Phase transitions in the sdg interacting boson model

Abstract

Abstract. A geometric analysis of the sdg interacting boson model is performed. A coherent-state is used in terms of three types of deformation: axial quadrupole (β 2 ), axial hexadecapole (β 4 ) and triaxial (γ 2 ). The phase-transitional structure is established for a schematic sdg hamiltonian which is intermediate between four dynamical symmetries of U(15), namely the spherical U(5) ⊗ U(9), the (prolate and oblate) deformed SU ± (3) and the γ 2 -soft SO(15) limits. For realistic choices of the hamiltonian parameters the resulting phase diagram has properties close to what is obtained in the sd version of the model and, in particular, no transition towards a stable triaxial shape is found.

Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian

“…A stability analysis of this surface leads to a set of conditions, Eqs. (34), (37) and (38), which are necessary and sufficient for the occurrence of a minimum with an intrinsic shape with octahedral symmetry.…”

“…(34), (37) and (38) are the necessary and sufficient conditions for the energy surface E(β 2 , β 4 , γ 2 , γ 4 , δ 4 ) to have a local minimum with octahedral symmetry. It is not necessarily a unique minimum and it may not be the global one.…”

Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the interacting boson approximation model

“…[29,37,38], which exhibits a PDS, are interesting tasks. Shape/phase transitions have recently been studied in both the parameter space of IBA-2, which is a tetrahedron [39,40,41], and the parameter space of sdg-IBA [42], which is a prism. …”

Rapid structural change in low-lying states of neutron-rich Sr and Zr isotopes

“…The abrupt changing in the lifetimes and excitation energies of 2 + 1 states, two-neutron separation energies and rms charge radii indicates a sudden onset of large quadrupole deformation at neutron number N = 60. In the past decades, various models have been employed to study such a dramatic transition in the low-energy structure of these nuclei [12][13][14][15][16][17][18][19][20][21][22][23][24][25], the description of which has been a challenge in theoretical nuclear physics.…”