Portal de Periódicos da CAPES

Glauber cross sections for arbitrary excitation of ground-state hydrogen by electron and proton impact

1981; American Institute of Physics; Volume: 23; Issue: 2 Linguagem: Inglês

10.1103/physreva.23.715

0556-2791

S. K. Sur, N. C. Sil,

X-ray Spectroscopy and Fluorescence Analysis

The Glauber scattering amplitude for $1s\ensuremath{-}nlm$ excitations of hydrogen by charged particle impact is reduced to a form numerically computable for arbitrary values of $n$, $l$, and $m$. The increasing number of repeated parametric differentiations appearing in earlier methods with the increase of $n$ is replaced in our method by a single contour integration, which is especially useful for large-$n$ states. In addition, whereas the available closed-form expressions would involve the calculation of a large number of hypergeometric functions as $l$ and $m$ increase for a given $n$, the present integral form involves only one hypergeometric function for any $n$, $l$, and $m$. The asymptotic form of the $1s\ensuremath{-}nlm$ amplitude as $n\ensuremath{\rightarrow}\ensuremath{\infty}$ is also presented. The procedure is applied for studying the $1s\ensuremath{\rightarrow}\mathrm{ns}(n=3, 4, 10, \mathrm{and} \ensuremath{\infty})$ and $1s\ensuremath{\rightarrow}\mathrm{np}(n=3, 4, \mathrm{and} \ensuremath{\infty})$ excitations of hydrogen by electron and proton impact. Tabular results of the cross sections are presented for differential and integrated cross sections in ${e}^{\ensuremath{-}}$-H collisions and for integrated cross sections in ${\mathrm{H}}^{+}$-H collisions. The qualitative features observed earlier for low $\mathrm{ns}$ and $\mathrm{np}$ excitations are found to exist also for $n\ensuremath{\ge}3$ excitations. The $1s\ensuremath{\rightarrow}\mathrm{ns}$ and $1s\ensuremath{\rightarrow}\mathrm{np}$ cross sections obey an ${n}^{\ensuremath{-}3}$ law asymptotically as ${n}^{\ensuremath{-}2}\ensuremath{\rightarrow}0$, which is in conformity with the analytical results obtained quite generally for $1s\ensuremath{\rightarrow}\mathrm{nlm}$ excitations. For proton impact $1s\ensuremath{\rightarrow}3p$ excitations, the Glauber results are in excellent agreement with a recent 34-state calculation. A unified graphical representation of various normalized cross sections above some specific energy is presented, whence a knowledge of the high-energy Born cross sections for any $1s\ensuremath{\rightarrow}\mathrm{ns}$ or $1s\ensuremath{\rightarrow}\mathrm{np}$ excitation suffices to determine the absolute Glauber cross sections for the process.