Characteristic X-Ray Production in AtomicLandMSubshells

Abstract

Explicit formulas are obtained for atomic form factors describing the energy loss and momentum transfer of a charged particle to electrons in the subshells of the L and M shells. The Bethe-Born approximation is used with hydrogenic wave functions. Application is made to the Lm ionization cross section for protons incident on copper in the energy range from 0.5 to 1.7 MeV.

Polynomial approximation to universal ionisation cross‐sections of K and L shells induced by H and He ion beams

“…In the present work, the $f_{n, o}\ast (Q, k)$ polynomial functions in Q and k from Merzbacher and Lewis23 for the K‐shell and from Merzbacher, Khandelwal and Choi24–26 for the L‐shell, were used instead of the Benka and Kropf ones used by Cohen and Harrigan,22 still all the remaining expressions necessary for calculating the PWBA cross‐sections are the same.…”

Thorium and uranium M-shell x-ray production by 0.4–4.0 MeV protons and 0.4–6.0 MeV helium ions

“…In these equations, ω i and f ij are the M-subshell fluorescence and the Coster-Kronig yields, respectively. For these atomic ) to the theoretical results of the first Born approximation [35][36][37][38][39][40] and ECUSAR theory [26,27] for both elements.…”

“…Following the development of the plane-wave Born approximation (PWBA) for the K-and L-shell direct ionization to the target's continuum [34], similar formulae were derived [35], corrected [36] and their results tabulated [37] for the M shell. Contemporaneously with [35], the Oppenheimer-Brinkman-Kramers approximation [38,39] was employed for an electron capture calculation by Nikolaev [40] (OBKN). Nikolaev used the same screened hydrogenic wavefunctions for the description of the M subshells as in the PWBA of Khandelwal and Merzbacher [35].…”

“…Contemporaneously with [35], the Oppenheimer-Brinkman-Kramers approximation [38,39] was employed for an electron capture calculation by Nikolaev [40] (OBKN). Nikolaev used the same screened hydrogenic wavefunctions for the description of the M subshells as in the PWBA of Khandelwal and Merzbacher [35]. The sum of cross sections for the direct ionization and electron capture evaluated with these approximations is known as the first-order Born approximation.…”

“…Figures 2 and 3 exhibit, respectively, for H and He ions, the ratio of the production cross sections for three of the four individual peaks Mζ , Mα and Mβ to the theoretical ionization cross sections that were converted according to equations (3)- 2) to the theoretical results of the first Born approximation [35][36][37][38][39][40] and ECUSAR theory [26,27] for both elements. [17], the first Born approximation [35][36][37][38][39][40] and ECUSAR theories [26,27]. (8) to x-ray production with the atomic parameters of Chen et al [31,42,43] as recently recommended by Puri [32,33].…”