The Isovector Quadrupole-Quadrupole Interaction Used in Shell Model Calculations
arXiv:nucl-th/9506019 · doi:10.1016/0370-2693(95)00899-V
Abstract
An interaction $-ÏQ\cdot Q(1+B\vecÏ(1)\cdot \vecÏ(2))$ 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 $S=1~L=1$ 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.
12 pages, revtex, 2 figures (available on request)