|
| |
FIZIKA A 12 (2003) 4 , 183 - 194
 
A SIMPLE AND EFFICIENT YET ACCURATE CALCULATION OF THE
DOUBLE-DIFFERENTIAL COMPTON CROSS SECTION WITHIN THE IMPULSE APPROXIMATION
SELIM PAŠIĆ
Department of Physics, Faculty of Science, University of Zagreb,
Bijenička 32, 10 000 Zagreb, Croatia
E-mail address: spasic@phy.hr
Received 5 November 2003; Accepted 15 December 2003
Online 19 April 2004
It is shown that with proper values of the effective charge, the hydrogen-like (HL)
wave functions are almost as good as the more sophisticated Hatree-Fock (HF) wave
functions in calculations of the double-differential cross section of Compton scattering
within the nonrelativistic impulse approximation (IA). Only a single value of the
optimized effective charge for a given subshell of an atom is required for an accurate
description of Compton spectra in a wide range of experimental conditions under which IA
is a good approximation. That is demonstrated by results obtained for the K-shell of
several atoms and for higher subshells in germanium. It has been found that a constant
value of the optimal effective charge can be used as a criterion for the validity of IA,
which is explained within the existing knowledge of IA. Simple analytical expressions for
HL-Compton profiles have a compact form and are a much faster way to calculate the cross
sections than using extensive tabulations of HF Compton profiles. These features can be
useful in very extensive numerical calculations of Compton scattering in radiation
physics, biomedicine, industry and in other practical applications.
PACS numbers: 32.80.Cy
UDC 539.122
Keywords: photon scattering, Compton profile, impulse approximation, effective charge
|
