Empirical Analysis of theH−Photodetachment Cross Section

Abstract

The zero-range photoelectric cross section of Bethe and Peierls, corrected according to effective range theory, is fitted to the ${\mathrm{H}}^{-}$ photodetachment cross section. The value of $2.64 a_0$ obtained for the effective range agrees with values obtained from the wave-function calculations of Schwartz, Burke and Schey, and others. A more accurate formula for the detachment cross section is obtained by allowing for distortion in the final $p$ state by means of an approximate formula for the phase shift. This formula agrees qualitatively with the close-coupling theory phase-shift results of Burke and Schey, and provides a photodetachment cross section that fits the experimental data slightly better than the results re cently obtained by Geltman with an elaborate variational treatment. There are two adjustable parameters: the binding energy, and one parameter in the phase-shift formula. By a slightly different choice of the parameters than is required to fit the experimental data, close agreement can also be obtained with the Geltman results.