indicates the maximum production cross section expected from one of the three reactions.

mentation of 2 3 8 U, 2 0 8 Pb and 174 W, According to these calculations, large progress is expected in this region of the chart of the nuclides, where the r-process path may even be reached around the end point N=126. Considering the primary intensities of the planned next-generation facilities these nuclei at the end point N=126 could be produced with a rate of about few nuclei per hour. The production of heavier neutron-rich nuclei close to the upper end of the r-process (Z^IOT, A^SOO) should be explored using fusion reactions induced by neutron-rich projectiles. According to the systematica of fusion cross sections 24 , next-generation RNB isol-type facilities like R1A11 will allow to produce such heavy neutron-rich nuclei in the charge region up to Z^104, A~270 with a production rate of a few nuclei per day.

5. Conclusion a n d future perspectives The experiments performed during the last years have demonstrated that radioactive beams offer a new access to fission. These beams allow to systematically investigate the fission properties of nuclei in continuously covered regions of the chart of the nuclides. The quality of the measured elemental distributions of fission residues have provided new evidences of the role of nuclear structure in low-energy fission. The analysis of the asymmetric component in the charge distributions of fission residues reveals an unexpected influence of proton shells. In

29 addition, t h e evolution of the fission components has been explained on the basis of a statistical population of transition states above a simple massasymmetric potential landscape determined semi-empirically. This result would indicate t h a t the dynamics of the fission process tends to wash out the influence of the details of the potential-energy landscape. These experiments with RNBs were also used t o investigate the fission probability at closed shells. In particular, t h e expected reduction of the fission probability around closed shells was not observed. This result was explained as a consequence of collective excitations t h a t compensates shell effects and d e m o n s t r a t e the importance of a good description of level densities t o estimate fission rates. All these results have direct consequences in the description of t h e observed abundances of r-process nuclei. However, next-generation R N B facilities, like RIA will enlarge these possibilities. In particular, nuclei close t o the N = 1 2 6 end point or the upper limit of the r-process will be accessible. References 1. E.M. Burbidge, G.R. Burbidge, W.A.Powler, F.H. Hoyle, Rev. Mod. Phys. 29, 547 (1957) 2. A.G.W. Cameron, Pub. Astron. Soc. Pacific 69, 201 (1957) 3. R A . Seeger, W.A. Fowler, D.D. Clayton ApJS 11, 121 (1965) 4. A.G.W. Cameron, ApJ. 562, 456 (2001) 5. Y.-Z. Qian, ApJ. 569, 103 (2002) 6. A. Mamdouh, et al. Nucl. Phys. A679, 337 (2001) 7. M. Hausmann et al. Hyp. Int. 132 291 (2001) 8. T. Enqvist et al., Nucl. Phys. A658, 47 (1999) 9. M. Bernas et al., Nucl. Phys. A725, 213 (2003) 10. A. Grewe et a l , Nucl. Phys. A614, 400 (1997) 11. http://www.phy.anl.gov/ria/ 12. K.H. Schmidt et al., Nucl. Phys. A665, 221 (2000) 13. H. Geissel et al., Nucl. Instr. Methods B 7 0 , 286 (1992) 14. V.V. Pashkievich, Nucl. Phys. A14, 1 (1976) 15. P. Moller et al., Phys. Rev. C61 047602 (2000) 16. A.V. Karpov et al., Phys. Rev. C63 054610 (2001) 17. J. Benlliure, et al. Nucl. Phys. A628, 458 (1998) 18. S.I. Mulgin et al., Nucl. Phys. A640, 375 (1998) 19. A.V. Ignatyuk et a l , Sov. J. Nucl. Phys. 29, 450 (1979) 20. A.R. Junghans et al., Nucl. Phys. A629, 635 (1998) 21. A. Heinz et a l , Nucl. Phys. A713, 3 (2003) 22. E. Casrejos, Phd disertation, U. Santiago de Compostela, Spain (2001) 23. J. Benlliure et a l , Nucl. Phys. A660, 37 (1999) 24. S. Hofmann, Z. Phys. A358, 125 (1997)

/3-DECAY STUDIES OF N E U T R O N RICH NICKEL ISOTOPES

P.T. HOSMER f R.R.C. CLEMENT*, A. ESTRADE, S.N. LIDDICKj P. P. MANTICA+, W.P. MUELLER, P. MONTES*, A.C. MORTON* M. OUELLETTE*, E. PELLEGRINI, P. SANTI§ H. SCHATZ*?M. STEINER, A. STOLZ, B.E. TOMLIN+ National Superconducting Cyclotron Laboratory Michigan State University East Lansing, MI 48824, USA O. ARNDT, K.-L. KRATZ, B. PPEIFFER Institut fur Kemchemie Universitat Mainz Fritz-Strassmann Weg 2, D-55128 Mainz,

Germany

W. B. WALTERS Dept. of Chemistry and Biochemistry University of Maryland College Park, MD 20742, USA P. REEDER Pacific Northwest National Laboratory MS P8-50 P.O. Box 999, Richland, WA 99352, USA A. APRAHAMIAN 1 AND A. WOHR Dept. of Physics University of Notre Dame Notre Dame IN 46556-5670, USA

The half-lives of neutron-rich Ni isotopes, including that of doubly-magic 78 Ni, have been measured at the Coupled Cyclotron Facility at the National Superconducting Cyclotron Laboratory. 30

31

1. Introduction Among the most important nuclear physics inputs into r-process calculations are masses, /3-decay half-lives, and neutron emission ratios (P„). The masses determine the waiting points of the process, the half-lives help to determine the final isotopic abundances as well as the required time-scale for the process to occur, and the P n values affect the final isotopic abundances of r-process nuclei. Very few of the /3-decay properties of nuclei participating in the r-process have been measured. Fortunately these properties, especially the gross /3-decay properties (Tj/2 and P„), may be measured with very low beam intensities. With the new Coupled Cyclotron Facility (CCF) at the National Superconducting Cyclotron Laboratory (NSCL) many r-process nuclei are now available for at least determinations of their half-lives. 2. Experimental Setup A secondary beam comprised of a mix of neutron rich nuclei around 78 Ni was produced by fragmentation of an 86 Kr primary beam on a thin Be target at the CCF. Fragments were separated using the A1900 fragment analyzer x operating with full momentum acceptance, using a position sensitive plastic scintillator at the intermediate focus to determine the momentum of each individual beam particle. Each nucleus in the secondary beam was individually identified in-flight by measuring energy loss and time of flight, together with the A1900 momentum measurement (see Fig. 1). The time of flight was measured between two scintillators, one located at the intermediate image plane of the A1900 and the other located inside the experimental vault. The beam was then stopped in the Si detector stack of the NSCL /? counting system 2 . Energy loss was measured with two Si PIN detectors separated by a passive Al de*and Department of Physics and Astronomy, Michigan State University t a n d Department of Chemistry, Michigan State University *current address: TRIUMF 4004 Wesbrook Mall, Vancouver, BC V6T 2A3 ^current address: Los Alamos National Laboratory, Safeguards Science and Technology Group (N-l), MS E540 Los Alamos, NM 87544 ^and Joint Institute for Nuclear Astrophysics

32

grader of variable thickness. The degrader thickness was adjusted to stop the nuclei In a 985pm double-sided SI strip detector (DSSD). The DSSD was segmented Into 40 1-mm strips on each side, yielding 1600 1-mm pixels. The beam was continuously Implanted Into the DSSD, and the position and time recorded for each fragment. The typical Implantation rate was under 0.1/s for the entire detector. Using the dual gain capabilities of the DSSD electronics, the time and position of subsequent /3-decays were also recorded on an event-by-event basis.

