Intermediate coupling in the asymmetric rotator model

Abstract

The asymmetric rotator model of Davydov and Filippov for maximum asymmetry ( γ = 30°) has been extended to odd-mass nuclei by coupling the odd nucleon to the deformed equilibrium shape of the even-mass nucleat core. Intermediate coupling is considered where the odd nucleon has available to it s 1 2 and d 3 2 single particle states. It is shown that the interaction matrix elements connecting the 0 + ground state and 2 + first excited state of the even-mass core are identical with those obtained with the vibrational model. Hence for weak or intermediate coupling, there is little difference between the asymmetric rotator model and the vibrational model. As the coupling becomes strong, it is practical to follow the transition to the strong coupling limit with the asymmetric rotator model whereas this is not practical in general with the vibrational model. Expressions for the magnetic dipole moment and the M1 and E2 transition probabilities are derived for states of the coupled system of the odd-mass nuclei. Important interference effects are found in the B(E2) expression and the B(E2) values are found to be sensitive to the coupling strength. Calculations are made for these quantities for vaious parameter values which enter into the model. Data for several odd-neutron nuclei (Sn 117, Sn 119, Te 123, Te 125 and Xe 129) are then interpreted in terms of the model. There is enough freedom in the choice of parameters to ensure that the theoretical results and experimental data are not inconsistent in most cases. However, serious inconsistencies in the cases Sn 119 and Te 123 show that the model of the asymmetric rotator is not nearly as successful for odd-mass nuclei as it was for even-mass nuclei. This raises the interesting question whether the vibrational model with strong coupling can overcome these inconsistencies, or whether the coupling term in the Hamiltonian needs to be modified: perhaps by an additional interaction term of the form J· j employed by Davydov, where J and j are the core and odd nucleon angular momenta, respectively.