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 $\hslash \omega =42\mathrm{}{A}^{-\frac{1}{3}}$ Mev for nuclear radius parameter $r_0=1.2\mathrm{}$. Combining this result with the integrated cross section, we find the bremsstrahlung-weighted cross section ${\sigma }_b=\int \left(\frac{\sigma }{W}\right)dW=0.36\mathrm{}{A}^{\frac{4}{3}}$ millibarns. The calculated ${\sigma }_b$ 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 $r_0:1.2\mathrm{} or 1.5$.