•=•

550

8SS#

m m

500

O

450

C

400

iJU

450

500

550

Time of Flight [a.u]

Figure 1. Particle Identification in Energy Loss vs. Time of Flight. For the displayed events, an additional cut in the parameter plane of the energy loss in the two Si PIN detectors has been applied. The plot represents 60 hours of beamtime

3. D a t a Analysis For 78 Ni 5 a total of 11 events were Identified over approximately 100 hours of beam time. Decay events were correlated to implants based on position and time. The decay half-lives of 78 Ni and the other NI isotopes were then extracted from the correlated decays using the Maximum Likelihood Method

33

(MLH) 3 , a method that has been utilized previously to extract half-lives, even in the case of very low statistics 4,5,6 . In this analysis, since neutronrich isotopes may have relatively large branching ratios to unbound states, the MLH formalism included the possibility of /?-delayed neutron emission. The method requires knowledge of the detector efficiency, background, and the half-lives and P n values of daughter and subsequent generations. Decay curves were produced for selected isotopes, and by fitting the decay curves, the /3-detection efficiency was extracted by comparing the number of parent decays of an isotope to the total number of implants of that isotope. The new half-lives of 77 Ni and 78 Ni, as well as improved measurements 75 for Ni and 76 Ni should help to further constrain theoretical half-life predictions relevant to r-process nucleosynthesis. Our preliminary analysis indicates that the RPA calculations by Kratz et al.7 and more recent QRPA calculations by Kratz et al.8 which include Gamow-Teller as well as firstforbidden transitions seem to agree well with the present results. QRPA predictions of Moller et al.9 which include Gamow-Teller as well as firstforbidden transistions, particularly those based on ETFSI-Q including empirical shell quenching, also seem to be in good agreement. Acknowledgments This research has been supported by the National Science Foundation under grants PHY 0110253 (NSCL) and PHY 0072636 (Joint Institute for Nuclear Astrophysics). References 1. 2. 3. 4. 5. 6. 7. 8. 9.

D.J. Morrisey et al., Nucl. Instr. and Meth. B204, 90 (2003). J.I. Prisciandaro et al., Nucl. Instr. Meth. A505, 140 (2003). M. Bernas et al, Z. Phys. A336, 41 (1990). R. Schneider, Ph.D thesis, TU Munchen, 1996. P. Kienle et al., Prog. Part. Nucl. Phys. 46, 73 (2001). T. Faestermann et al., Eur. Phys. J. A15, 185 (2002). K.-.L Kratz et al., Z. Phys. A332, 419 (1989). K.-.L Kratz et al. Kernchemie Mainz Evaluaton of Tl/2 and Pn Values (1996). P. Moller et al, Phys. Rev. C67, 055802 (2003).

WEAK STRENGTH FOR ASTROPHYSICS

SAM M. AUSTIN AND R. ZEGERS National Superconducting Cyclotron Laboratory and Joint Institute for Nuclear Astrophysics (JINA) NSCL, Michigan State University, East Lansing MI 48824, USA E-mail: [email protected] The strengths of electron capture processes strongly affect the evolution of accreting neutron stars and of Type II and Type la supernovae. We discuss techniques for measuring these strengths for both stable and radioactive nuclei using hadronic charge exchange reactions.

1. I n t r o d u c t i o n Electron capture (EC) strength plays an important role in explosive astrophysical phenomena. During the pre-collapse evolution of the core of a massive star, electron capture rates on nuclei with A ~ 60 determine t h e temperature, entropy, electron density, and mass of t h e core. 1 Both stable and radioactive nuclei are important. After collapse begins, rates of electron capture on still heavier nuclei, u p to A > 100, have recently been shown 2 , 3 to be more important t h a n c a p t u r e on protons and t o strongly affect t h e evolution of the core properties. In the case of the T y p e l a supernova t h a t take place in binary star systems and t h a t produce much of t h e iron-like elements in the universe, nuclei with A ~ 60 are most important. One cannot appeal purely t o experiment to fix these rates. Because of the high temperatures involved, excited states of nuclei are thermally populated, and transitions from these states to other excited states occur, b u t cannot be measured. Large basis shell model calculations 4 give transition strengths for the lighter nuclei, b u t more complex, less well justified calculations must be used for the heavier nuclei. 2 T h e role of experiment is then t o examine a sufficient number of cases with sufficient accuracy and resolution to validate the model calculations. In general, direct determinations of E C strength are not useful for this purpose; the bulk of t h e strength lies in a giant resonance located a few MeV above the ground state and is not accessible to energetically allowed 34

35

/3-decay transitions. Consequently one must rely on surrogate reactions. It is fortunate that the extensive work on the measurement and interpretation of (p, n)reactions 5 has shown that the cross section for this hadronic chargeexchange reaction (CER) is proportional to within about 10% to allowed EC strength. The relationship is a(9«0)aB(GT)a|J 0 in most cases, especially for giant resonance states, because the reaction has a significantly negative Q value. In addition q is larger for a given Q at low bombarding energies, scaling roughly as 1/Eg . This results in a smaller cross section, but one can correct for this effect using the known dependence of the cross section on q (or 6). At lower energies multiple step processes become more important, and the separation in angle of L = 0 strength and higher L strength lessens; the L = 2 cross section at 9 = 0 may be significant. All of these effects of lower-than-ideal energy are most significant for weak transitions. In this paper we discuss possible experimental techniques for extending these measurements to a wide variety of stable and radioactive nuclei. 2. M e a s u r e m e n t s of E C s t r e n g t h Improving the accuracy and range of EC measurements falls naturally into two parts: for stable nuclei and for radioactive nuclei. We discuss first techniques that have dominated CER measurements of EC strength for stable nuclei, and then turn to possible new approaches. In this context we discuss some of the issues involved in extracting weak strength from hadronic charge exchange cross sections. We then turn to the additional techniques and problems involved in CER measurements for radioactive nuclei. 2.1. Stable

nuclei

The bulk of EC data that satisfy the conditions discussed above are from the (n,p) measurements at En = 200 MeV performed at TRIUMF. 6 These

36

measurements benefit from a well understood reaction mechanism. Their limitations are the relatively poor resolution, typically ~ 1 MeV, and the limit on the nuclei available for study, because of the need for large amounts of target material. The most certain and reliable approach to obtaining better information of EC strength would be to extend the (n,p) measurements to achieve better statistics and resolution. We are not aware of impending measurements and, unfortunately, it is not clear that they are possible, given the presently available accelerators. Another approach is to use reactions involving heavier projectiles. Of these the (rf,2He) and (t,3He) reactions seem most promising. If this approach is used, however, a significant effort must be made to validate the accuracy of these reactions, as has been done for the (p, n) and {n,p) reactions. 5 Preliminary studies have been made for (d, 2 He), 7 and for (i, 3 He) 8 but these are not yet sufficient in detail or in the range of nuclei studied. In this regard the (i, 3 He) reaction may have an advantage, since one can take advantage of the more easily studied mirror reaction, ( 3 He, A number of groups have studied the ( 100. 1 1 1 2 ' 1 3 A major program of measurements, with a broad focus, is underway. The available deuteron energy from the KVI cyclotron, 85 MeV/nucleon, is somewhat low, but is probably adequate, at least for strong transitions. Studies involving the (i, 3 He) reaction have been much more limited, for two reasons. First, accelerating a radioactive ion in an accelerator generally involves a significant manpower cost to deal with radiation safety requirements. And second, tritium is magnetically rigid which limits the energy of extracted beams in cyclotrons. As a result the only studies that come close to satisfying the "ideal" conditions outlined in the introduction have been performed with secondary beams. In the published work, 8,14 and in a to-be-published experiment on 58 Ni(i, 3 He), 1 5 the triton beam was obtained from breakup of a 560 MeV a-particle beam in a thick Be target. 14 The momentum spread of the 350 MeV tritium beam was limited to 0.5% by slits downstream from the A1200 fragment separator. The resulting beam was dispersed by a beam preparation line and then entered the S800

37

spectrograph which has an equal and opposite dispersion. The dispersion matching technique resulted in an energy resolution of 160 keV for a 12 C target, of which 140 keV was attributed to system (beam-spectrometer) resolution, with most of the remainder due to energy loss in the target. The beam intensity achieved in these experiments was approximately 6 10 /second. We have measured the production of tritium in the NSCL K500(g)K1200 coupled-cyclotron facility for a 150 MeV/nucleon l e O beam. Beam intensities of > 10 7 /sec are achieved at an energy of 125 MeV/nucleon, assuming presently available 1 6 0 beam intensities. Such intensities will permit reliable measurements in 1 or 2 days.

