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We show that the existing and widely used results for an approximation to eikonal exchange amplitudes, which contain an indeterminate phase, are not valid. We derive a new analytic result, containing a well-defined phase, which can be used unambiguously with direct amplitudes to calculate full differential cross sections. The modulus of our result also differs from that of the previous formulations. Comparisons are made with the earlier ${e}^{\ensuremath{-}}$-H approximate exchange calculations and with exact eikonal exchange calculations.

Theoretical angular distributions for p-H charge transfer to the 1s state for energies of 1 keV and above have been examined and compared for three approximation schemes: the plane-wave Born approximation of Jackson and Schiff (JS), the Coulomb projected Born approximation of Geltman (G), and the distorted-wave eikonal approximation of one of the authors (D). The sharp dip in the forward distribution characteristic of JS is found to exist in G and D as well. As expected, G and D give identical results for all but the lowest energies. In the cases of G and D the dip, which is located close to that of JS, disappears and then reappears as the energy rises. Analytic high-energy limits for the angular dependence in both the JS and G cases have been found and are discussed.

The author has developed a technique for testing various charge-transfer approximation schemes for consistency with the requirements of the Kohn variational principle for the amplitude to guarantee that the amplitude is correct to second order in the scattering wave functions. Applied to Born-type approximations for charge transfer it allows the selection of particular groups of first-, second-, and higher-Born-type terms that obey the consistency requirement, and hence yield more reliable approximation to the amplitude.

We have calculated K-shell pickup cross sections using the full first Born approximation developed by Jackson and Schiff for a number of heavy-ion collisions for which experimental data have recently become available. These include protons on argon at a range of velocities and fully stripped ions Z = 1, 6, 7, 8, 9, on argon at three velocities. The calculations attempted to include the effect of screening by target electrons with a crude effective potential. We conclude that the full first Born charge-exchange cross section gives nonphysical results for the systems examined, thus casting further doubt on the theoretical significance of the good agreement with experiment one obtains for protons on hydrogen.

A detailed derivation of a first-order analytic approximation to the electron-hydrogen charge-exchange amplitude in both the Glauber approximation and eikonal approximmations in both post and prior forms is presented. The results are applicable to arbitrary initial states. The approximation is applied to elastic scattering by hydrogen in its ground state, and numerical results for both the modulus and phase of the exchange amplitude are obtained. the analytic approximation converges rapidly to the exact eikonal result with increasing energy. The techniques used in approximating the contribution to the exchange amplitude arising from the electron-nucleus part of the interaction potential are discussed in detail.

K-shell charge-transfer cross sections are calculated for swift fully stripped ions impinging on target atoms in a post-interaction distorted-wave formalism. The projectile interaction with the residual target atom is part of the unperturbed Hamiltonian and is approximated by its asymptotic form while the consequent projectile distortion is approximated by an eikonal wave function. The results are compared to experiment and to other theoretical calculations and are used to shed light on some aspects of the three-body Coulombic rearrangement process and in particular on the significance of asymptotic properties of interactions and wave functions on the results of simple approximation schemes. (AIP)

All of the ordinary hyperfine terms of the ${(p\ensuremath{\mu}p)}^{+}$, $L=1$, ortho, bound state, except for the muon-proton contact term, are evaluated to sufficient accuracy so that they would not mask a hyperfine discrepancy associated with proton structure effects. These and other pertinent contributions to the hyperfine structure are discussed in the light of recent interest in checking for a discrepancy in the hyperfine structure of a muon-proton system.

In obtaining the wave functions of three-body Coulomb systems in which two heavy equally charged, and one light oppositely charged, particles are involved, one can use a type of Born-Oppenheimer coupling scheme, to obtain nonadiabatic effects. In this paper we decompose the coupled differential equations of such a scheme in terms of the total orbital angular momentum and parity of the states, and reduce these equations to one-dimensional ones in a form suitable for calculation.

A first-order correction is presented to a previously derived zeroth-order approximate eikonal exchange amplitude for electron-hydrogen scattering and both the modulus and the phase are compared with those of the exact eikonal exchange amplitude for elastic scattering. The correction term dramatically improves the approximation, even at energies as low as 50 eV.