Three-body boundary-corrected continuum-intermediate-state method for single charge exchange with the general transition amplitude (1s→nlm) applied to the p–H(1s), α–H(1s), and p–He(1s2) collisions with n≤4

Abstract

We derive a general quantum-mechanical transition amplitude in the prior version of the three-body boundary-corrected continuum-intermediate-state (BCIS-3B) method for single charge exchange in collisions of heavy nuclei with atomic hydrogenlike targets. The obtained expression is valid for all the transitions from the initial ground to any final hydrogenlike bound states $(1s\ensuremath{\rightarrow}nlm),$ where ${n,l,m}$ is the usual triple of the quantum numbers (principal, angular, magnetic). The outcome is semianalytical: a judicious combination of an analytical calculation (as far as feasible) and the subsequent numerical computations (quadrature for integrals that could not be reduced to closed formulas). The final results for the $T$-matrix elements are a compact double integration computed by numerical quadratures over real variables in finite intervals. The ensuing total cross section is a single numerical quadrature of the squared absolute value of this transition amplitude integrated over the magnitude of the transverse momentum transfer vector. This can provide detailed information on the cross sections for each individual subshell ${n,l,m}$ of the newly formed hydrogenlike atom or ion comprised of a projectile nucleus and the captured electron. Using these general expressions, we computed a large number of state-selective and state-summed cross sections (both differential and total) for electron capture in the $p\text{\ensuremath{-}}\mathrm{H}$, $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{H}$, and $p\text{\ensuremath{-}}\mathrm{He}$ collisions at intermediate and high impact energies. The energy dependence of the cross sections for the individual shells and their subshells with the fixed quantum numbers $n$, ${n,l}$, and ${n,l,m}$ are reported via detailed tables and figures. Also, differential cross sections (state selective and summed) are computed for the $p\text{\ensuremath{-}}\mathrm{H}$ collisions at 60, 125, and 5000 keV. All the present results from the BCIS-3B method are found to be in very good agreement with the existing experimental data on differential and total cross sections, both state selective (whenever available) and state summed. The provided cross-section database can find important applications in several investigative fields ranging from plasma physics, astrophysics, and heavy-ion transport physics through fusion research and technology to hadron therapy.