Nucleonic Binding States in Nonspherical Nuclei: Asymptotic Representation

An alternative description is given for Nilsson's analysis of nucleonic motion in a strongly deformed nuclear field. The aim is to obtain the single-particle states for the region of strong deformation in terms of a representation which is especially suited for that region in contrast to the spherical representation used by Nilsson.The eigenvectors of a 3-dimensional anisotropic harmonic oscillator (H.O.) are used as a basic set to calculate the single-particle wave functions and energy eigenvalues. Two immediate advantages of choosing this basic set are: first, the matrix elements between single-particle states are expressible in terms of the rather simple analytic expressions obtained for these matrix elements in the H.O. representation and second, the expansion of the particle wave functions generally is rather pure, so that in many instances the leading term in the expansion is sufficient for calculations. Thus, good approximate calculations are easily obtainable. The high degree of purity of state has been taken advantage of previously by several authors to classify states in the strong-deformation region using the "almost good" quantum numbers of the basic set (asymptotic quantum numbers).Separate level spectra are given for protons and neutrons similar to the Mottleson and Nilsson scheme but more extensive (including some $N=7$ shell neutron levels). A large gap at neutron number 152 offers a partial explanation of the closing of a subshell there previously interpreted by Ghiorso et al. from α-decay curves.New approximate transition selection rules are given for allowed and first-forbidden β decay. For allowed transitions the relative speed varies approximately as 10^-|ΔNz|. For first forbidden transitions, relative speeds are tabulated as functions of ΔNᵣ. The latter transitions are generally cut down by a factor (10^-5-10^-3) for |ΔNᵣ|≥2.