Excitation cross section of some of the states of NE II, Ar II, and KR II by electron collision

The sudden perturbation method has been used to calculate the excitation cross section of some of the states of Ne II, Ar II, and Kr II by high energy electrons. In this method, the ground state of the noble gas atom, after a collision with a fast electron, is considered to lose one of its valence electrons in a time shorter than the relaxation time of the atom. The resulting configuration is then assumed to be a
|(p^{5}) ^{2}P_{j}\rangle
state with
J = 3/2
or 1/2, with the remaining five valence electrons having the same radial coordinates as in the original
|(p^{6})^{1}S_{0}\rangle
state of the neutral atom. The configuration
|(p^{5})^{2}P_{j}\rangle
is then expanded in terms of the ionic wave functions having the form of
|(p^{4})\bar{L}\bar{S}, nl', LSJ\rangle
, where
\bar{L},\bar{S}
designate the total orbital angular momentum and the total spin angular momentum of the core electrons,
l'
is the orbital angular momentum of the excited running electron, and
LSJ
designates the final orbital, spin, and total angular momenta of the atom. The coefficients of the expansion are calculated in terms of the coefficients of fractional parentage and
3-j
symbols. The radial wave functions for the neutral atoms and their excited ionic states for the involved radial integrals are obtained by using a computer program giving the self-consistent Hartree-Fock wave functions in the Slater approximation. Since no experimental measurements for the excitation cross sections with fast electrons are given, the results of the calculations are indirectly compared with the available work reported on the pulsed Ar II laser. Population of various excited ionic states is calculated assuming a uniform energy distribution of electrons having 1.8 times the ionization threshold of argon, and the results are compared with experimental data reported in the literature.