Generalized oscillator strengths and inelastic scattering cross sections for allowed and nonallowed transitions in lithium atoms

Abstract

The generalized oscillator strengths $f(\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}})$ as a function of momentum transfer $\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}$ are calculated for the (i) $2s\ensuremath{-}2p$, $3s$, $3p$, $3d$, (ii) $2p\ensuremath{-}3s$, $3p$, $3d$, (iii) $3s\ensuremath{-}3p$, $3d$, and (iv) $3p\ensuremath{-}3d$ transitions of the lithium atom using the Hartree-Fock wave function of Weiss. Calculations are carried out using both the length and velocity formulations of the Born-approximation integrals. For these transitions of lithium, the $f(\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}})$ values were used to obtain integrated inelastic cross sections within the first Born approximation for electron impact. The results of the total cross section for $2p$, $3s$, and $3d$ from the ground state are compared with the available Born calculations and recent experimental data.