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 $B\left(E2\mathrm{}\right)\mathrm{}$ $6_1^{+}\to 4_1^{+}$ is much stronger than the $6_2^{+}\to 4_1^{+}$ 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 $6_2^{+}\to 4_1^{+}$ $E2\mathrm{}$ transition is the strong one. When configuration mixing is introduced, the $E2\mathrm{}$ transition $6_2^{+}\to 4_1^{+}$ 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 $\mu$ and Q for the two $6^{+}$ states are also considered. The experimental $B\left(E2\mathrm{}\right)\mathrm{}\mathrm{’}\mathrm{s}$ from the $6^{+}$ states to the $4_1^{+}$ state are not well known.

• Received 1 December 2000

DOI:https://doi.org/10.1103/PhysRevC.63.057301