($\Delta I$=2)-staggering and Possible Manifestations of Nuclear Symmetries

Another group of subjects strongly related in particular to the SD bands, concerns the often discussed, but not satisfactorily documented, problem of the so-called ($\Delta I$=2)-staggering. This effect, claimed to exist in some SD bands, corresponds to an up-ward (down-ward) shift of states with spins I = I₀, I = I₀+4, I = I₀+8 etc. with respect to the rotor-type average [E $\sim$ I(I+1)], and a down-ward (up-ward) shift of the states with spins I = I₀ +2, I = I₀+6, I = I₀+10 etc., with respect to the same average. This problem is related more generally to the question of possible systematic deviations in rotational bands from the rotor-type behaviour - deviations that may signify new, specific point group symmetries as proposed e.g. by I. Hamamoto and B. Mottelson.

We would like to study the problem of the ($\Delta I$=2)-staggering and other possible forms of deviations from the usual, regular rotational pattern in super- and hyper-deformed nuclei. It was shown that the nuclear average field theory both non-selfconsistent (see the former reference) and the self-consistent Hartree-Fock (the latter one) do not support the idea of the C₄-symmetry as a possible origin of the ($\Delta I$=2)-staggering at least in the A $\sim$ 150 superdeformed nuclei. We would like to study other mechanisms that may produce either regular (cyclic) or irregular deviations from the "rigid-rotor" behaviour. We would also like to correlate possible intrinsic symmetries with the precise forms of those deviations. Both studies will be done by using the model hamiltonians expressed as expansions in terms of the nuclear angular momentum operators ( $\hat{I}{_x}$, $\hat{I}{_y}$, $\hat{I}{_z}$).

Another aspect related to the C₄-symmetry hypothesis (and even if this particular symmetry does not hold in the nuclei considered today) can be studied by using the microscopic model hamiltonians containing explicitly the two-body nucleon-nucleon interactions but in this case solved within the limited many-body bases. The "exactly" soluble models of this type have on some occasions been employed within e.g. single j-shell spaces employing the standard multipole-multipole and pairing type interactions. We would like to apply this technique with suitably selected model nucleon-nucleon forces (hexadecapole-hexadecapole components to start with) in order to examine in detail the possible scenarios of the perturbations in the rotor spectra in function of the intrinsic symmetry of the hamiltonian.