Isospin symmetry ofTz=±3∕2→±1∕2Gamow-Teller transitions inA=41nuclei

Abstract

Under the assumption that isospin $T$ is a good quantum number, isobaric analog states and various analogous transitions are expected in isobars with mass number $A$. The strengths of ${T}_{z}=\ifmmode\pm\else\textpm\fi{}3∕2\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}1∕2$ analogous Gamow-Teller (GT) transitions and analogous $M1$ transitions within the $A=41$ isobar quartet are compared in detail. The ${T}_{z}=+3∕2\ensuremath{\rightarrow}+1∕2$ GT transitions from the ${J}^{\ensuremath{\pi}}={3∕2}^{+}$ ground state of $^{41}\mathrm{K}$ leading to excited ${J}^{\ensuremath{\pi}}={1∕2}^{+}$, ${3∕2}^{+}$, and ${5∕2}^{+}$ states in $^{41}\mathrm{Ca}$ were measured using the $(^{3}\mathrm{He},t)$ charge-exchange reaction. With a high energy resolution of $35\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$, many fragmented states were observed, and the GT strength distribution was determined up to $10\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ excitation energy $({E}_{x})$. The main part of the strength was concentrated in the ${E}_{x}=4--6\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ region. A shell-model calculation could reproduce the concentration, but not so well details of the strength distribution. The obtained distribution was further compared with two results of $^{41}\mathrm{Ti}$ $\ensuremath{\beta}$ decay studying the analogous ${T}_{z}=\ensuremath{-}3∕2\ensuremath{\rightarrow}\ensuremath{-}1∕2$ GT strengths. They reported contradicting distributions. One-to-one correspondences of analogous transitions and analog states were assigned up to ${E}_{x}=6\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ in the comparison with one of these $^{41}\mathrm{Ti}$ $\ensuremath{\beta}$-decay results. Combining the spectroscopic information of the analog states in $^{41}\mathrm{Ca}$ and $^{41}\mathrm{Sc}$, the most probable ${J}^{\ensuremath{\pi}}$ values were deduced for each pair of analog states. It was found that ${5∕2}^{+}$ states carry the main part of the observed GT strength, while much less GT strength was carried by ${1∕2}^{+}$ and ${3∕2}^{+}$ states. The gross features of the GT strength distributions for each $J$ were similar for the isospin analogous ${T}_{z}=\ifmmode\pm\else\textpm\fi{}3∕2\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}1∕2$ transitions, but the details were somewhat different. From the difference of the distributions, isospin-asymmetry matrix elements of $\ensuremath{\approx}8\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ were deduced. The Coulomb displacement energy, which is sensitive to the configuration of states, showed a sudden increase of about $50\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ at the excitation energy of $3.8\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$. The strengths of several $M1$ transitions to the IAS in $^{41}\mathrm{Ca}$ were compared with the strengths of analogous GT transitions. It was found that ratios of the $M1$ and GT transition strengths were similar, suggesting that the contributions of the $\ensuremath{\ell}\ensuremath{\tau}$ term in $M1$ transitions are small.