Shapes of theN16andC15beta spectra and extraction of matrix elements forC15(β−)N15(g.s.)

The ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{15}{}_{}{}^{}\mathrm{C}$ spectra measured by Alburger, Gallmann, and Wilkinson were reanalyzed to obtain more accurate branching ratios as well as a shape factor for the first-forbidden, nonunique ${}_{}{}^{15}{}_{}{}^{}\mathrm{C}\left({\frac{1}{2}}^{+}\right)\to {}_{}{}^{15}{}_{}{}^{}\mathrm{N}\left({\frac{1}{2}}^{-}\right)$ decay. ${}_{}{}^{16}{}_{}{}^{}\mathrm{N} {\beta }^{-}$ branches were derived to the levels at 0 and 6.13 MeV of 27.9(5)% and 66.3(6)%, respectively; ${}_{}{}^{15}{}_{}{}^{}\mathrm{C} {\beta }^{-}$ branches were found to ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ levels at 0 and 5.30 MeV of 36.8(8)% and 63.2(8)%, respectively. The ${}_{}{}^{15}{}_{}{}^{}\mathrm{C}$ shape factor was found to deviate significantly from the allowed shape. Analysis of the shape factor results in the determination of the rank zero component of the transition and determination of the two independent matrix elements which contribute to the rank one component. The possible role of muon capture in determining the rank zero matrix elements is considered. Comparisons, for both the ${}_{}{}^{15}{}_{}{}^{}\mathrm{C}\left({\frac{1}{2}}^{+}\right)\to {}_{}{}^{15}{}_{}{}^{}\mathrm{N}\left({\frac{1}{2}}^{-}\right)$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}\left(0^{-}\right)\to {}_{}{}^{16}{}_{}{}^{}\mathrm{O}\left(0^{+}\right)$ transitions, are made to shell-model calculations with particular emphasis on the sensitivity of the nuclear matrix elements to the choice of the single particle wave function. It is found that rank zero rates calculated with Woods-Saxon wave functions are much smaller than those calculated with harmonic oscillator wave functions. Possible meson-exchange contributions to the rank zero rates are discussed in light of this finding.