Rotational bands in nuclei as induced group representations

Abstract

A one-to-one correspondence between all constant deformation rotational bands in nuclei and the set of all unitary irreducible representations of the symmetry group T 5 ⊚ SU2 is successfully made. The physical observables corresponding to the generators of this noncompact symmetry group are the angular momentum operator j and the traceless mass quadrupole moment operator q. Three types of band structure are found: α bands, having zero quadrupole moment, and a single j value; β bands (three kinds: β | k| a and β 0, ± a ) representing axial nuclei; and γ bands (five kinds: γ ±,± a, b and γ τ a, b ) representing nonaxial deformed nuclei. The fifth γ-band type, γ τ [ sua, b], is especially interesting in that it has, intrinsically, half-integer angular momenta; this band, in particular, has not been obtained previously as an elementary structure. Properties of these bands (representations) are discussed in detail. It is noteworthy that all irreps of this symmetry group ( T 5 ⊚ SU2 ) find physically occurring counterparts, and, conversely, no known rotational band system fails to find an associated irrep structure.