Effects of Delta -isobar degrees of freedom on low-energy electroweak transitions in few-body nuclei.

Abstract

Variational wave functions with \ensuremath{\Delta}-isobar components are used to study trinucleon magnetic moments, the Gamow-Teller matrix element of tritium \ensuremath{\beta} decay, thermal neutron radiative capture on $^{3}\mathrm{He}$, and low-energy proton weak capture on $^{3}\mathrm{He}$. The \ensuremath{\Delta}-isobar components are generated by transition correlation operators acting on realistic nuclear wave functions. These correlations are obtained from a fit to exact two-body ground-state and low-energy scattering solutions for the Argonne ${\mathit{v}}_{28}$ and ${\mathit{v}}_{28\mathit{Q}}$ interaction models, which include \ensuremath{\Delta}-isobar degrees of freedom. Contributions of \ensuremath{\Delta} isobars to electroweak current operators appear at the one-body level in this formalism. Their effect on low-energy electroweak transitions is significantly smaller than that obtained in perturbation theory analyses, where \ensuremath{\Delta}-isobar effects are commonly subsumed into effective two-body current operators. The resulting theoretical cross section for thermal neutron radiative capture on $^{3}\mathrm{He}$ is \ensuremath{\approxeq}86 \ensuremath{\mu}b, compared to an experimental value of 55\ifmmode\pm\else\textpm\fi{}3 \ensuremath{\mu}b; the astrophysical S factor for proton weak capture on $^{3}\mathrm{He}$ is predicted to be in the range (1.4--3.2)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}23}$ MeV b.