2015/08/04 by P. Buganu, P Buganu, R. Budaca +1
Physics and Astronomy · #Nuclear physics research studies #Quantum Chromodynamics and Particle Interactions #Quantum Mechanics and Non-Hermitian Physics #nucl-th
paper · pdf · doi:10.1088/0954-3899/42/10/105106
published as J. Phys. G: Nucl. Part. Phys. 42 (2015) 105106 · 21 pages, 4 figures
arxiv created 2015/08/04 · openalex publication_date 2015/09/14 · arxiv updated 2015/09/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
The equation of the Bohr-Mottelson Hamiltonian with a sextic oscillator potential is solved for γ-rigid prolate nuclei. The associated shape phase space is reduced to three variables which are exactly separated. The angular equation has the spherical harmonic functions as solutions, while the β equation is brought to the quasi-exactly solvable case of the sextic oscillator potential with a centrifugal barrier. The energies and the corresponding wave functions are given in closed form and depend, up to a scaling factor, on a single parameter. The 0+ and 2+ states are exactly determined, having an important role in the assignment of some ambiguous states for the experimental β bands. Due to the special properties of the sextic potential, the model can simulate, by varying the free parameter, a shape phase transition from a harmonic to an anharmonic prolate β-soft rotor crossing through a critical point. Numerical applications are performed for 39 nuclei: 98-108Ru, 100,102Mo, 116-130Xe, 132,134Ce, 146-150Nd, 150,152Sm, 152,154Gd, 154,156Dy, 172Os, 180-196Pt, 190Hg and 222Ra. The best candidates for the critical point are found to be 104Ru and 120,126Xe, followed closely by 128Xe, 172Os, 196Pt and 148Nd.