Phenomenological Analysis of Ground-State Bands in Even-Even Nuclei

Abstract
A variable-moment-of-inertia (VMI) model is proposed which permits an excellent fit of level energies of ground-state bands in even-even nuclei. In this model the energy of a level with angular momentum I is given by the sum of a potential energy term (gIg0)2 (where g0 is the ground-state moment of inertia) and a rotational energy term 2I(I+1)2gI. It is required that the equilibrium condition Eg=0 be satisfied for each state. Each nucleus is described by two adjustable parameters, g0 and σ (the softness parameter), which are determined by a least-squares fit of all known levels. The calculated level energies and moments of inertia gI, g0, and σ are tabulated for 88 bands, ranging from Pd to Pt and from Th to Cm. Projections of three-dimensional arrays of g0 and σ on the (N,Z) plane are shown. These parameters are found to vary smoothly as function of N and Z. Breaks occur at N=98, 104, and 108. The osmium nuclei show a pronounced maximum for g0 and an equally pronounced minimum for σ at 108 neutrons. In Pt, g0 decreases steeply to 110 neutrons and then more slowly, while σ increases correspondingly. The stable Pt nuclei with A=190,192, and 194 still possess appreciable moments of inertia and large but "finite" softness parameters. Hence they may be characterized as "pseudospherical." For nuclei exhibiting a near-harmonic level pattern (like Xe130, Sm150, and other neutron-deficient rare-earth isotopes), g0 becomes exceedingly small, but already for the 2+ state g is several orders of magnitude larger. The parameters of some K=2 bands in even-even nuclei and of bands found in odd-odd nuclei are related to those of appropriate ground-state bands in even-even nuclei. Evidence for a rotational band in Ir194 is deduced from recently published experimental results. A plot of E4E2 versus A, presented for the discussion of the region of validity of the model, namely, 2.23<E4E2<3.33, reveals new regularities. The empirical "Mallmann curves" (EIE2 plotted versus E4E2) are deduced from the VMI model within its region of validity. Graphs are presented which allow the determination of EI (for I16) and of σ and g0 for each even-even nucleus for which the first 2+ and 4+ states are known. The model suggested by Harris, which includes the next-higher-order correction of the cranking model, is shown to be mathematically equivalent to the VMI model. The recently discovered appreciable quadrupole moments of 2+ states of "spherical nuclei" are compatible with the moments of inertia of these states given by the VMI model. The relation between B (E2)(22)B (E2)(20) and E4E2 is explored.