R -matrix approach to collision processes: Study of the threshold behavior of γ + He → He +(2s)+e− or He +(2p)+e−

Abstract

We report on a study of one-photon single ionization of He($1{s}^{2}$) accompanied by excitation to He${}^{+}(2s)$ or He${}^{+}(2p)$ for photon energies at, and up to a few eV above, the excitation threshold. We find, both numerically and analytically, that as the photon energy approaches threshold from above the photoionization cross section turns sharply at about 200 meV and has a cusp at threshold. The cusp is associated with the adiabatic transfer of population between the $2s$ and $2p$ bound states of the ion. The photoelectron's electric field induces an energy splitting between the otherwise degenerate $2s$ and $2p$ states, and consequently the $2s$ and $2p$ populations oscillate with a period defined by this energy splitting. The number of oscillations is almost independent of the photoelectron's asymptotic speed $v$ since over most of its outward journey the photoelectron moves with a speed much larger than $v$. However, on the last leg of its journey, after it has slowed down sufficiently in the Coulomb field of the ion, the photoelectron does move with an almost constant speed $v$. On this last leg the energy splitting is so small that there is insufficient time for $2s$ and $2p$ populations to undergo a full oscillation; rather, the (equal and opposite) changes in the $2s$ and $2p$ populations are proportional to $v$ (i.e., to the square root of the excess photoelectron energy, which gives rise to a cusp).