Description of the Shape Coexistence in ⁹⁸ Mo with IBM2

Abstract

We investigate the properties of the low-lying states and the relevant shape dynamics of 98 Mo within the framework of the proton-neutron interacting boson model (IBM2). By considering the relative energy of the 𝑑 proton boson to be different from that of the neutron bosons, the low-lying levels and the key observable 𝐵(𝐸2) transition branching ratios are calculated. The characteristic feature of the energy spectrum and the most crucial available structure indicator indicate that the substantial mixing between the spherical-vibrational and 𝛾-unstable shapes in 98 Mo. The calculation results of the overall deformation in 98 Mo are almost the same for both the ground and the first excited 0 + states, showing a weak deformation. While the triaxiality parameter indicates that the mostly triaxial shape with some oblate for the ground state, and the triaxial shape with some prolate for the excited 0 + 2 state, being equilibrium shapes of spherical-vibrational and 𝛾-unstable in 98 Mo.

Coexistence of Prolate and Oblate Shapes in 98 Sr Nuclei Using IBM2

“…More recently, this method was extended to study the shape coexistence in 98,100 Mo isotopes. [28,29] The calculated results correctly described the strong mixing between the coexisting states in 98,100 Mo isotopes. In particular, the calculated values of the quadrupole shape invariants for 98 Mo are in good agreement with the experimental results both quantitatively and qualitatively.…”

“…For the description of 98 Sr, our investigation is based on the validity of the 𝑍 = 40 subshell closure, and we consider the 90 40 Zr 50 as a doubly magic core the same as in Refs. [19,22,29]. In this case, two valence proton holes form 𝑁 𝜋 = 1 hole-like proton-boson from the 𝑍 = 40 shell, and ten valence neutrons form 𝑁 𝜈 = 5 particle-like neutron-bosons from the 𝑁 = 50 shell for 98 Sr.…”

“…In this calculation we have taken the relative energy of the 𝑑 proton boson to be different from that of the neutron boson, i.e., 𝜀 𝑑𝜋 ̸ = 𝜀 𝑑𝜈 the same as in Refs. [27][28][29][30]. To fix the free parameters in the Hamiltonian Eq.…”

Shape coexistence close to N = 50 in the neutron-rich isotope 80 Ge investigated by IBM-2

“…Unfortunately, only absolute B(E2) transition strengths of 2 + 1 → 0 + 1 , and 2 + 2 → 0 + 1 in 80 Ge have been observed so far. However, one can further explore shape coexistence in 80 Ge based on the other key sensitive quantities [47,48]. To calculate the E2 transition strengths, the effective charges of proton and neutron bosons were determined to reproduce the experimental data of B(E2,2 + 1 → 0 + 1 ) and B(E2,2 + 2 → 0 + 1 ).…”