Differential and total cross sections of mutual neutralization in low-energy collisions of isotopes ofH++H−

Abstract

Mutual neutralization in the collisions of ${\mathrm{H}}^{+}$ and ${\mathrm{H}}^{\ensuremath{-}}$ is studied both theoretically and experimentally. The quantum-mechanical ab initio model includes covalent states associated with the $\mathrm{H}(1)+\mathrm{H}(n\ensuremath{\le}3)$ limits and the collision energy ranges from 1 meV to 100 eV. The reaction is theoretically studied for collisions between different isotopes of the hydrogen ions. From the partial wave scattering amplitude, the differential and total cross sections are computed. The differential cross section is analyzed in terms of forward- and backward-scattering events, showing a dominance of backward scattering which can be understood by examining the phase of the scattering amplitudes for the gerade and ungerade set of states. The isotope dependence of the total cross section is compared with the one obtained using a semiclassical multistate Landau-Zener model. The final state distribution analysis emphasizes the dominance of the $n=3$ channel for collisions below 10 eV, while at higher collision energies, the $n=2$ channel starts to become important. For collisions of ions forming a molecular system with a larger reduced mass, the $n=2$ channel starts to dominate at lower energies. Using a merged ion-beam apparatus, the branching ratios for mutual neutralization in ${\mathrm{H}}^{+}$ and ${\mathrm{H}}^{\ensuremath{-}}$ collisions in the energy range from 11 to 185 eV are measured with position- and time-sensitive particle detectors. The measured and calculated branching ratios satisfactorily agree with respect to state contributions.