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

The integral I R (k, l, k', l', lambda )= integral ;r -( lambda +1) F l (kr)F l' (k'r)dr for dr R to infinity where F l (kr)= square root k rj l (kr), j l 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. lim E to infinity Omega Bethe I / Omega Born I =2, is clarified.