2.1.1. Normalization

issues

Obtaining an absolute value of B(GT) from CER is a significant problem. Even if the cross sections are proportional to EC strength, one has to fix the constant of proportionality. In the /3-decay direction one can normalize to the strength of the isobaric analog of the target ground state which has B(F) = (N — Z); only small corrections for differential absorption effects need to be made. 5 This option is not available for EC; there is no isobaric analog state in the product nucleus. A second possibility, in the /3-decay direction, is to determine the CER cross sections for states for which B(GT) is known. Since there are significant samples of such states, especially for the lighter nuclei, one can define a unit cross section, the ratio -B(GT)/ strength in (p, n)reactions? One can, in principle, observe the T0 + l states at high excitation energies in the product nucleus using the well-documented (p, n)reactions. The matrix elements describing such transitions are identical to EC matrix elements, except for a geometrical isospin factor. We have applied this technique to eo,62Nii7 gs s hown in Fig. 1. A problem with this approach is that charge exchange reactions do not provide an isospin meter, and unambiguous identification of T0 + 1 states is difficult. It may be possible, however, to provide better isospin identification and to extend such measurements to nuclei with higher isospin. One can in principle identify the isospin of an excitation by measuring relative cross sections for (p,p') and (p, n) reactions leading to analog 1 + states; this ratio depends on isospin. For T0 + 1 states a(p,p')/o~(p,n) is 2T0 + 1 and for T0 states it is T0. The difference of a factor of two or more should be sufficient to determine the isospin as long as the resolution is sufficient to resolve the states or regions dominated by isoscalar and isovector excitations. A complication is that there may be unresolved isoscalar contributions to (p,pr) cross sections. In the future, the( 6 Li, 6Li*(3.56 MeV, 0 + , T = 1)7) reaction 18 could provide a pure inspector probe for the inelastic channel, eliminate any contributions from isoscalar amplitudes, and provide a more secure identification. Because of different optical model potentials for 6 Li and nucleons, inelastic 6 Li scattering, (6Li, 6 Li*(0 + , T = 1)7), will have to be calibrated to give results closely similar to (p, n). Fortunately, the isospin analog reaction, ( 6 Li, 6 He), has been shown to provide an accurate measure of GT strength 19 ' 20 and can be used to provide the necessary calibration. Extending the technique to heavier nuclei requires better energy resolution. Because the strength of a transition is roughly proportional to 1/T 2 , the present technique is applicable only to nuclei with isospin sufficiently small that the T0 + 1 states are observable. At the same time the isospin

39

1.2 >

(a)

,-x

^Ni TRIUMF •

1

^ 0.8 o

^

1

„ ,

^ 0.6 £ 0.4 b 0.2

• x

' •

/ / /

/

\ \ «v

J

1

^«

2 E(MeV)

Figure 1. Comparison of the T> spectra for the 6 0 N i ( p , n ) 6 0 C u and 6 0 N i ( n , p ) 6 0 C o reaction measured at IUCF (135 MeV) and TRIUMF (200 MeV), respectively. These d a t a are not consistent. A similar lack of consistency with the TRIUMF measurements has been noted in the (d, 2 He) measurements on 5 8 Ni mentioned above.

must be large enough that the splitting of T0 and T0 + 1 states allows one to isolate T0 + 1 strength with reasonable certainty. Thus for a T0 = 1 nucleus like 58 Ni the T0 and T0 + 1 excitations are strongly intermixed as has been discussed in detail. 21 With better resolution it should be possible to observe T0 +1 states above the background for nuclei with higher isospin. For example, a resolution of 35 keV (14 times better than in 17 ) has been achieved with the ( 3 He, t) reaction, and one could in principle examine cases where the relative strength of the T0 + 1 excitations is a factor of 14 smaller than in 62 Ni. This would make possible studies of T0 + 1 states in nuclei with T0 as large as 12 ( 62 Ni has T0 = 3). It is not clear whether such

40

limits can be reached in practice; one may be limited by the intrinsic decay widths of these states, even though neutron decay is isospin forbidden. 2.1.3. Effects of strong absorption A general problem for these more strongly absorbed projectiles is that they sample only a limited region at the outer edge of the nucleus and, by the uncertainty principle, are sensitive to the GT transition form factor F(q) over a significant range of momentum transfer. Since B(GT) is a property of F(q) at q ~ 0, it is not clear that CER will provide reliable JB(GT)s. This issue has been examined for B(GT) and for L = 1 transition strengths in specific cases involving light nuclei. 22,23 These papers find that the q range sampled is indeed significant, but is biased toward small q; if the F(q) for the various states have a similar shape in the sampled region at low q, CEXR cross sections and -B(GT)s will be proportional. In the absence of more general theoretical guidance this proportionality would have to be checked for the particular nuclei being studied. 2.2. Radioactive 2

nuclei 3

While ( 1. Since Wigner's supermultiplet theory, based on SU(4) spin-isospin symmetry, gives rise to a similar sharp cusp for nuclei with N — Z 6 the term became known as the Wigner term. But the cusp of supermultiplet theory arises from repulsive terms that are proportional to \N — Z\, which become increasingly important as one moves away from the N = Z line, in contrast to the apparent highly localized phenomenon. Fortunately, a more direct description of the observed effect seems to be available in terms of T = 0 neutron-proton pairing, the contribution of which rapidly vanishes as N moves away from Z 7>8>9. However, T = 0 pairing is a more complex phenomenon than T = 1, \TZ\ = 1 pairing, and no global mass formula constructed so far includes T = 0 pairing explicitly, phenomenological representations such as the one of Eq. (5) having been judged more convenient. In the first HF mass formula 10 , HFBCS-1, pairing was treated in the BCS approximation, while the full HFB approach was adopted in all subsequent versions, HFB-1 to HFB-7 ".",13,14. Both HFBCS-1 10 and HFB-1 11 were fitted to the 1995 mass-data compilation 15 , but new data were subsequently made available to us 16 , with 382 "new" nuclei. These revealed drastic limitations in both the HFBCS-1 and HFB-1 models, but in a new model 12 , HFB-2, considerable improvement was obtained primarily by modifying the prescription for the cutoff of the spectrum of s.p. states over which the pairing force acts, although the use of a generalized Wigner term helped to improve the fit to the lighter nuclei. We stress that as far as masses are concerned, the choice of pairing-cutoff prescription seems to be more important than the replacement of the HFBCS method by the HFB method (assuming always that the force is refitted to the data). With the pairing cutoff parameter being adjustable, this mass formula had 19 parameters fitted to the mass data. HFB-2 replaces all our earlier mass models, including in particular the various ETFSI models 17-18>19 based on the "extended Thomas-Fermi plus Strutinsky integral" semi-classical approximation to the HF method.

46

Of the five Skyrme-HFB models published since HFB-2 we mention here only the last two, HFB-6 and HFB-7 14 . Although these models do not lead to any improvement in the quality of the mass fit (see Table 1), nor to any substantial change in the extrapolations to the neutron-rich region, they are of considerable interest in that they were constrained to take an isoscalar effective mass M* of 0.8M at the equilibrium density po of symmetric infinite nuclear matter (INM). This is the usually accepted INM value (see Section IIIB5e of Ref. 1 f o r a discussion), but is to be compared with a value of M*/M much closer to 1 that is needed if one is to reproduce the density of s.p. states close to the Fermi surface of medium and heavy nuclei. (The difference between these two values of M* can be understood in terms of a particle-vibration coupling 20 ' 21 .) In the mass fit of HFB-2 there was no constraint on M*/M and the value that emerged was close to 1, with a much better s.p. spectra at the Fermi surface than was obtained with HFB-6 and HFB-7. However, the mass fits of HFB-6 and HFB-7 are seen (Table 1) to be as good as that of HFB-2: the mass fit and the s.p. spectra at the Fermi surface are effectively decoupled in HFB-6 and HFB-7 (this was achieved by tuning the pairing cutoff). In an astrophysical context the advantage of models HFB-6 and HFB-7 over HFB2 is that they are particularly well adapted to following the transition from isolated nuclei to neutron-star matter taking place in stellar collapse, and to the inverse process in the neutron-matter decompression associated with neutron-star mergers. Of course, if one required good s.p. spectra (or if the cutoff prescription turned out to be inconsistent with a more microscopic treatment of pairing), one would have to abandon models HFB-6 and HFB7, but it would still be possible to obtain good s.p. spectra along with an M* of around 0.8M by generalizing the Skyrme force (1) to include a t± term, i.e., a term with simultaneous density and momentum dependence 4,22

The feature distinguishing HFB-6 from HFB-7 is that the pairing of the latter has a density dependence of the form (4), with 77 and a taking values suggested by realistic INM calculations 23 . This makes very little difference as far as mass fits are concerned, or for any other property that we have so far investigated, but we shall nevertheless prefer it, since it is more realistic.

