EFFECTIVE CADMIUM CUTOFF ENERGIES

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ORN L-2823

UC-4

- Chemistry-Genera

EFFECTIVE CADMIUM CUTOFF ENERGIES

R, W, Stoughton J. Halperin Mo P o Bietske

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U N I O N CARBIDE CORPORATION for the

U.S. A T O M I C ENERGY C O M M I S S I O N

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om2823

DATE ISSUED

OAK RIDGE PTATIOTJAL U B O W O R P

Oak Ridge, Tennessee operated by UT?IOIT CAR3ZDE CORPO€U!ITOT? f o r the Ud S + AT01!IC EIERGY COPdNISSION '

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Effective CadmLum CytofZ Ehergies R . W . Stoughton, J. Halperir,, and Marjorie P, Lietzke

Abstract Effective cutoff energies for poir-t

_1.I/. absorbers

inside of spherical

and cylindrical cadmim f i l t e r s have been calculated f o r thermal reactor neutrons. plus a

The neutron s p e c t m was assumed t o consist of a Maxwellian

1/E component,

and the parmeters varied were the thickness of

f i l t e r , the Maxwellian tenrperature and the b ~ w e l l i a aLo

_1/E flux r a t i o .

Because of the s e n s i t i v i t y of the el’fective cutoff t o Maxwellian f l u x parameters for t h i n f i l t e r s it i s recornended %‘fiatf i l t e r thicknesses of about 40 m i l s be used.

Forty mil f i l t e r s show effective cutoffs a t about

0.50 t o 0.55 ev. for temperahres up t o about 500°A ( o r about 0.045 ev).

Effective cutoff energies f o r boron f i l t e r s were also calculated for purposes of comparison.

The cutoffs f o r cylindrical cadnium f i l t e r s

should be applicable to a properly designed experLxen+ual f a c i l i t y .

-3h t r o d u c t ion

For many yems cadm3m has been used as a fiJ,ter for thermal neutrana in maswing t h e r m 1 vs epithermal reaction r a t e s f o r reactor spectrum neutrons. Yaa e f ' f e c t l v s Cd cutoff er,ergy kras been estimateil as several

depenaing on the t h i c h e s s ~f the f j l t e r .

Hughes

a

e s t h a t e d about 0.4Q and

0.57 ev for 10 and 30 m i l cadmium -t;taFcknesses, -respe:tiveljr, calculated r e l a t i v e number of neufxoos transmi3Aed vs enezgy Dayton and Pettus

tenths ef an ev

from a p l o t of %he

.

More recently

calculated effective Cd cutoff energies f o r flat f i l t e r s

of ,large area f o r both a monodirectional and an isotropic flux. only a

& flux,

w i t h lower wii upper lj.aits of 0.025 ev

%he upper liiit was not

and energy.

They assumed

aQa 10nev (althorn

important) i n the* numerical integrations over the angle

They defined the effective cutoff energy as the cutoff of a perfect

( I n f i n i t e l y sharp) f i l t e r that allows t h e same tu"al xmiber of-absorptions by the f i l t e r e d sample as does the gLven cailmkm ffl%er. In - h e i r calczila%irms they

assumed that the f i l t e r e d sanple had a The purpose of thLs paper is

tb

& cross

sectian.

calculate ef"fec-i;5.-veCd cutoff enezgies, as absorber and for an idealized

defined by Dayton and Pettus, f o r a 12ypo-khetical&l

Two geometrical configurations have been conside;-ed:

spherica4. and cylLndrica1

f i l t e r s (one cm dim. by two cn high.) ix resctor ixz*adiai;ions. Fdihfle %e ampl.es

occurred) and rather smal.1 3x1 ares,.

Xt c a s be s$mm that if a point san2le is moved

a signtficant distance f r D m the cen%er of the cyl-bdrical s h e l l i t s correaponfiir&

effective C d thickness is changed very l i t t l e .

For example, i f t h e p0b-k is moved

along the axis half way t o ogle of %he f a c e s (i. .e.

to one q w t e r '3f t h e height from

the nearer face) the effective Cd thickness is changed about G.$.

Eence a th4.n

-4f i n i t e sample which approximates an i n t e p a l of such points should shov very rxarly the sane effective cutoff as does the central point.

Actually an e f -

fective thickness could be calculated and a correction made, i f desired. the case of the spherical f i l t e r s the correction would be larger.

In

From an

experimental point of view, however, the cylindrical f i l t e r s are easier to make and to use, i n addition L ' o allowing an effective cutoff which is r e l atively insensitive t o position of sample. Effective cutoff energies were also calculated f o r boron f i l t e r s LEIorder t o compare the variation of effective cutoffs with f i l t e r thickness and spectral parameters t o t h a t of cadmium.

I n general r e a l fiYcers such as caclnriurn a.~ad boron o n l y approxiaate o m defined perfect f i l t e r .

An additional factor t h a t a f f e c t s the u s e m e s s of a

f i l t e r is the sharpness w i t h iflich the t r t z x i t f o n fi-on opacity t o transparency i s made a t the cutoff.

A siaple measure of t b . i s efficiency was made here by

calculating the f'raction of %he ",tal number of reactions occurring i n t h e l / v t e s t sample a t energies below

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