Independent-Particle Model and the Nuclear Photoeffect. II

Abstract

A simple harmonic oscillator independent-particle model is used for sum-rule calculation of electric dipole transitions in the nuclear photoeffect. First we find the level spacing $\ensuremath{\hbar}\ensuremath{\omega}=42{A}^{\ensuremath{-}\frac{1}{3}}$ Mev for nuclear radius parameter ${r}_{0}=1.2$. Combining this result with the integrated cross section, we find the bremsstrahlung-weighted cross section ${\ensuremath{\sigma}}_{b}=\ensuremath{\int}(\frac{\ensuremath{\sigma}}{W})dW=0.36{A}^{\frac{4}{3}}$ millibarns. The calculated ${\ensuremath{\sigma}}_{b}$ is not inconsistent with a preliminary analysis of experimental measurements for He, Be, C, Al, Cu, Mo, Ag, Ta, Pb, and U. We also use the simple harmonic oscillator independent-particle model to calculate the increase in the integrated cross section due to neutron-proton exchange forces. We find that the relative increase is not far from the Levinger-Bethe value of $0.8x$ (where $x$ is the fraction of exchange force) for the closed-shell nuclei ${\mathrm{He}}^{4}$, ${\mathrm{O}}^{16}$, and ${\mathrm{Ca}}^{40}$, for both Gaussian and Yukawa neutron-proton potentials, and for two values of the radius parameter ${r}_{0}:1.2 or 1.5$.