Dipole Transitions in the Nuclear Photo-Effect

Abstract

In this paper we apply sum rules to calculate under certain approximations the integrated cross section and the mean energy for photon absorption by heavy nuclei. In Section II we calculate the summed oscillator strength for dipole transitions as $\Sigma n^{}{f}_{\mathrm{on}}=\left(\frac{\mathrm{NZ}}{A}\right)(1+0.8x)\mathrm{}$ where $x$ is the fraction of attractive exchange force for the neutron-proton potential. For $N=Z$ this gives the cross section integrated over photon energy $\int 0^{\infty }\sigma \mathrm{dW}=0.015A(1+0.8x)\mathrm{}$ Mev-barns. In Section III we calculate the mean energy $\overline{W}$ for photon absorption. The mean energy is 4/3 the average kinetic energy of a nucleon for pure ordinary forces, or about 19 Mev; and is greatly increased by attractive exchange force. The harmonic mean energy $W_H=\frac{\Sigma \stackrel{}{n}{f}_{\mathrm{on}}}{\left[\frac{\Sigma \stackrel{}{n}{f}_{\mathrm{on}}}{(E_n-E_o)}\right]}$ is much too low using the model of uncorrelated nucleons, but is reasonable if we use the alpha-particle model of the nucleus. In Section IV we develop a sum rule for quadrupole transitions, and show that quadrupole transitions can account for only about six percent of the experimentally observed integrated cross section. In Section V we apply the sum rules for dipole transitions to the photo-disintegration of the deuteron, and compare the results from sum rules with those from direct calculations of the cross section. In Section VI we determine the asymptotic behavior of the cross section for dipole transitions at high photon energies. This is determined by the nature of the singularities in the neutron-proton potential. In the last section we discuss the G.E. experiments on the cross section for photo-disintegration, and its energy dependence, and find that our calculations explain the general features of the experiments. It is not necessary to assume the Goldhaber-Teller model of dipole vibrations by the entire nucleus.