L-subshell ionization of Ce, Nd, and Lu by4–10−MeVC ions

Abstract

$Ll,L\ensuremath{\alpha},L\ensuremath{\beta},L\ensuremath{\gamma},L{\ensuremath{\gamma}}_{1+5},L{\ensuremath{\gamma}}_{2+3},L{\ensuremath{\gamma}}_{4+{4}^{\ensuremath{'}}}$ x-ray production cross sections of $_{58}\mathrm{Ce}$, $_{60}\mathrm{Nd}$ and $_{71}\mathrm{Lu}$ induced by 4-, 6-, 8-, and $10\text{\ensuremath{-}}\mathrm{MeV}$ carbon ions were measured. For Lu, $L{\ensuremath{\gamma}}_{2+3}$ is separated from $L{\ensuremath{\gamma}}_{2+3+6}$ after revision of the technique of Datz et al. so that $L{\ensuremath{\gamma}}_{1+5}$ was used instead of $L{\ensuremath{\gamma}}_{1}$, the $L{\ensuremath{\gamma}}_{4+{4}^{\ensuremath{'}}}∕L{\ensuremath{\gamma}}_{1+5}$ ratio was corrected for multiple ionization, and uncertainties in $L{\ensuremath{\gamma}}_{4+{4}^{\ensuremath{'}}}$ were incorporated in the fitting process. $L$-subshell ionization cross sections were extracted as a weighted average from two combinations of these cross sections, ${L\ensuremath{\alpha},L{\ensuremath{\gamma}}_{1+5},L{\ensuremath{\gamma}}_{2+3}}$ and ${L\ensuremath{\alpha},L{\ensuremath{\gamma}}_{1+5},L\ensuremath{\gamma}}$. It is shown that, to within a few percent, the first of these two combinations results in the identical cross sections as this weighted average. Within 10%, permutations of different sets of single-hole atomic parameters yielded the same ionization cross sections. These cross sections are typically within 15% and at most 35% of the cross sections obtained with atomic parameters that were altered in two different ways for multiple ionization. Extracted subshell and total $L$-shell ionization cross sections as well as Ce and Nd data of Braziewicz et al. are compared with the ECPSSR theory of Brandt and Lapicki that accounts for the energy-loss (E), Coulomb-deflection (C), perturbed-stationary-state (PSS) and relativistic (R) effects. These measurements are also compared with the ECPSSR theory after its corrections---in a separated and united atom (USA) treatment, and for the intrashell (IS) transitions with the factors of Sarkadi and Mukoyama normalized to match $L$-shell cross section with the sum of $L$-subshell cross sections---as well as with the similarly improved semiclassical approximation of Trautmann. For Ce and Nd, the agreement of the extracted ionization cross sections with these theories is poor for ${L}_{1}$ and good for ${L}_{2}$, ${L}_{3}$, and total $L$ shell ionization. For the ${L}_{2}$ subshell, this agreement is better for Ce and Nd than for Lu. The ECPSSR theory corrected for the USA and IS effects is surprisingly good for the ${L}_{1}$-subshell ionization of Lu, while at $4\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ a similarly corrected semiclassical approximation is in excellent agreement with ${L}_{2}$ and ${L}_{3}$ data but overestimates the ${L}_{1}$ measurement by almost a factor of 2.