Relativistic Electron Capture Research Articles

Second-order relativistic electron capture

Starting with the impulse approximation, we analyse second-order effects in relativistic electron capture. The relation of this model with relativistic distorted-wave approximations is clarified. In particular it is shown that the second-order spin-coupling terms in the RCDW theory are consistent with the correct form given by perturbation theory. In the semirelativistic limit, the RCDW results are shown to accord with the formulae of Moiseiwitsch for flip and nonflip transitions in the ultra-relativistic limit. This confirms that the continuum-distorted-wave model generalises to relativistic spinors, and highlights the defects of scalar models. We also present a new symmetric eikonal theory which gives reliable results for capture without change of spin, but leads to a divergent total cross section for spin-flip transitions in the second-order term. This effect, which is quite distinct from the spurious spin-flip amplitudes of the scalar symmetric eikonal theory, is taken as further evidence that the eikonal approximation is not valid for magnetic transitions.

Asymmetric theories of relativistic electron capture

New versions of the relativistic continuum-distorted-wave and eikonal models, in their asymmetric form, are presented. These models are characterized by a two-centre spinor which improves the description of intermediate scattering through continuum states. It is demonstrated that this is especially important for electron capture with spin-flip. Results are compared with experiment and with the conventional scalar distortion models. The agreement with experiment is good for total cross sections from inner shells for medium size charges and at GeV amu-1 energies. The suitability of the eikonal approximation for spin-flip processes and large momentum transfer is discussed.

Relativistic electron capture including inter nuclear interaction

Relativistic charge transfer cross sections for proton hydrogenic ion systems have been calculated using relativistic first Born approximation including inter nuclear interaction for the first time. Two processes 1) without spin flip, 2) with spin flip have been investigated in the energy range 10 to 50000 MeV/amu. Appreciable changes are found in the cross sections for both the processes when inter nuclear interaction is included.

Exact second-order Born calculations for relativistic electron capture.

Second-order Born cross sections for electron capture in relativistic collisions have been calculated without further approximations for a large number of projectile-target combinations and energies. Within the regime of high-Z target atoms and energies of a few GeV/u, the exactly evaluated cross sections are considerably larger than first-order cross sections, which already overestimate the experimental results. This shows that the Born expansion is not a suitable perturbation series in the charge and energy regime considered. At the same time it is demonstrated that previous evaluations using peaking approximations and \ensuremath{\alpha}Z expansions are in error by more than an order of magnitude. For p+H collisions the differential cross section exhibits a peak at the classical relativistic Thomas angle.

Second Born approximation for relativistic electron capture: Exact Monte Carlo calculations forC6+-Au andAr18+-Ag collisions

The second-order Oppenheimer-Brinkman-Kramers approximation for relativistic electron capture is formulated, and rigorously calculated K-K cross sections are presented for the first time. Theoretical cross sections for electron capture in collisions of ${\mathrm{C}}^{6+}$-Au at 400 MeV/u and ${\mathrm{Ar}}^{18+}$-Ag at 400 and 1050 MeV/u projectile energy are compared with the experimental data and other approximate second Born results. It is shown that exact second Born cross sections grossly overestimate the experimental data.

Continuum distorted-wave theory of relativistic electron capture

Electron capture between the ground states of highly charged ions travelling at relativistic velocities is investigated. By extending the non-relativistic continuum distorted-wave approximation to the relativistic regime the authors obtain results for total cross sections allowing for spin-flip transitions. These results are compared with first- and second-order plane-wave perturbation theory.

Third Born approximation for electron capture at relativistic energies

A relativistic generalisation of the third Born approximation is used to investigate the ground-state to ground-state capture of an electron from a hydrogenic ion A by a fully stripped positive ion B having atomic numbers ZA and ZB respectively. Formulae are obtained for the scattering amplitudes by expanding in powers of alpha ZA and alpha ZB and retaining the leading terms, alpha being the fine-structure constant. Closed analytical expressions for the relativistic electron capture cross sections for the cases without and with spin flip from the initial to the final states are derived making suitable approximations. In the limit of non-relativistic but high impact energies the authors obtain complete agreement with the electron capture cross section derived by Shakeshaft (1978) using the non-relativistic third Born approximation. At ultra-high relativistic impact energies E they find that the contributions to the total capture cross sections to leading order in alpha ZA and alpha ZB arising from the third Born correction terms fall off as E-4 and E-3 for the cases without and with spin flip respectively, which are both much more rapid than the E-1 decay obtained with the second Born approximation.