3. Quality of d a t a fits The mass models whose fits to the data we consider here are HFB-2 12 , HFB-6 14 , HFB-7 14 , FRDM 2 , and DZ 3 . The mass data for which we

47

calculate and show in Table 1 the rms deviations a and mean deviations e (experiment - calculated) of all these models are those of the latest compilation 24 , which became available only in December 2003. Of these data we exclude all entries that do not satisfy N, Z >8, and also all those for which the stated mass is an estimate based on systematics rather than a measured value. We are thus left with 2149 mass data, for which we show a and e in columns 3 and 4 of Table 1. This data set 24 is so new that none of the mass models considered here was fitted to it, and we thus show (column 2) the number N/u of masses to which the model in question was originally fitted. Table 1. The rms error (a) and mean error (e, experiment - theory) of fits given by various mass formulas to the data of the 2003 compilation 2 4 . Nfu denotes the number of nuclei to which the corresponding model was originally fitted. For the definitions of the various sub-sets of the 2003 data see Section 3. All errors in MeV.

HFB-2 12 HFB-6 14 HFB-7 14 FRDM2 DZ3

Nfit 2135 2135 2135 1654 1751

2149 nuclei a e 0.659 -0.005 0.666 0.014 0.657 0.026 0.656 0.058 0.360 0.009

70 "new" nuclei a e 0.835 0.211 0.816 0.244 0.824 0.276 0.522 -0.015 0.449 0.030

The largest data set to which any model was fitted consists of the 2135 masses of the 2001 compilation 16 , used for the HFB-2, HFB-6, and HFB-7 models. Thus in order to compare the extrapolatory power of the different models we consider the sub-set of 70 "new" nuclei in the 2003 compilation 24 that did not appear in the 2001 compilation 16 (note that 56 masses quoted as measured in the latter compilation had this status removed in the 2003 compilation 2 4 ); the corresponding a and e are shown in columns 5 and 6 of Table 1. It will be seen that in all respects the DZ model gives a better agreement with experiment than do any of the other models. The FRDM model likewise is more successful than the HFB models in its predictions for the 70 "new" nuclei; indeed, this model is unique in that its predictions are actually better than the original fit. It should furthermore be realized that both the DZ and FRDM models would probably fare still better relative to

48

the HFB models if they were refitted to the same data as those to which the HFB models were fitted 16 . On the other hand, the predictions of HFB2, HFB-6, and HFB-7 for these 70 "new" nuclei are tolerably good, and do not present the same crisis as that with which the 2001 compilation 16 confronted the HFBCS-1 and HFB-1 models. In any case, it must not be concluded that we can eliminate all but the DZ models. We shall see in the next section that the different models give quite different extrapolations into the neutron-rich region, and in the case of the HFB-7 and FRDM models, at least, it is clear that these differences have nothing to do with the quality of the corresponding fits to the presently available data, their rms deviations with respect to the complete data set of the 2003 compilation being virtually identical. Furthermore, the DZ model in its present form cannot give ground-state deformations or be used to calculate fission barriers, and is inherently inapplicable to the calculation of other quantities of astrophysical interest such as the equation of state of neutron-star matter, the giant dipole resonance, level densities, and betadecay strength functions. Thus we believe rather that all three approaches should be retained, pending further developments, and their implications for the r-process compared.

4. Extrapolation towards the neutron drip line As discussed in Ref. 1, different mass models giving comparable fits to the data will give quite different masses when extrapolated out to the neutron drip line. However, it is differential quantities such as the neutronseparation energy Sn and the beta-decay energy Qp, rather than the absolute masses, that are relevant to the r-process, and here the differences between the different extrapolations are much less pronounced in general. For example, in the case of all the mass models considered here the neutron drip lines themselves, which are characterized by Sn = 0, more or less coincide, except at the magic neutron numbers. However, there are considerable differences in the predicted shell effects for highly neutron-rich nuclei, as discussed in Refs. 1 ' 12 > 14 . A striking feature for all three of the HFB mass formulas considered here, i.e., for HFB-2, HFB-6, and HFB-7, is the strong quenching of the N = 50 and 82 shell gaps with decreasing Z, i.e., as the neutron drip line is approached. The FRDM model, on the other hand, shows no such quenching. For No = 126 and 184 the HFB gaps are more or less constant as a function of Z, while the FRDM gaps are actually enhanced as the neutron drip line is

49 approached. This quite different behaviour of the HFB and FRDM shell gaps has important consequences for the r-process, but there is no experimental evidence at the present time to discriminate conclusively in favour of one or the other possibility, although in the case of N0 = 50 the data strongly suggest the onset of quenching. Turning to theory for guidance, we know from our experience with HFB-1 and HFB-2 that the treatment of pairing has a strong influence on shell gaps 12 , but there is nothing compelling in this respect with any of the presently available models. There is thus an urgent need for a more fundamental theory of pairing, pending the extension of mass measurements into much more neutron-rich regions of the nuclear chart.

5. Fission barriers Any mass model that gives the binding energy of a nucleus as a function of its deformation can be applied in principle to the calculation of its fission barriers. However, at the present time there exist only two published calculations of the fission barriers of all the highly neutron-rich nuclei that are needed for the full elucidation of the r-process. The first of these, due to Howard and Moller 25 , is a mic-mac calculation based on an early form of the droplet model, without the refinements of the FRDM. The second, due to Mamdouh et al. 26 is based on the ETFSI approximation to the HF-BCS method, using the SkSC4 force. There are some very striking differences between the predictions made by the two calculations, the most remarkable of which occurs close to the neutron drip line in the vicinity of N = 184 (proton-deficient nuclei): for Z = 84 the Howard-Moller calculation gives 6.7 MeV for the barrier height, while the ETFSI calculation predicts 39.0 MeV. There are several reasons why one can expect this ETFSI value to be too high, the main one being that with our new prescription for the pairing cutoff the N = 184 shell gap is now known to be much smaller (1.2 MeV in the case of HFB-2) than that found in the original ETFSI mass table (4.2 MeV) 17 . However, recent HFB calculations of Samyn 27 using several of our new forces were unable to reduce this barrier height below 28.0 MeV (for force BSk-2, the force of the mass formula HFB-2). There is thus a very serious contradiction between HF and older micmac calculations of the barriers of these highly neutron-rich nuclei. It would thus be interesting if the new barrier calculations based on the FRLDM 2 8 ,

50

a simplified form of the FRDM, were to be applied to this region of the nuclear chart. (The FRDM itself cannot be used in general for barrier calculations.)

6. Symmetry coefficient for Skyrme-HF mass models Skyrme-force fits to the mass data tend to be optimized when the INM symmetry coefficient asym lies between 27 and 28 MeV. However, for asym < 28 MeV an unphysical collapse of neutron matter sets in at subnuclear densities. In the fits HFB-2, HFB-6, and HFB-7 we were able to avoid this contradiction with the known stability of neutron stars by imposing asym = 28.00 MeV, slightly degrading thereby the quality of the mass fit. However, the resulting energy-density curve of neutron matter still tends to be a little softer than that given by the Friedman-Pandharipande (FP) 29 calculation made with realistic two- and three-nucleon forces. Preliminary studies show that increasing asym to 30 MeV leads to an almost perfect agreement with the FP curve, although the cost is a further slight deterioration in the quality of the mass fit. Further evidence that the correct value of asym lies significantly higher than 28 MeV comes from measurements of the neutron-skin thickness of finite nuclei, i% m s - RTpms, where i?£ ms is the rms radius of the neutron distribution and Rpms that of the point proton distribution. Taking an experimental value of 0.14 ± 0.04 fm for the case of 2 0 8 Pb 30 led Ref. 3 1 to the value of asym = 29± 2 MeV. A more recent measurement 32 of the same quantity gave 0.20 ± 0.04 fm, which we find to be consistent with o-sym — 32± 2 MeV. Both of these experiments involved nucleon-nucleus scattering, and are very difficult, but a newly proposed method based on parity-violating electron-nucleus scattering is promising 33 . However, whatever the outcome of these new measurements of neutronskin thickness, we find that imposing the constraint asym — 32 MeV leads to mass fits that are unacceptably poor. Moreover, the corresponding neutronmatter curve is definitely stiffer than the FP curve. Imposing asym = 30 MeV would thus seem to be a reasonable compromise, and we are currently investigating the implications of such a constraint; earlier studies on these lines 34 suggested that there will be a minimal effect on the Sn and Qp, and thus on the r-process. On the other hand, shifting asym from 27 to 30 MeV is found to have a drastic effect on the composition of the inner crust of neutron stars 35 , at least within the framework of Skyrme-force models.

