Transition Matrix Elements in the Even-Even Osmium Isotopes: A Comparison with Pairing-Plus-Quadrupole Model Calculations

The energy-level structures and transition matrix elements between collective excitations in the even-even osmium isotopes ($A=186-192\mathrm{}$) have been studied using Coulomb excitation with oxygen projectiles having incident energies between 42 and 80 MeV. The deexcitation $\gamma$ radiations have been observed with NaI(Tl) and Ge(Li) detectors, singly, in coincidence with inelastically backscattered ${\mathrm{O}}^{16}$ ions, and in coincidence with $\gamma$ rays from the $2^{+}$→$0^{+}$ and $4^{+}$→$2^{+}$ transitions in each isotope. Angular-correlation studies have been performed on all observed transitions following Coulomb excitation by backscattered ions. In the four isotopes studied, all levels through the $6^{+}$ state of the ground-state band as well as the second excited $2^{+}$′ and $4^{+}$′ states have been populated, and the transition moments associated with the excitation of these states have been measured. In ${\mathrm{Os}}^{192}$, previously unobserved radiations have been assigned to the deexcitation of a $6^{+}$ state at 1088 keV and a $4^{+}$′ state at 907 keV. Except for the observation of the $0^{+}$ state at 1086 keV in ${\mathrm{Os}}^{188}$, a search for low-lying $0^{+}$ states in the other osmium isotopes did not reveal any definite candidates. Electric-quadrupole transition matrix elements have been deduced from the data with a model-independent analysis using the Winther-de Boer computer code for multiple Coulomb excitation. The latter quantities, together with measured branching ratios and $B\left(M1\mathrm{}\right)\mathrm{}$ values, have been compared with several macroscopic and microscopic nuclear models, with particular attention to the pairing-plus-quadrupole model of Kumar and Baranger. The latter has proved to be the most complete and successful of the models tested in predicting both absolute $B\left(E2\mathrm{}\right)\mathrm{}$ values, and the variation of these with neutron number in the osmium isotopes. However, the model in its original form makes the transition from deformed to spherical shape more rapidly, with increasing mass, than appears to be the case experimentally, thereby suggesting the need for small variations in the relative strength of the pairing and quadrupole nucleon-nucleon residual forces assumed as input to the microscopic calculations. A description of the osmium isotopes, as typified by shallow potential minima for moderately prolate deformations (in the cases of ${\mathrm{Os}}^{190,192}$ asymmetric equilibrium configurations) and by pronounced softness to both $\beta$ and $\gamma$ vibrations, emerges from the comparisons made.