Asymmetric rotator model of odd-mass nuclei

Abstract

The asymmetric rotator model of Dadydov and Filippov has been extended to odd-mass nuclei by coupling a single nucleon to an inert core of well stabilized asymmetric equilibrium shape. Rotational energies are calculated for states with spin I through numerical diagonalization of ( I + 1/2) × ( I + 1/2) rotational matrices which depend in a complicated way on the state of the odd nucleon. The state of the odd nucleon is described by single particle wave functions such as those calculated by Newton, generalizations for the asymmetric case of the wave functions computed by Nilsson for axially symmetric nuclei. The rotational energy spectrum for a given particle excitation is in general very rich in number of levels and may consist of a complicated sequence of spin values. In many cases, however, particularly for small asymmetries, the rotational spectra may consist of several well separated or overlapping sequences of spin states which resemble the rotational bands of axially symmetric nuclei, especially insofar as K (which gives the projection of I on the body-fixed z-axis) may be approximately a good quantum number for each sequence. In an initial survey of odd-mass nuclei around A = 190, no clear-cut evidence has been found for the existence of nuclei with a well defined asymmetric equilibrium shape. Calculations for Ir 191 and Re 185 indicate only that it may be very difficult to distinguish between a symmetric and an asymmetric rotator model when the asymmetry is small. Calculations for Pt 195 show that, although the observed level scheme can be reproduced by asymmetric rotator theory, the observed electromagnetic transition probabilities are not in agreement with the predictions of the simple asymmetric rotator model.