51 7. Conclusions In the foregoing we have briefly described the available HFB mass models. They do not fit the latest mass-data compilation quite as well as do the FRDM and the 1995 Duflo-Zuker mass formulas, but the rms error is still less than 0.7 MeV. Far more striking than the slight differences in the quality of the data fits given by the different models is the way in which they diverge when extrapolated to the neutron drip line; the problem is particularly acute when one considers the possibility of a quenching of the neutron shell gaps as the neutron drip line is approached, a matter of great astrophysical importance. The treatment of pairing is crucial in this respect, and there is an urgent need for a more fundamental approach, pending the accumulation of more data in the vicinity of closed shells. We have also discussed the extension of mass models to the calculation of the fission barriers of highly neutron-rich nuclei. Some very serious contradictions between mic-mac and HF calculations have been noted. References 1. D. Lunney, J. M. Pearson, and C. Thibault, Rev. Mod. Phys. 75 (2003) 1021. 2. P. Moller, J. R. Nix, W.D. Myers, and W.J. Swiatecki, At. Data Nucl. Data Tables 59 (1995) 185. 3. J. Duflo and A. P. Zuker, Phys. Rev. C 52 (1995) R23. 4. M. Farine, J. M. Pearson, and F. Tondeur, Nucl. Phys. A696 (2001) 396. 5. W. D. Myers and W. J. Swiatecki, Nucl. Phys. 81 (1966) 1. 6. E. Wigner, Phys. Rev. 51 (1937) 106. 7. W. Satula and R. Wyss, Phys. Lett. B393 (1997) 1. 8. W. Satula, D. J. Dean, J. Gary, S. Mizutori, and W. Nazarewicz, Phys. Lett. B407 (1997) 103. 9. W. Satula and R. Wyss, Nucl. Phys. 676 (2000) 120. 10. S. Goriely, F. Tondeur, and J. M. Pearson, At. Data Nucl. Data Tables 77 (2001) 311. 11. M. Samyn, S. Goriely, P.-H. Heenen, J.M. Pearson, and F. Tondeur, Nucl. Phys. A700 (2002) 142. 12. S. Goriely, M. Samyn, P.-H. Heenen, J.M. Pearson, and F. Tondeur, Phys. Rev. C 66 (2002) 024326. 13. M. Samyn, S. Goriely, and J. M. Pearson, Nucl. Phys. A725 (2003) 69. 14. S. Goriely, M. Samyn, M. Bender, and J.M. Pearson, Phys. Rev. C 68 (2003) 054325. 15. G. Audi and A. H. Wapstra, Nucl. Phys. A595 (1995) 409. 16. G. Audi and A. H. Wapstra, private communication (2001). 17. Y. Aboussir, J. M. Pearson, A. K. Dutta and F. Tondeur, At. Data Nucl. Data Tables 61 (1995) 127. 18. J. M. Pearson, R. C. Nayak, and S. Goriely, Phys. Lett. B 387 (1995) 455.

52 19. S. Goriely, in Capture Gamma-Ray Spectroscopy and Related Topics, edited by S. Wender, AIP Conf. Proc. No. 529 (AIP, Melville.NY), p.287. 20. G. F. Bertsch and T. T. S. Kuo, Nucl. Phys. A112,(1968) 204. 21. V. Bernard and Nguyen Van Giai, Nucl. Phys. A348 (1980) 75. 22. M. Onsi and J. M. Pearson, Phys. Rev. C 65 (2002) 047302. 23. E. Garrido, P. Sarriguren, E. Moya de Guerra, and P. Schuck, Phys. Rev. C 60 (1999) 064312. 24. G. Audi, A. H. Wapstra, and C. Thibault, Nucl. Phys. A729 (2003) 337. 25. W. M. Howard and P. Moller, At. Data Nucl. Data Tables 25 (1980) 219. 26. A. Mamdouh, J. M. Pearson, M. Rayet, and F. Tondeur, Nucl. Phys. A679 (2001) 337. 27. M. Samyn, Doctoral thesis, Universite Libre de Bruxelles (2004). 28. P. Moller, A. J. Sierk, and A. Iwamoto, Phys. Rev. Lett. 92 (2004) 072501. 29. B. Friedman and V. R. Pandharipande, Nucl. Phys. A361 (1981) 502. 30. G. W. Hoffmann, L. Ray, M. Barlett, J. McGill, G. S. Adams, G. J. Igo, F. Irom, A. T. M. Wang, C. A. Whitten,Jr., R. L. Boudrie, J. F. Amann, C. Glashausser, N. M. Hintz, G. S. Kyle, and G. S. Blanpied, Phys. Rev. C 21 (1980) 1488. 31. F. Tondeur, M. Brack, M. Farine, and J. M. Pearson, Nucl. Phys. A420 (1984) 297. 32. V. E. Starodubsky and N. M. Hintz, Phys. Rev. C 49 (1994) 2118. 33. C. J. Horowitz, S. J. Pollock, P. A. Souder, and R. Michaels, Phys. Rev. C 63 (2001) 025501. 34. J. M. Pearson and R. C. Nayak, Nucl. Phys. A668 (2000) 163. 35. A. K. Dutta, M. Onsi, and J. M. Pearson, preprint (2004).

U N D E R S T A N D I N G BETA DECAY FOR T H E R PROCESS

J. E N G E L Department of Phillips University Chapel Hill, E-mail:

Physics and Astronomy, Hall, CB3255, of North Carolina, NC 27599-3255, USA [email protected]

I review recent attempts to calculate beta-decay rates in unstable nuclei created during the r process, and briefly discuss the effects of differences in calculated rates on the abundance distributions produced by r-process simulations.

1. Preliminaries 1.1. Beta-Decay

Rates are

Important

Many of the nuclei made temporarily during r-process nucleosynthesis are currently inaccessible to experiment. Their properties, however, help determine the abundances of stable elements we observe in the solar system. Beta-decay rates are among the most important of these properties. Rates near the tops of closed-neutron-shell "ladders" in the r-process path are slow because the nuclei there are relatively close to the valley of stability. The slow rates, which are partly responsible for large abundance peaks, characterize the time it takes for nuclei to work themselves through the ladder. If we want to know how long the r process takes, we need good estimates of rates along the ladders (some of the slowest have already been measured). Even away from the ladders, beta-decay rates are important. They help determine, for example, the fraction of material that ends up outside (or inside) the three large abundance peaks. They also quantify the size of smaller abundance features, such as the "bump" in the rare-earth region. While measuring or calculating lifetimes of neutron-rich nuclei may not be necessary for determining the site of the r process, it is crucial for a detailed understanding of the r-process abundance curve. 53

54

1.2. Calculating

Beta Decay is Hard

While important, beta-decay rates are not easy to calculate. They depend both on matrix elements and on phase space, which means that a nuclear model must provide good estimates of nuclear masses, excitation energies and matrix elements of transition operators. The phase space associated with the decay to any particular state is roughly proportional to (AE)~5, so a modest error in the energy of a strongly populated state can lead to a significant error in the decay rate. Most of the transition strength is governed by the Gamow-Teller operator UT- , but in some nuclei forbidden transitions (governed by operators of the form far-) can compete. The allowed and forbidden operators are quite different from one another, and we must be able to calculate the matrix elements of both well. There is one feature of neutron-rich nuclei that makes our task easier: the further a nucleus is from stability, the larger its Q-value. This means that errors in excitation energies will be less significant than in nuclei near stability, where a small mistake can push one of the few accessible daughter states above threshold. When the Q-value is so large that a significant fraction of the total transition strength is below threshold, small errors in the distribution of that strength are much less significant. 2. Review of Approaches Several theoretical schemes have been applied over the years to /? decay far from stability. I review several of the most prominent, in approximate chronological order (approximate because the methods are continually updated). Some methods emphasize global applicability, others selfconsistency, and still others the comprehensive inclusion of nuclear correlations. None of the methods includes all important correlations, however. As a result, the value of the axial vector coupling constant is renormalized from gA — 1.26 to g^ = 1.0, at least for allowed transitions, in all the calculations discussed below.

