Mixed-mode shell-model calculations

A one-dimensional harmonic oscillator in a box is used to introduce the oblique-basis concept. The method is extended to the nuclear shell model by combining traditional spherical states, which yield a diagonal representation of the usual single-particle interaction, with collective conpoundgurations that track deformation. An application to Mg-24, using the realistic two-body interaction of Wildenthal, is used to explore the validity of this mixed-mode shell-model scheme. Specipoundcally, the correct binding energy (within 2% of the fall-space result) as well as low-energy conpoundgurations that have greater than 90% overlap with full-space results are obtained in a space that spans less than 10% of the full-space. The theory is also applied to lower pf-shell nuclei, Ti44-48 and Cr-48. using the Kuo-Brown-3 interaction. These nuclei show strong SU(3) symmetry breaking due mainly to the single-particle spin-orbit splitting. Nevertheless, the results also show that yrast band B(E2) values are insensitive to fragmentation of the SU(3) symmetry. Specipoundcally, the quadrupole collectivity as measured by B(E2) strengths remains high even though the SU(3) symmetry is rather badly broken. The IBM and broken-pair models are considered as alternative basis sets for future oblique-basis shell-model calculations.