The isovector quadrupole-quadrupole interaction used in shell model calculations

Abstract

The interaction − χ Q · Q(1 + Bτ(1) · τ(2)) is used in a shell model calculation for 10Be. 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.