2.1. Macroscopic/Microscopic QRPA

Mass Model -f-

Schematic

The essence of this and several related approaches discussed below is to divide the problem into two parts. First, the ground state masses of nuclei involved in the decay are calculated, then the excited states and transition

55

matrix elements are generated. The macroscopic/microscopic mass model is based on the Strutinski method of adding shell-model effects to a collective description 1 . The latest refinement of one particular mass model is called the "Finite-Range Droplet Model" (FRDM) 2 . Daughter states accessible by Gamow-Teller decay are generated from the FRDM ground state through a separable interaction V = 2\GT '• ^r_ • ar+ : (with XGT = 23 MeV/A) in the charge-changing Quasiparticle Random Phase Approximation (QRPA). The latest version of this approach 3 also includes first-forbidden transitions in a statistical way, the result of which is to shorten important half-lives at N = 82 and (particularly) N = 126. This model is not self-consistent — that is, the schematic interaction used in the QRPA is not related to the folded-Yukawa interaction used in the FRDM. Self consistency is desirable in principal, but only if the effective two-body interaction is well grounded. The advantage of the more phenomenological approach used here is that it can be more easily adjusted to data, and (because of the simple separable QRPA interaction) can be used in deformed nuclei as well as spherical ones, odd systems as well as even ones. More sophisticated approaches have not yet been consistently applied in deformed nuclei. Figure 1 illustrates the accuracy of the calculations and shows the effects of the newly included first-forbidden corrections. The average error for nuclei with lifetimes less than 1 second is a factor of about 3. Although we really need to know the lifetimes of important r-process nuclei more accurately, we should bear in mind that these calculations are designed to reproduce all lifetimes, not just those important for the r process, and that for reasons noted above, the results are better than average in the r-process region far from stability. Related global calculations with different prescriptions for obtaining the masses and mean fields exist (most notably a Nilsson-based approach 4 and the "Extended Thomas-Fermi with Strutinski Integral" (ETFSI) framework5, which has been married to a less schematic QRPA) but have not been updated as recently as the calculations illustrated here.

2.2. Self-Consistent

Skyrme-HFB

+

QRPA

In 1999 a paper appeared 6 that focused on the important "ladder" nuclei at closed neutron shells along the r-process path. These nuclei are spherical and therefore allowed a more sophisticated QRPA treatment than in the global approach discussed above. The calculation first employed the

56

104

I I I • 111

I I I I 11111

I I I I llll|

1 IJ I llllj

1 I I NIB

p decay (Theory: GT)

103

• •

102 101

• •

10-1 10"2 10- 3 104

h i 103

•

\••: *^? ^ \ y* *>v>t

zTOS&S&fift

10°

I tf I

1 I I I llllj

• * 1—a * * J9*

*SV> * — ^ « . .*

• Total Error = 3.73 for 184 nuclei, 7"p-sl

:::t < : :

-6

[••' i

0.0

.-•" 1

,

0.5

1

,

1

1.0

1.5

.

1

,

2.0

1

2.5

7

go

Figure 4. Error in Gamow-Teller resonance energy (bottom) and percentage of strength in the resonance (top) predicted by the Skyrme functional SkO', as a function of the Landau parameter g'0 for three nuclei. The value g'0 = 1.2 adequately reproduces all the experimental data.

4. Effects on the R Process It's hard to say exactly what a new set of rates in a particular region means for nucleosynthesis because we don't yet understand the conditions under which the r process takes place. It is crucial to measure or calculate the rates, and given a particular set of astrophysical conditions they fix many features of the abundance curve. At this point, however, uncertainties about the r-process environment dwarf those in the nuclear physics of nuclides far from stability. Nevertheless, it is possible to use beta-decay

61 rates to address particular issues. In a recent paper 15 it is argued on the basis of a measurement of a strength distribution far from stability that the transitions at N = 82 calculated by the shell model, HFB+QRPA, and Density-functional+FFS are too fast. As part of their argument, the authors show that slower rates better reproduce the width of the observed abundance peak. Although this conclusion depends on assumptions about the r-process environment, it will force the other groups to go back and examine their calculated strength distributions (so far they have focused on total decay half-lives). That the new rates are faster than previously believed at closed neutron shells was one of the main points made in recent work. The current suggestion that they may not be so fast after all is part of the give-and-take between observations, nuclear-structure theory, simulations, and astrophysics that promises to reveal the site of the r process and the details of how it occurs.

Acknowledgments This work was supported in part by the U.S. Department of Energy under grant DE-FG02-97ER41019.

References 1. P. Ring, and R. Schuck The Nuclear Many-Body Problem (Springer-Verlag, Berlin, 1980). 2. P. Moller, J. R. Nix, W. D. Myers,and W. J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995). 3. P. Moller, B. Bfeiffer, and K. -L. Kratz, Phys. Rev. C67, 055802 (2003). 4. M. Homma et al., Phys. Rev. C54, 2972 (1999) and references therein. 5. I. N. Borzov and S. Goriely, Phys. Rev. C62, 035501 (2000) and references therein. 6. J. Engel, M. Bender, J. Dobaczewski, W. Nazarewicz, and R. Surman, Phys. Rev. C60, 014302 (1999). 7. G. Martinez-Pinedo and K. Langanke, Phys. Rev. Lett. 83, 4502 (1999). 8. G. Martinez-Pinedo, Nucl. Phys. A668, 357c (2000). 9. P. -G. Reinhard et al., Phys. Rev. C60, 014316 (1999). 10. B.A. Brown et al., Nucl. Phys. A719, 177c (2003). 11. I. N. Borzov, Phys. Rev. C67, 025802 (2003). 12. M. Bender, J. Dobaczewski, J. Engel, and W. Nazaewicz, Phys. Rev. C65, 054322 (2002). 13. S. J. Puglia, A. Bhattacharyya, and R. J. Purnstahl, Nucl. Phys. A723, 145 (2003); R. J. Furnstahl, Int. J. Mod. Phys. B17, 5111 (2003).

62 14. M. A. L. Marques and E. K. U. Gross, in A Primer in Density Theory (Springer-Verlag, Berlin Heidelberg, 2003). 15. I. Dillmann et al., Phys. Rev. Lett 9 1 , 162503 (2003).

Functional

N E U T R O N C A P T U R E S A N D T H E R-PROCESS

T. RAUSCHER Department of Physics Klingelbergstr. E-mail:

and Astronomy, University of Basel 82, 4056 Basel, Switzerland [email protected]

The r-process involves neutron-rich nuclei far off stability for which no experimental cross sections are known. Therefore, one has to rely on theory. The difficulties in the predictions are briefly addressed. To investigate the impact of altered rates, a comparison of r-process production in hot bubble models with largely varied rates is shown. Due to the (n,7)-(7,n) equilibrium established at the onset of the r-process, only late-time neutron captures are important which mainly modify the abundances around the third r-process peak.

1. Introduction Nucleosynthesis of elements beyond the iron peak requires reactions with neutrons due to the high Coulomb barriers which prevent charged particle reactions. Except for the relatively underabundant proton-rich p nuclei, two processes have been identified for the production of intermediate and heavy nuclei: the slow neutron-capture process (s-process) and the rapid neutron-capture process (r-process). With neutron number densities around 108 c m - 3 and low effective neutron energies of around 30 keV, the s-process synthesizes nuclei along the line of stability as the neutron captures are generally slower than all beta-decays encountered along its path (with the exception of several branching points where the two timescales become similar). Approximately half of the intermediate and heavy elements are created in the much faster r-process with neutron number densities exceeding 1022 c m - 3 , effective neutron energies around 100 keV, and much shorter process times of up to a few seconds. These conditions point to an explosive site but the actual site has yet to be identified. The long favored idea of a high-entropy bubble in the neutrino wind ejected from a type II supernova shows persistent problems in explaining production across the full mass range of r-nuclei. Furthermore, there are indications that there must be two distinct sites ejecting r-process material at different frequencies (see 63

64

other contributions in this volume). In consequence, most r-process investigations focus on simplified, parameterized models which allow to study the required conditions and their sensitivities to nuclear inputs. Due to the high neutron densities the r-process synthesizes very neutron-rich nuclei far off stability which subsequently decay to stability when the process ceases due to lack of neutrons or low temperatures. This raises the question whether we can predict reactions far off stability sufficiently well to make statements about r-process conditions. In the following two main topics are briefly addressed: The difficulties in predicting neutron captures far off stability, and the impact of neutron captures on the resulting r-process abundances.

