Photodisintegration of Helium

Abstract

In this paper, we extend the sum-rule calculations of Levinger and Bethe to include two-body Heisenberg and tensor forces. We apply these sum rules to calculate for the alpha particle the bremsstrahlung-weighted cross section (${\ensuremath{\sigma}}_{b}$) and the integrated cross section (${\ensuremath{\sigma}}_{\mathrm{int}}$) using Irving's wave function for tensor force. We compare our results with values found from experiments integrated to 150 Mev. The experimental values are ${\ensuremath{\sigma}}_{b}=2.7$ mb and ${\ensuremath{\sigma}}_{\mathrm{int}}=124$ Mev-mb, while the theoretical values are found to be ${\ensuremath{\sigma}}_{b}=1.23$ mb and ${\ensuremath{\sigma}}_{\mathrm{int}}=60[1+0.70(x+\frac{1}{2}y)+0.18({x}^{\ensuremath{'}}+\frac{1}{2}{y}^{\ensuremath{'}})]$ Mev-mb. Here $x$ and ${x}^{\ensuremath{'}}$ are the fractions of central and tensor potentials, respectively, that have Majorana exchange character; $y$ and ${y}^{\ensuremath{'}}$ represent fractions of the central and tensor potentials that have Heisenberg exchange character. The low theoretical values for ${\ensuremath{\sigma}}_{b}$ may be related to the small root-mean-square radius of the alpha particle given by Irving's wave function. The photodisintegration experiments seem to support Hofstadter's value for the size of the alpha particle, when one takes account of the proton size in his electron-scattering experiments.