Theoretical Investigation of the Nuclear Properties ofPr143in the Unified Model

Experimental data on the low-energy nuclear properties of ${\mathrm{Pr}}^{143}$ are analyzed by using the intermediate-coupling approach in the unified nuclear model. For this purpose it is assumed that the last odd proton, having available the $1g_{\frac{7}{2}}$ and $2d_{\frac{5}{2}}$ states, is coupled to the quadrupole vibrations of the surface of the even-even core of the nucleus. The resulting Hamiltonian of the coupled system is diagonalized including all states with up to three phonons in the space of the basis eigenvectors of the uncoupled system. With reasonable values for the coupling strength and for the "effective" spacing in energy between $g_{\frac{7}{2}}$ and $d_{\frac{5}{2}}$ states, the calculated energy levels for the low-lying levels of ${\mathrm{Pr}}^{143}$ and their spins and parities are in fairly good agreement with the experimental data. Further, the wave functions obtained from our model are used to calculate the electric and magnetic transition probabilities, and these results are also found to be in good agreement with the experimentally observed values. Finally, discussions are given of the validity of the approximations used in the present analysis and also of the circumstances in which more extensive experimental investigations are needed.