Charge-transfer cross sections in collisions of ground-state Ca andH+

Abstract

We have investigated collisions of $\mathrm{Ca}(4{s}^{2})$ with ${\mathrm{H}}^{+}$ in the energy range of $200\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{u}\ensuremath{-}10\phantom{\rule{0.3em}{0ex}}\mathrm{keV}∕\mathrm{u}$ using the semiclassical molecular-orbital close-coupling (MOCC) method with 18 coupled molecular states ($11\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ and seven $^{1}\ensuremath{\Pi}^{+}$ states) to determine charge-transfer cross sections. Except for the incoming channel $6\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$, the molecular states all correspond to charge-transfer channels. Inclusion of ${\mathrm{Ca}}^{2+}\text{\ensuremath{-}}{\mathrm{H}}^{\ensuremath{-}}$ is crucial in the configuration-interaction calculation for generating the molecular wave functions and potentials. Because of the Coulomb attraction, the state separating to ${\mathrm{Ca}}^{2+}\text{\ensuremath{-}}{\mathrm{H}}^{\ensuremath{-}}$ creates many avoided crossings, even though at infinite separation it lies energetically above all other states that we included. Because of the avoided crossings between the incoming channel $6\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ and the energetically close charge-transfer channel $7\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ the charge-transfer interaction occurs at long range. This makes calculations of charge-transfer cross sections by the MOCC method very challenging. The total charge-transfer cross sections increase monotonically from $3.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$ at $200\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{u}$ to $4.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$ at $10\phantom{\rule{0.3em}{0ex}}\mathrm{keV}∕\mathrm{u}$. Charge transfer occurs mostly to the excited ${\mathrm{Ca}}^{+}(5p)$ state in the entire energy range, which is the sum of the charge transfer to $7\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ and $4\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}^{+}$. It accounts for $\ensuremath{\sim}47%$ of the total charge transfer cross sections at $200\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{u}$. However, as the energy increases, transfer to ${\mathrm{Ca}}^{+}(4d)$ increases, and at $10\phantom{\rule{0.3em}{0ex}}\mathrm{keV}∕\mathrm{u}$ the charge-transfer cross sections for ${\mathrm{Ca}}^{+}(5p)$ and ${\mathrm{Ca}}^{+}(4d)$ become comparable, each giving $\ensuremath{\sim}38%$ of the total cross section.