Marita C. Chidichimo

High-energy Born collision strengths for optically forbidden transitions

Collision strengths for optically forbidden transitions in positive ions excited by electron impact tend to finite limits as the energy of the colliding electron becomes infinitely great. This statement applies to theoretical data obtained by means of approximations which ignore relativistic effects. The high-energy limiting values are given by the Born approximation, which Bethe showed can be reduced to a closed expression requiring integration over momentum transfer and the radial distance of the atomic orbital. In the appendix we describe an accurate numerical procedure for evaluating this double integral and also show how to perform the Racah algebra which arises when mixed configurations are used to describe the target. We make applications to several isoelectronic sequences taking configuration interaction into account.

An asymptotic expansion for the hypergeometric function 2F1(a,b;c;x)

Watson’s treatise expresses the ordinary Bessel function as a limit of a hypergeometric function, where the first two parameters go to infinity, while simultaneously the argument goes to zero. We have extended Watson’s method of proof to derive an asymptotic expression for the hypergeometric function to second order in the inverse of the first two parameters, with the ordinary Bessel function as its leading-order term. We show, as an example, that the use of this new result is pivotal in showing the correspondence between quantal and classical results of the differential cross section in Coulomb excitation.

Partial wave completion technique for scattering amplitudes in Coulomb dipole excitation

When a charged particle collides with an ion, the dominant contribution to the inelastic scattering amplitude may come from partial waves having large values of the angular momentum l of the colliding particle. It is important, when calculating the scattering amplitude by summing over l, to ensure that this contribution is taken into account since numerical truncation of the infinite sum can lead to unphysical oscillations in the angular distributions of the amplitude. We derive, in the case of Coulomb dipole transitions, an analytic expression for the contribution to the scattering amplitudes coming from partial waves with l greater than some prescribed value Λ. We make use of the Coulomb Bethe approximation to obtain this result.

Radiative data for allowed transitions in Ni XXV

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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.