Investigation on systematic trend of shape evolution for the Os nuclei

The energies, in particular the lifetimes of the first excited states in even-even nuclei provide a worthful information about the quadrupole deformation of the nuclear shape. For the even-even Os isotopes (Z = 76) with neutron numbers N≤126, the systematics of the excited energies of the first 2+ states indicates that ¹⁸⁴Os (N=108) has maximal deformation. From the N = 108 towards the closed shell at N = 82, nuclear shape changes slightly with decreasing neutron number. Especially from ¹⁷⁶Os to ¹⁸⁰Os, the quadrupole deformation β₂ (E_γ) extracted from the energies of the 2⁺ excited states remain almost constant at about 0.23. This behavior may be related to the possible X (5) structures for these nuclei. Two systematics of the excited energies for both the 2⁺ states and with the addition of the 4⁺ states show similar trend of shape evolution and make an appearance of a maximal deformation at ¹⁸⁴Os for the even-even Os nuclei. On the other hand, it is shown that the β₂ (r) deduced from the lifetimes of the 2⁺ states in the Os nuclei are gradually increasing from N = 116 when going toward the N = 82 closed shell, and reach a maximum at ¹⁸²Os (N = 106) where neighbors with the expectation of N = 104 obtained from a simple relation proposed by Casten based on the Interacting Boson Approximation for the description of the B(E2, 0⁺ → 2⁺) values as a function of the product of valence proton and neutron numbers. Beyond the N = 106 the β₂ (r) values decrease with decreasing neutron number. However, ¹⁷⁴Os and ¹⁷⁶Os do not follow this simple systematic trend, whereas exhibit anomalously high β₂ (r) values which can not be explained by any theory. Therefore, it would be of interest to remeasure the lifetimes more precisely for the 2⁺ states of these two nuclei to see if this in apprehensible effect could be reproduced. In association with the lifetimes of the 4+ states, the systematics of the transition probability ratio B(E2, 4⁺)/B(E2, 2⁺) reveals that ¹⁸⁶Os (N = 110) exhibits a typical rotational behavior characterized by the B(E2, 4⁺)/B(E2, 2⁺) = 1.453 ± 0.071 close to the ideal rotor value of 1.428. This result deviates from the prediction coming from the empirical relation of Casten. It is worth noting that in order to make a consummate investigation on systematics of the B(E2, 4⁺)/B(E2, 2⁺), it is necessary to measure the lifetimes of the 4⁺ states in ^176,178,180Os for lack of the lifetime data of these states. (authors)