2. Predicting Neutron Capture As the astrophysical reaction rate is obtained by folding the energydependent cross section with the Maxwell-Boltzmann velocity distribution of the projectiles, the relevant energy window for neutrons is given by the location E0 « 0.172T 9 (^+ 1/2) [MeV] and width A w 0.194T 9 (£+ 1/2) 1 / 2 [MeV] of the maximum of the Maxwell-Boltzmann distribution at the given stellar temperature. Since the cross section is integrated over this energy window, the available number of levels within determines the dominating reaction mechanisms. With a sufficient number of overlapping resonances (about 10) the statistical model (Hauser-Feshbach) can be used which employs averaged transmission coefficients and describes the reaction proceeding via a compound nucleus [1]. Single, strong resonances destroy the notion of the simple energy window as the integrand is split in several terms. Finally, in between resonances or without resonances, direct capture will become important. The temperatures above which the statistical model is applicable for the calculation of neutron- and charged-particle induced reaction rates have been estimated in [2]. Explicit limits are given in the global calculation of statistical model rates of [1]. These limits should be taken as a guideline when applying the rates given therein. Fig. 1 shows how direct capture becomes more and more important for nuclei with lower and lower neutron separation energy. Basically, there are three groups of problems connected to the prediction of rates far from stability. The first two (partially overlapping) groups concern the difficulty in predicting nuclear properties relevant for HauserFeshbach and direct capture. For more details on these, see, e.g., [3]. Here, only the most important topics are outlined.

65

"n

"n

"n

~n

Figure 1. Portion of direct capture in the (11,7) cross section for a series of Ti isotopes from a comparison of Hauser-Feshbach and DC calculations. Clearly, the DC contribution increases with decreasing neutron separation energy.

Direct capture calculations are extremely sensitive to the nuclear input, such as neutron separation energies, spins, parities and excitation energy of low-lying states, and the potential used in the neutron channel [4]. One of the largest problems is the determination of the spectroscopic factor which is difficult to calculate. At stability it is usually derived from (d,p) data. However, even there a considerable uncertainty is involved as it is taken from a comparison of prediction and data and thus is not independent of theory. Due to the nature of the statistical model and its use of average quantities its sensitivity to most nuclear inputs is not as extreme as in the direct capture case. Nevertheless, it is yet uncertain how well the relevant nuclear properties, such as the particle separation energies, neutron optical potential, level density, and the low-energy tail of the GDR, can be described far off stability. Global models, in which the properties are not optimized to a few nuclei or a single mass region but rather are attempted to be consistently predicted for all nuclei, fare very well along stability. However, since the used descriptions are derived from data at stability (by either adjusting phenomenological or microscopic parameters) it remains

66 an interesting question whether they are still valid far off stability. Nevertheless, as pointed out above, the statistical model is not applicable at low neutron separation energies and therefore the impact of the uncertainties far off stability are limited. The third problem is the identification of the dominant reaction mechanism and the interplay of different reaction mechanisms when their contributions are of similar size. Clearly, more work has to be done on this in the future. Lacking other data, basically all astrophysical investigations use Hauser-Feshbach rates even for isotopes where it is not applicable. With a low level density it is usually expected that the statistical model overestimates the actual cross section, unless strong, wide resonances are found in the relevant energy window.

3. Implementation of Neutron Capture in the r-Process 3.1.

General

Given the difficulties in predicting rates far off stability, one might wonder whether it is possible at all to study the r-process, even if one resorts to simply parameterized networks. However, the situation is not that bad since it is not necessary to know the rates directly in the r-process path. Contrary to a sometimes still persisting misconception, the formation of r-isotopes cannot be viewed as occurring by a sequence of neutron captures until reaching an isotope with a /J-lifetime shorter than the neutron-capture lifetime, somewhat like an s-process but moving further out from stability. As shown in Fig. 2, all neutron captures and photodisintegrations occur faster by several orders of magnitude than any /3-decay in a given isotopic chain. In fact, the reactions are so fast that almost instantaneously (< 10~ 8 s) an equilibrium state is reached in which the abundance Y for each isotope is determined by the balance of the reactions creating and destroying it: r(n^)YA = r( 7i „)iOi+i. Since the two rates are related by detailed balance, the cross sections cancel out and the ratio is mainly depending on 5 n , T, and p. Neutron captures will only start to matter during freeze-out when the lifetimes become longer due to lower temperatures and lower neutron number densities. It has been shown that the freeze-out proceeds very quickly for realistic conditions [5]. On one hand this limits the importance of neutron captures, on the other hand it validates the investigations which were performed using approximations such as instantaneous freeze-out [6].

67 i

1

"

0.01

-

Lifetime [s]

0.0001

•.

i

i

carturo capture 9am

—

bemtl • -

'-'•'•'•-- -. j | nn=4.8£e+26 T9=2.5Q \

1e-06 '

l(

'i " '•' l ; \ ,\

/ VA A i,

^r

II

\

.;

/

-

1e-08

A/V

1e-10

''' i/ 'v' " \ i

AvA A

'' :'. t< f\ A k 1fl.15

160

170

180

190

B !/ V i. 200

vvvyv\/v^ vi 210

220

230

Mass Number A

Figure 2. Lifetimes against (11,7) (full line), (7,11) (dashed), and /3-decay (dotted) of neutron-rich T m isotopes. Captures and photodisintegrations are much faster than j3decays and abundances are determined by an (n,7)-(7,n) equilibrium. (Lifetimes at the edges of the considered chain have been set to high values to prevent mass loss from the network.)

3.2.

Dynamic

r-process

simulations

In order to study neutron captures in the freeze-out it is necessary to perform dynamic r-process simulations. As an example, calculations in the model of an adiabatically expanding hot bubble were performed, similar to [5] but with updated, temperature-dependent rates, including the theoretical rates of [1]. In this model of a primary r-process, a blob of matter at high temperature (Tg m 9) expands and cools. For the calculations here the same expansion was chosen as used by [5] in their case of 50 ms expansion timescale. Due to the initial high temperature, all reactions, including charged-particle reactions, are in equilibrium and the resulting abundances can be calculated for each temperature from the equations describing a full NSE. The charged-particle reactions, in particular the a captures, cease at around TQ RJ 2.5. Below that temperature it is not necessary to use a full network but one can utilize a simpler network, only including (n,7), (7,n), and /3-decays. The seed abundances for this r-process network are given

68

S=150,t=1 S=150,f=100 S=150,f=0.01

-j 60

oi

i 80

Li_i—ii 100

i 120

L_^ 140

1 160

1 180

Hi 200

Mass Number A

Figure 3. Decayed final abundances of the S = 150 models. The neutron rates were multiplied by factors 1.0 (full line), 100. (dashed), and 0.01 (dotted), respectively.

by the freeze-out abundances of the charged particle network. More specifically, depending on the freeze-out conditions the slow triple-a rate will either be able to convert all a's to heavy mass nuclei or it will be too slow, leaving a certain a mass fraction. The latter is called o r i c h freeze-out. The process conditions are specified by the entropy S, the electron abundance Ye, and the expansion timescale. Depending on the conditions, more or less free neutrons per heavy seed nucleus are available after the charge-particle freeze-out. Due to the still high temperature an (n,7)-(7,n) equilibrium is established. The /?-halflife of the most abundant nuclei in each isotopic chain (these are only one or two due to the shape of the equilibrium equation) determine how fast material can be converted to the next element. Each chain remains in equilibrium until finally the r-process freezes out. For this comparative study, representative seed abundances were chosen without following the full charged particle network. The calculations always started by only populating the Fe chain but with realistic Yn/Yseed and Ya (depending on entropy and y e ) taken from parameterized results of full calculations. Since the uncertainties in the neutron capture rates might be large, for two entropies 3 exemplary cases are shown here: with standard

69 1e+28

•

'

S=150,f=100 S=150,f=0.01

.

