Analytic Expressions for the Born Approximation to Certain Elements of the Reactance Matrix ine−-H Scattering

Analytic expressions are presented for the elements of the reactance matrix connecting the ground state ($1s$) and the degenerate first excited states ($2s, 2p$) of the hydrogen atom in the Born approximation to $e^{-}$-H scattering. The results can be expressed entirely as algebraic functions of Legendre functions of the second kind and their first, second, and third derivatives. A discussion of computational methods which illustrates the usefulness of these expressions is also given.