Anomalous Band Structure in Odd-Odd Nuclei with the Quadrupole-Quadrupole Interaction

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We perform shell model calculations in odd-odd nuclei using a quadrupole-quadrupole interaction and single-particle splittings chosen so as to obtain the SU(3) results. Elliott had shown that such an interaction gives rotational bands for which the energies go as I(I+1). This is certainly true for eve-even and for odd-even or even-odd nuclei with K≠ 1/2. We have looked at odd-odd nuclei e.g ²²Na and found somewhat different behaviour. In ²²Na the I=1+₁ T=0 and I=0+₁ T=1 states are degenerate, and a rotational band built on the I=0+₁ T=1 state behaves in a normal fashion. For the I+1+₁ T=0 band however, we find that the energy is given by E(I)-E(1+₁)=AI(I+1). This differs from the `normal' behaviour which would be E(I)-E(1+₁)=AI(I+1)-2A.