1e+26 -

1e+24

1e+22

-

V

1e+20

1e+16

1e+14 0.001

0.01

0.1 Time [s]

Figure 4. Time evolution of the neutron number density in the S = 150 models. The neutron rates were multiplied by factors 1.0 (full line), 100. (dashed), and 0.01 (dotted), respectively.

rates and with neutron captures multiplied by a factor of 100 and a factor of 0.01, respectively (this implies that the photodisintegrations are changed by the same factor). Figs. 3 and 5 show the final abundances, the neutron number densities as a function of time are shown in Figs. 4, 6. At low entropy there are not enough free neutrons to considerably change the seed abundance, the neutron freeze-out is also fast. It was already shown in [5] that the freeze-out at higher entropy is slower and that final neutron captures can alter the resulting abundances of heavy nuclei but not of light ones. The trough before the high-mass peak was filled by late neutron captures. The freeze-out behavior obtained here depends on the chosen neutron rates. The time at which the n n for the three cases diverge indicates the fallout from the rate equilibrium. After this point it depends on the entropy how far up in mass nuclei have been produced and on the neutron captures how their abundances are altered. As can be seen in Figs. 4 and 6, the final freeze-out phase is faster for larger rates. This reflects the increased capture when the forward and reverse rates fall out of equilibrium which uses up

70 0.001

S=250,f=1 S=250,f=100 S=250,f=0.01

0.0001 -

1e-05

1e-06

1e-07

1e-08 60

120

140

Mass Number A

Figure 5. Decayed final abundances of the S = 250 models. The neutron rates were multiplied by factors 1.0 (full line), 100. (dashed), and 0.01 (dotted), respectively.

neutrons faster. The masses above about 140 are mainly produced in this late freeze-out phase and are therefore more sensitive to the value of the neutron captures. Especially in the high entropy case shown in Fig. 5 it is evident that faster neutron captures smooth the abundance distribution and fill the trough before the A as 200 peak. For both entropies, the artificially suppressed rates do not allow to build up considerable abundances beyond A w 140. 4. Conclusion The simple comparison shown above for the hot bubble model has to be interpreted cautiously. Despite the fact that there might be considerable uncertainties in the theoretical rates far off stability changing all rates in a range of 4 orders of magnitude seems unrealistic. Even if new effects (like pygmy resonances [7] or overestimated cross sections [3]) might change the rates by factors of 10 for extremely neutron-rich nuclei, late-time captures will not include such nuclei but will occur closer to stability. Moreover, for reproducing the solar r-process pattern it is necessary to superpose a number of components with different entropies. Thus, effects of rates

71 1e+28 S=250,f=1 S=250,f=100 S=250,f=0.01 1e+26

1e+24

1e+22

1e+18

1e+16

0.001

0.01

0.1 Time [s]

Figure 6. Time evolution of the neutron number density in the S = 250 models. The neutron rates were multiplied by factors 1.0 (full line), 100. (dashed), and 0.01 (dotted), respectively.

altered on a large scale, as shown above, can be compensated by a scaling in entropy and a different weight distribution. Thirdly, a more realistic seed abundance distribution might also decrease the difference in heavy element production between the different cases. Higher entropies realistically start with seed abundances in the A ss 110 region and require less neutrons to form more heavy elements. However, this was not taken into account here to purely show the influence of altered neutron captures. Despite the above caveats the main conclusions are consistent with other studies [5,8]. Components with high entropy freeze out slower and latetime neutron captures can modify the final abundance distribution mainly in the region A > 140. Therefore, emphasis has to be put on improving the prediction of nuclear cross sections and astrophysical reaction rates in that mass region. Acknowledgments This work was supported by the Swiss NSF, grant 2000-061031.02. T. R. acknowledges a PROFIL professorship of the Swiss NSF (grant 2024-

72 067428.01). References 1. T. Rauscher and F.-K. Thielemann, Atomic Data Nucl. Data Tables 75, 1 (2000). 2. T. Rauscher, F.-K. Thielemann andK.-L. Kratz, Phys. Rev. C56, 1613 (1997). 3. P. Descouvemont and T. Rauscher, Nucl. Phys., in press; astro-ph/0402668. 4. T. Rauscher, R. Bieber, H. Oberhummer, K.-L. Kratz, J. Dobaczewski, P. Moller and M. M. Sharma, Phys. Rev. C 5 7 , 2031 (1998). 5. C. Freiburghaus et al, Ap. J. 516, 381 (1999). 6. K.-L. Kratz, J.-P. Bitouzet, F.-K. Thielemann, P. Moller and B. Pfeiffer, Ap. J. 403, 216 (1993). 7. S. Goriely and E. Khan, Nucl. Phys. A706, 217 (2002). 8. R. Surman and J. Engel, Phys. Rev. C 64, 035801 (2001).

SUPERNOVA NEUTRINO-NUCLEUS PHYSICS A N D THE R-PROCESS

W. C. HAXTON Institute for Nuclear Theory and Department of Physics Box 351550, University of Washington Seattle, WA 98155 E-mail: [email protected] This talk reviews three inputs important to neutrino-induced nucleosynthesis in a supernova: 1) "standard" properties of the supernova neutrino flux, 2) effects of phenomena like neutrino oscillations on that flux, and 3) nuclear structure issues in estimating cross sections for neutrino-nucleus interactions. The resulting possibilities for neutrino-induced nucleosynthesis - or the i/-process - in massive stars are discussed. This includes two relatively recent extensions of v-process calculations to heavier nuclei, one focused on understanding the origin of 138 La and 180 Ta and the second on the effects following r-process freezeout. Prom calculations of the neutrino post-processing of the r-process distribution, limits can be placed on the neutrino fluence after freezeout and thus on the dynamic timescale for the expansion.

1. Basic Supernova Neutrino Characteristics A massive star, perhaps 15-25 solar masses, evolves through hydrostatic burning to an "onion-skin" structure, with a inert iron core produced from the explosive burning of Si. When that core reaches the Chandresekhar mass, the star begins to collapse. Gravitational work is done on the infalling matter, the temperature increases, and the increased density and elevated electron chemical potential begin to favor weak-interaction conversion of protons to neutrons, with the emission of i/es. Neutrino emission is the mechanism by which the star radiates energy and lepton number. Once the density exceeds ~ 10 12 g/cm 3 in the infall of a Type II supernova, however, neutrinos become trapped within the star by neutral-current scattering, —diffusion \ -.collapse

/-i \

That is, the time required for neutrinos to random walk out of the star exceeds T c o " o p s e . Thus neither the remaining lepton number nor the gravitational energy released by further collapse can escape. 73

74

After core bounce a hot, puffy protoneutron star remains. Over times on the order of a few seconds, much longer than the 100s of milliseconds required for collapse, the star gradually cools by emission of neutrinos of all flavors. As the neutrinos diffuse outward, they tend to remain in flavor equilibrium through reactions such as ve + ve 4+ i/M + i/M

(2)

producing a rough equipartition of energy/flavor. Near the trapping density of 10 12 g/cm 3 the neutrinos decouple, and this decoupling depends on flavor due to the different neutrino-matter cross sections, vx + e 44 vx + e : aVli /aVt ~ 1/6 ue + n +•> p + e+ De+p2- The former could be measured in long-baseline neutrino oscillation experiments (with the ease of this depending on the size of 8\3), while the latter could influence rates for double beta decay. These new neutrino physics discoveries could have a number of implications for supernova physics: • Because of solar neutrinos, we have been able to probe matter effects up to densities p ~ 100 g/cm 3 characteristic of the solar core. As the density at the supernova neutrinosphere is p ~ 10 12 g/cm 3 , supernova neutrinos propagate in an MSW potential that can be 10 orders of magnitude greater than any we have tested experimentally. In addition, the neutrinos propagate in a dense neutrino background, generating new MSW potential contributions due to v — v scattering. Such effects, as well as the magnitude of the ordinary-matter MSW effects, may be unique to the supernova environment. • We do not know #13, which is the crucial mixing angle for supernovae. This angle governs the ve -heavy flavor level crossing encountered at depth in the star. This crossing occurs near the base of the carbon zone in the progenitor star, and remains adiabatic for sin2 2#i 3 > 10~ 4 . For the ordinary hierarchy, the resulting ve *rt fMir crossing would lead to a hotter ve spectrum. For an inverted hierarchy, the crossing would be ve ++ ^ , T • Presumably the position of this crossing will be influenced by the neutrino background contribution to the MSW potential. This nonlinear problem is rather complicated because the flavor content of the background evolves with time (being ve-dominated at early times).

77

V*

VT

V,

Vn

~10^g/cmJ

density

vacuum

Figure 1. A three-level MSW level-crossing diagram showing the second crossing that should occur at densities characteristic of the base of the carbon zone in a Type II supernova progenitor star.

3. Nuclear Structure Issues Inelastic neutrino-nucleus interactions are important to a range of supernova problems, including neutrino nucleosynthesis, the detection of supernova neutrinos in terrestrial detectors, and neutrino-matter heating that could boost the explosion. The heavy-flavor neutrinos have an average energy (E) ~ 3. I T ~ 25 MeV. However the most effective energy for generating nuclear transitions can be substantially higher because cross sections grow with energy and because nuclear thresholds are more easily overcome by neutrinos on the high-energy tail of the thermal distribution. For the neutrino energy range of interest the allowed approximation, which includes only the Gamow-Teller 5>icr(z)r±(f) and Fermi r±(i) operators, is often not adequate. (These are given for charge-current reactions; the allowed operator for inelastic neutral current reactions is gA