On the use of the Bethe approximation in the treatment of long-range multipole interactions in electron-neutral-atom collisions

Abstract

The integral IR(k, l, k', l', lambda )= integral ;r-( lambda +1)Fl(kr)Fl'(k'r)dr for dr R to infinity where Fl(kr)= square root k rjl(kr), jl is a spherical Bessel function and R>or=0, is considered and expressed in terms of well known functions. Its use in electron-atom collision theory is discussed. The interesting result of Burgess and Tully (1978) concerning the relationship of the weak-coupling Bethe and Born collision strengths in the limit of infinite impact energies, i.e. limE to infinity Omega Bethe I/ Omega Born I=2, is clarified.