Isospin mixing in37K and spin decomposition of Gamow-Teller strength in37Ca decay

Abstract

We measured ${}^{36}$Ar$(p\ensuremath{\rightarrow}{,p}_{0})$ cross sections and analyzing powers for ${E}_{p}$ between 3.22 and 5.98 MeV, and used these data to deduce spin, parity, and widths of 17 levels in ${}^{37}$K. Our results, combined with existing information on ${}^{37}$Ca ${\ensuremath{\beta}}^{+}$ decay, yield information on the distribution of Fermi and Gamow-Teller strength in this decay. A $T=1/2$ level lying 31 keV below the ${J}^{\ensuremath{\pi}}{=3/2}^{+}$, $T=3/2$ analog of the ${}^{37}$Ca ground state was found to have ${J}^{\ensuremath{\pi}}{=3/2}^{+}$. The relative proton widths of the two levels imply an isospin-mixing matrix-element of $4.84\ifmmode\pm\else\textpm\fi{}0.43$ keV. This agrees with the value ${5.93}_{\ensuremath{-}0.65}^{+0.23}$ keV extracted from the ${\ensuremath{\beta}}^{+}$-decay intensities to the two levels, plus the Gamow-Teller to Fermi strength ratio for the 5018 keV level. We decompose the Gamow-Teller strength in ${}^{37}$Ca decay into components feeding daughter levels with ${J}^{\ensuremath{\pi}}{=1/2}^{+}$, ${3/2}^{+}$, or ${5/2}^{+}$, and compare the results to theory. None of the available shell-model calculations gives a satisfactory account of the data.