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

We perform shell model calculations in odd-odd nuclei using a quadrupolequadrupole interaction with 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 certainly is true for eveneven and for odd-even or even-odd nuclei with K 6= 1/2. We have looked at odd-odd nuclei e.g. Na and found somewhat different behaviour. In 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.