Oblique-Basis Calculations for $^{44}$Ti

Abstract

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.