The Original Mixed Symmetry States - 6⁺₁ and 6⁺₂ in ⁴⁸Ti

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The 6⁺₁ and 6⁺₂ in ⁴⁸Ti 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 6₂⁺ does not (even signature). As a consequence the calculated B(E2) 6₁⁺→ 4₁⁺ is much stronger than the 6₂⁺→ 4₁⁺ and the Gamow-Teller matrix element to the 6₂⁺ 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 6₂⁺→ 4₁⁺ E2 transition is the strong one. When configuration mixing is introduced, the E2 transition 6₂⁺→ 4₁⁺ persists in being large. However the Gamow-Teller strengths reverse, with the large matrix element to the 6₁⁺ state in agreement with experiment. Static properties μ and Q for the two 6⁺ states are also considered. The experimental B(E2)'s from the 6⁺ states to the 4₁⁺ state are not well known.