Effect of Long-Range Final-State Forces on the Negative-Ion Photodetachment Cross Section near Threshold

The accepted threshold law for the photodetachment cross section may be written as $\sigma =\mathrm{const}{k}^{2l_0+1\mathrm{}}[1+\mathrm{O}(k^2\left)\right]$, where $l_0$ is the lowest value of the angular momentum allowed the electron and $k$ is its momentum. This law presupposes that the forces in the final state are of finite range. In the present work, the effect of the long-range ($r^{-3\mathrm{}}$ and $r^{-4\mathrm{}}$) multipole forces between the residual neutral atom and the outgoing electron on the threshold behavior is investigated. It is found that the behavior of the total cross section is changed to $\sigma =\mathrm{const}{k}^{2l_0+1\mathrm{}}[1+C{k}^2\ln k+\mathrm{O}(k^2\left)\right]$, where the coefficient $C$ is determined entirely by the long-range force. The effect of an $r^{-2\mathrm{}}$ potential is also found. In this case, even the leading term is altered from the standard form.