Unexpected transitional paths in the prolate to oblate shape phase transitions for Bose–Fermi systems

Review of Shape Phase Transition Studies for Bose-Fermi Systems: The Effect of the Odd-Particle on the Bosonic Core

“…In this review paper, we present a summary of the most important results we have obtained within the IBFM for shape phase transitions in odd-even nuclei, namely the critical point symmetries for the specific E(5/4) [13] and E(5/12) [11,14] cases; the U BF (5)-SU BF (3) transition in odd nuclei for multi-j orbits, j = 1/2, 3/2, 5/2 [15]; the results of our recent works related to the case of a single-j fermion coupled to the bosonic core that performs different transitions mentioned in previous paragraph [16,[18][19][20]. The paper is organized as follows.…”

“…With particular choice of the control parameter x in Hamiltonian (20), one can obtain the U BF (5) and SU BF (3) dynamical symmetries. The values are x = 0 for U BF (5) and x = 1 for SU BF (3).…”

“…In the well deformed oblate region, close to x = 1, once again we see that the oblate core drives all states to the oblate shape, with approximately the same β min −1.28. Recently, we investigated [20] the case of a single-j = 9/2 fermion coupled to a bosonic core with N B = 5 that performs a transition from prolate to oblate shapes. We focused on the effect of the coupled fermion on the whole system along the transitional path from prolate to oblate shapes, passing through the γ-unstable shape.…”

“…During the last decade, we have developed a systematic investigation of the quantum shape phase transition in Bose-Fermi systems for the case of a single-j fermion coupled to a bosonic core [16][17][18][19][20], making use of the intrinsic frame formalism to associate a given shape to the solution of a IBFM Hamiltonian. Transitions from spherical to γ-unstable shape [16], from spherical to prolate shape [18], from spherical to oblate shape [19] have been studied up to now, with the aim of understanding the effect of the coupled fermion on the core when moving to the transition paths and around the critical points.…”

“…Transitions from spherical to γ-unstable shape [16], from spherical to prolate shape [18], from spherical to oblate shape [19] have been studied up to now, with the aim of understanding the effect of the coupled fermion on the core when moving to the transition paths and around the critical points. More recently, we have closed the circle, by investigating the phase transition from prolate to oblate shape passing through the γ-unstable shape in odd-even systems [20]. The different paths are marked in Figure 1.…”