We evaluate the weak magnetism and other higher order matrix elements for the beta decays of ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$, and ${}_{}{}^{35}{}_{}{}^{}\mathrm{S}$. The matrix elements were obtained from $\mathrm{sd}$ shell-model wave functions derived from the one- and two-body effective interactions of Chung and Wildenthal. The shapes of the beta spectra are calculated assuming zero-mass neutrinos and allowing for the higher order matrix elements. The calculations suggest that precise measurements of these spectra would be useful to search for heavy neutrinos with intensities of the order of > ${10}^{-3\mathrm{}}$ over the neutrino mass range from 20 keV to 2 MeV. While other observations may rule out such parameters for mixing of massive neutrinos, the measurements of spectra would provide the most direct and least uncertain limits. For the allowed decays of ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ and ${}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$ the weak magnetism form factor appears to be the dominant higher order effect. The analog $M1\mathrm{}$ matrix elements are known experimentally in both cases and thus the weak magnetism terms are determined through the conserved vector current theory. One might alternatively regard measurements of these spectra as tests of the conserved vector current predictions.

RADIOACTIVITY ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{35}{}_{}{}^{}\mathrm{S}$; calculated nuclear matrix elements, shapes of beta spectra. Relationship to searches for heavy neutrinos.

• Received 4 October 1982

DOI:https://doi.org/10.1103/PhysRevC.27.1175