The Original Mixed Symmetry States - 6^{+}_{1} and 6^{+}_{2} in ^{48}Ti
Abstract
The 6^{+}_{1} and 6^{+}_{2} in ^{48}Ti form a nearly degenerate doublet. In a 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}^{+}\to 4_{1}^{+} is much stronger than the 6_{2}^{+}\to 4_{1}^{+} and the Gamow-Teller matrix element to the 6_{2}^{+} state vanishes. When using some popular interaction e.g. FPD6 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 transition is the strong one. When configuration mixing is introduced, the E2 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(E2)'s from the 6^{+} states to the 4_{1}^{+} state are not well known.