ar X iv : n uc l - th / 0 30 40 31 v 1 9 A pr 2 00 3 Oblique - Basis Calculations for 44 Ti ∗

The spectrum and wave functions of 44 Ti are studied in oblique-basis calculations using spherical and SU(3) shell-model states. Although the results for 44 Ti are not as good as those previously reported for 24 Mg, due primarily to the strong spin-orbit interaction that generates significant splitting of the single-particle energies that breaks the SU(3) symmetry, a more careful quantitative analysis shows that the oblique-basis concept is still effective. In particular, a model space that includes a few SU(3) irreducible representations, namely, the leading irrep (12,0) and next to the leading irrep (10,1) including its spin S = 0 and 1 states, plus spherical shell-model configurations (SSMC) that have at least two valence nucleons confined to the f 7/2 orbit – the SM(2) states, provide results that are compatible with SSMC with at least one valence nucleon confined to the f 7/2 orbit – the SM(3) states. Introduction. In a previous study we demonstrated the feasibility of the oblique-basis calculations.[1] The successful description of 24 Mg followed from the comparable importance of single-particle excitations, described by spherical shell-model configurations (SSMC), and collective excitations, described by the SU(3) shell model. An important element of the success is that SU(3) is a good symmetry in sd-shell nuclei.[2] For the lower pf-shell nuclei, there is strong breaking of the SU(3) symmetry induced by the spin-orbit interaction.[3] Therefore, it is anticipated that adding the leading and next to the leading SU(3) irreps may not be sufficient in lower pf-shell. Here we discuss oblique-basis type calculations for 44 Ti using the KB3 interaction.[4] We confirm that the spherical shell model (SSM) provides a significant part of the low-energy wave functions within a relatively small number of SSMC while a pure SU(3) shell-model with only few SU(3) irreps is unsatisfactory. This is the opposite of the situation in the lower sd-shell. Since the SSM yields relatively good results for SM(2), combining the two basis sets yields even better