Semiclassical Coulomb differential excitation function: Asymptotic expansions

We have obtained asymptotic expansions of the electric dipole (E1) differential excitation function for large values of the adiabaticity parameter ξ and for all values of the eccentricity (e) of the projectile orbit. To accomplish this, we have developed a new asymptotic power series of exponential integrals related to the Airy integrals, introduced originally in a paper by Brussaard et al. [Ann. Phys. (N.Y.) 7, 47 (1962)], in which asymptotic expansions of the total excitation function were derived.