The Isovector Quadrupole-Quadrupole Interaction Used in Shell Model Calculations

Abstract

An interaction $-\chi Q\cdot Q(1+B\vec{\tau }(1)\cdot \vec{\tau }(2))$ is used in a shell model calculation for ${}^{10}Be$. Whereas for $B=0$ the $2_1^{+}$ state is two-fold degenerate, introducing a negative $B$ causes an `isovector' $2^{+}$ state to come down to zero energy at $B=-0.67$ and an $S=1L=1$ triplet ($J=0^{+},1^{+},2^{+}$) to come down to zero energy at $B=-0.73$. These are undesirable properties, but a large negative $B$ is apparently needed to fit the energy of the isovector giant quadrupole resonance.

Comments: 12 pages, revtex, 2 figures (available on request)