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

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 ∝(gI-g₀)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 ∂E∂g=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 I≤16) 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)(2^'→2)B (E2)(2→0) and E₄E₂ is explored.