Structure of Ti44 and the Role of Single-Particle Energies and the T=0 Two-Body Interaction in the Development of Rotational Properties in Nuclei

The structure of low-lying states in $^{44}\mathrm{Ti}$ is studied in terms of a conventional shell model. The calculated spectrum is in reasonable agreement with available experimental information. The results of the "exact" shell-model calculation are compared with calculations of the $^{44}\mathrm{Ti}$ spectrum in terms of the stretch scheme and the deformed Hartree-Fock with projection scheme. We find that these two approximations are not in good agreement with the exact calculation. We study the effects on the calculated spectrum of varying the single-particle energy spectrum. We find that the "rotational" character of the calculated spectrum is sensitive to the single-particle energies. The sensitivity can be accounted for by assuming that the wave functions of the members of a rotational band are projections from an intrinsic state with a strong quadrupole deformation. The effect of the $T=0$ part of the residual interaction, and of the Pauli principle, on the rotational character of the calculated spectrum of low-lying states is discussed.