Probe of the shell crossing at A=40 via beta decay: Experiment and theory

The ${\beta }^{\mathrm{-}}$ decays of ${}_{}{}^{35}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{37}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{S}$, and ${}_{}{}^{38}{}_{}{}^{}\mathrm{Cl}$ were studied both experimentally and via shell-model calculations. The four decaying nuclei were formed by bombardment of 81% enriched ${}_{}{}^{36}{}_{}{}^{}\mathrm{S}$ by triton and deuteron beams. Gamma-ray spectroscopy was carried out with Ge detectors, either bare or surrounded by a Compton suppression NaI(Tl) shield. One new Gamow-Teller decay was observed in ${}_{}{}^{35}{}_{}{}^{}\mathrm{P}$ decay, and one new first-forbidden decay was observed in ${}_{}{}^{38}{}_{}{}^{}\mathrm{S}$ decay. Otherwise γ-ray measurements of $E_{\gamma }$ and $I_{\gamma }$ (and limits on $I_{\gamma }$ for unobserved transitions) were improved significantly over previous results. Shell-model studies were undertaken in order to bring these beta decay results to bear on an understanding of the shell structure in the (sd) to (fp) transition region at A=40. An interaction was constructed in the 1$d_{5/2}$, 1$d_{3/2}$, 2$s_{1/2}$, 1$f_{7/2}$, 1$f_{5/2}$, 1$p_{3/2}$, 1$p_{1/2}$ model space. This interaction started from the Wildenthal ‘‘USD’’ (sd) interaction and the van Hees-Glaudemans (fp) interaction, which were connected by the cross-shell Millener-Kurath interaction. Certain important two-body matrix elements and single-particle energies were adjusted to fit experimental binding energies in A=40, 41, 42. This interaction was then used to calculate level spectra for the daughter nuclei ${}_{}{}^{35}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Cl}$, and ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}$ as well as Gamow-Teller and unique first-forbidden beta decays leading to these nuclei. The techniques used in these relatively large scale calculations are discussed in detail, as are the results.