Electric Dipole Ground-State Transition Width Strength Function and 7-Mev Photon Interactions

TLDR

The paper presents formulas showing how a Porter‑Thomas distribution of ground‑state transition widths affects photon–nucleus interactions, and gives an approximate expression for the average photon absorption cross section near 7 MeV. Reinterpreting data with these formulas yields photon‑interaction parameters that agree with neutron‑capture results and with a generalized giant‑dipole‑resonance extrapolation, leading to a ground‑state transition‑width strength function that deviates from the usual \(E^{2}A^{2/3}\) dependence and aligns better with experiments.

Abstract

Formulas are given which describe some significant effects that a Porter-Thomas distribution of ground-state transition widths would have on the interpretation of the nuclear interaction of photons which reach closely spaced, but separated energy levels. When these formulas are used to reinterpret existing data, the parameters implied by photon interaction become consistent with those resulting from neutron capture data.These compatible parameters are further shown to be consistent with a crude generalized extrapolation of the giant dipole resonance. At energies near 7 Mev, the average photon absorption cross section can be written approximately as $〈{\ensuremath{\sigma}}_{a}〉=5.2$ mb ${(\frac{E}{7}\mathrm{Mev})}^{3}$ ${(\frac{A}{100})}^{\frac{8}{3}}$. This extrapolation also implies a ground-state transition width strength function which does not have the ${E}^{2}{A}^{\frac{2}{3}}$ dependence usually used because of single-particle model predictions. Near 7 Mev, $\frac{〈{\ensuremath{\Gamma}}_{0}〉}{D}=2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ ${(\frac{E}{7} \mathrm{Mev})}^{5}$ ${(\frac{A}{100})}^{\frac{8}{3}}$; below 3 Mev, $\frac{〈{\ensuremath{\Gamma}}_{0}〉}{D}=6.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9} {(\frac{E}{1}\mathrm{Mev})}^{4} {(\frac{A}{100})}^{\frac{7}{3}}$. These estimates, while subject to refinements, are in better accord with experiments than are the more popular single-particle estimates.