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

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

1998-06-23

arxiv.org/abs/nucl-th/9806072v2

Physics

Nuclear Physics

Nuclear Theory

Scientific paper

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 $K\neq 1/2$. We have looked at odd-odd nuclei e.g $^{22}Na$ and found somewhat different behaviour. In $^{22}Na$ 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 $E(I)-E(1^+_1)=AI(I+1)-2A$.

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