Direct and Indirect Production of Characteristic X-Rays

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1 Jones, J. H., Proc. Roy. Soc., 105, 600 (1924). Epstein, P. S., Ann. Physik, 50, 509; 51, 184 (1916). 3 Sommerfeld, A., Elster und Geitel-Festschrift, 575 (1916); Epstein, P. S., Zeitschr. Physik, 9, 107 (1922). 4Kramers, H. A., Danish Academy (1919). 6 Epstein, P. S., Physic. Rev., 19, 578 (1921). 6 Bohr, A., Danish Academy (1917). Sommerfeld, A., Ann. Physik, 51, 1 (1916). 2

DIRECT AND INDIRECT PRODUCTION OF CHARACTERISTIC X-RA YS By DAVID L. W1BSTER STANFORD UNIVERSITY, CALIFORNIA Communicated April 26, 1927

I. The Problem.-When electrons are ejected from the K orbits of atoms in the target of an X-ray tube, the question arises: Are most of them ejected by direct action of the cathode rays through their repulsive forces; or are they ejected by an indirect process, the photoelectric effect of continuous-spectrum X-rays excited by the cathode rays; or perhaps, do both processes occur often? From the experimental standpoint, this question takes the form: Are the characteristic rays from the target of a tube mostly "direct primary rays," or are they mostly "indirect primary rays" (really a restricted class of secondary rays), or are they a mixture of comparable amounts of both classes? Beatty,' in 1912, said they were mostly direct and presented such clear experimental evidence that his answer was accepted for many years as conclusive. In 1926, however Balderston,2 by calculations from data of wholly different types, came to exactly the reverse conclusion. Evidently, the question calls for further investigation. II. Emergence-Angle Experiments.-Two methods were used in the present work, both based on the fact that such indirect rays as may exist are produced at a variety of depths averaging somewhat greater than the mean depth of production of rays in the continuous spectrum. This is obvious qualitatively from the fact that, in any fairly heavy element, X-rays of the types needed for fluorescence of its K series are more penetrating than the cathode rays producing them. If, therefore, any means can be found for revealing differences in the depths of production of X-rays, of these two classes, the question at hand can be answered. The first of the two methods was an adaptation of Ham's3 experiment on total, or unresolved, X-rays, applied here to the

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rays as resolved by the spectrometer. The underlying principle is that if the rays from any atom are emitted with equal intensities in all directions, then the deeper the atom is within the target, the more effect the absorption by the target material will have in causing differences of intensity between rays emerging from its surface nearly perpendicularly or at small angles. In the present case, the target was a layer of silver, 25 microns thick, electroplated upon copper. When it was bombarded by cathode rays driven by a steady voltage of 35 kv., d. c., the continuous-spectrum rays were produced, as will be shown below, at mean depths of less than a micron, while the indirect characteristic rays came from depths averaging several microns. The difference between these depths is such as to cause considerable changes in the ratio of indirect characteristic rays to continuous-spectrum rays of the same wave-length, when the emergence angle e, between the target surface and the rays to the spectrometer, is reduced below 200. For quantitative calculation, this ratio must be defined more specifically in terms of spectrum graphs in which electrometer readings are plotted against glancing angles. As the tube is turned to re4uce the angle of emergence, the change in apparent size of the focal spot, as seen from the spectrometer crystal, causes a change in the resolving power of the spectrometer. A simple ratio of the maximum ordinate of the Ka peak to that of the continuous spectrum under it would, therefore, be misleading, and the only true basis for comparison is the ratio of the area, A, of the Ka peak, to the ordinate, C, of the continuous spectrum in its neighborhood. This ratio, which is of the dimensions of an interval of glancing angles, gives the width of a block of continuous spectrum carrying the same total energy as the a lines. The next problem is to calculate this ratio, assuming all the line radiation to be indirect. For this purpose the following assumptions, definitions and data were adopted, and will prove useful in the theory of the second method: (1) The continuous spectrum, as emitted from any atom, is of the same form and intensity in all directions. (2) Continuous-spectrum rays of the a-line frequency emerging from the target are reduced by absorption to a fraction, exp { - Ilaxa csc e} where , is their absorption coefficient and Xa their mean depth of production. (3) The mean depth of production for rays of any frequency may be found by the method of Webster and Hennings,4 depending on the extent to which the K-absorption limit of the target material affects the observed emission spectrum. (4) Mean depths as thus found for the present case are small enough

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so that for calculation of the indirect radiation one may treat the continuous-spectrum rays as if they all originated at the surface. (5) The absorption coefficient , at any frequency above the K limit is A.aRLK-Y7, where 1 =- and RL is the absorption limit ratio, given by Va

Richtmyer5 for silver as 7.8; in calculations on the second (more accurate) method, this assumption is replaced by Richtmyer's more accurate formula for IA. (6) The number of a-line quanta emitted indirectly is a constant fraction, ua, of the number of absorbed quanta of frequency greater than the 5 K-limit frequency VK, and Ua is as given by Balderston2 for silver, - X 0.75, 6 or 0.625. (7) The total intensity of the a-line rays, or energy leaving the target per unit time and per unit solid angle in the direction e, is Ea, and is made up of two parts, direct and indirect, called E' and E, respectively. (8) The observed a peak has an area A = A' + A", likewise determined by the equation A = SE,, where S is the over-all sensitivity of the spectrometer and its accessories. (9) The continuous spectrum has its true intensity per unit frequency interval I (V, v), and they are related through the formula

Cd =_ C tanO I(V, v)dv vI(V, v) where 0 is the glancing angle for the frequency v. (10) For a single element,

S=

I(V, v) = K{(vo-P) + BVa} where K is a constant and hvo = e V; the term Bva is expressed as a multiple of va merely for convenience in integration, and is treated as if it were constant with B = 0.10, this value being a rough estimate from Webster and Hennings'6 data on Mo. With these assumptions and definitions, it is a simple-matter to set up the integral, r/2 so

P

Ea = -2 ff0 O vK

u

a V

,uI(V, v) exp {-,ur-/,ar cos 4 sin E} sin 4drd4dv

where ,6 is the colatitude in a spherical coordinate system. This integrates readily as far as

Ea

2- Ua xK a. I(V, v) log 1 + Ha csce) dv 2 K P Ha CcscEe

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from which, A" iuaRfRtanO sin C (io - 1+B) exp{-Ma,a csce

I

-

PROC. N. A. S.

+ Bl( j B log

where no = ° and lK = K. va

va

Evaluating this graphically for silver at 35 kv., the results are as follows: e = 200, 5° 1°; A" = 11.9', 7.4', 4.0'. C The observed values of the area-to-ordinate ratios for these angles are obtained from figure 1, as 50 ,