Structure of the nearly degenerate61+and62+states in48Ti

Abstract

The ${6}_{1}^{+}$ and ${6}_{2}^{+}$ in ${}^{48}\mathrm{Ti}$ form a nearly degenerate doublet. In single-j shell calculation with the matrix elements from experiment the ${6}_{1}^{+}$ changes sign under the interchange of protons and neutron holes (odd signature) while the ${6}_{2}^{+}$ does not (even signature). As a consequence the calculated $B(E2)$ ${6}_{1}^{+}\ensuremath{\rightarrow}{4}_{1}^{+}$ is much stronger than the ${6}_{2}^{+}\ensuremath{\rightarrow}{4}_{1}^{+}$ and the Gamow-Teller matrix element to the ${6}_{2}^{+}$ states vanishes. When using some popular interaction, e.g., FPD 6 in single-j shell the ordering of the even signature and odd signature states gets reversed, so that the Gamow-Teller matrix element to the ${6}_{1}^{+}$ state vanishes and the ${6}_{2}^{+}\ensuremath{\rightarrow}{4}_{1}^{+}$ $E2$ transition is the strong one. When configuration mixing is introduced, the $E2$ transition ${6}_{2}^{+}\ensuremath{\rightarrow}{4}_{1}^{+}$ persists in being large. However the Gamow-Teller strengths reverse, with the large matrix element to the ${6}_{1}^{+}$ state in agreement with experiment. Static properties $\ensuremath{\mu}$ and Q for the two ${6}^{+}$ states are also considered. The experimental $B(E2)\mathrm{'}\mathrm{s}$ from the ${6}^{+}$ states to the ${4}_{1}^{+}$ state are not well known.