At the borderline of shape coexistence: Mo and Ru

Abstract

Background: Even-even isotopes of Mo (Z = 42) and Ru (Z = 44) are nuclei close to the subshell closure at Z = 40, where shape coexistence plays a significant role. As a result, their spectroscopic properties are expected to resemble those of Sr (Z = 38) and Zr (Z = 40). Exploring the evolution of these properties as they move away from the subshell closure is of great interest. Purpose: The purpose of this study is to reproduce the spectroscopic properties of even-even [96][97][98][99][100][101][102][103][104][105][106][107][108][109][110] 42 Mo and 98-11444 Ru isotopes and to determine the influence of shape coexistence. Method: We employed the interacting boson model with configuration mixing as the framework to calculate all the observables for Mo and Ru isotopes. We considered two types of configurations: 0-particle-0-hole and 2-particle-2-hole excitations. The model parameters were determined using a least-squares fitting to match the excitation energies and the B(E 2) transition rates. Results: We obtained the excitation energies, B(E 2) values, two-neutron separation energies, nuclear radii, and isotope shifts for the entire chain of isotopes. Our theoretical results show good agreement with experimental data. Furthermore, we conducted a detailed analysis of the wave functions and obtained the mean-field energy surfaces and the nuclear deformation parameter, β, for all considered isotopes. Conclusions: Our findings reveal that shape coexistence plays a significant role in Mo isotopes, with the crossing of intruder and regular configurations occurring at neutron number 60 (A = 102), which induces a quantum phase transition. In contrast, in Ru isotopes, the intruder states have minimal influence, remaining at higher energies. However, at neutron number 60, also a quantum phase transition occurs in Ru isotopes.

Shapes and structure for the lowest states of the 42,44Ca isotopes

“…Recently, a proxy-SU(3) model [11][12][13] has been used for a better localization of these regions, conventionally called islands of shape coexistence [14,15]. Algebraic approaches, as the Interacting Boson Model (IBM) [16][17][18][19] and the Partial Dynamical Symmetry (PDS) [20], proved to be also appropriate tools in addressing this behavior in nuclei [21][22][23][24][25], especially in heavy mass region where the dimension of the SM configuration space is prohibitive. However, taking into account that mainly the discussion is about shapes of the lowest collective states of the same nucleus, perhaps the natural choice in the description of the shape coexistence and mixing phenomena would be the Bohr-Mottelson Model (BMM) [26], where the nucleus is considered as a liquid drop which vibrates and oscillates around spherical and deformed shapes.…”