Symmetry solutions at γ ⁰ = π/6 for nuclei transition between γ ⁰ = 0 and γ ⁰ = π/3 via a variational procedure

Abstract

A Bohr Hamiltonian model suitable for triaxial shapes is found via inverse square potentials in the β part and the solutions of the γ part are obtained via a harmonic oscillator, centered around π/6. The symmetry solutions from a triaxial vibrator to a rigid triaxial rotator are achieved through variational procedure. The solutions of some selected Z(5) symmetry candidates are fitted and compared with the available experimental data.

Relative variation between γ coordinate and the potential of the Bohr Hamiltonian producing X(4) from Z(4)

“…Albeit, in the literature [16,24,25,[31][32][33][34], the variation of the potential parameter has provided some shape phase transitions at some constant or approximate values of γ, a simultaneous relative variation between γ and the potential has not been reported until in this present paper. These special shape phase solutions provide some geometric coordinates which link the potential and γ, as their relative variations link Z(4) and X(4) CPSs together.…”

“…where the additional β is from equation (26) and β 3 comes from the volume element corresponds to Z(4) shape model. Calculation of B(E2) is the similar to Z(5) formalism [24], the difference is the integrals over β, that is equation (29).…”

“…Consequently, the candidate nuclei are expected to be found in the region between X(3) and X(5) candidate nuclei. The non-exact or an approximate solution, for γ 0 ≈ π/6, is referred to as Z( 5) in [9,24,25] and others. Just like the case of X(3) in [24,[26][27][28][29], the γ-variable of the Z( 4) is treated as a fixed parameter.…”

“…The non-exact or an approximate solution, for γ 0 ≈ π/6, is referred to as Z( 5) in [9,24,25] and others. Just like the case of X(3) in [24,[26][27][28][29], the γ-variable of the Z( 4) is treated as a fixed parameter.…”

“…The description of these CPSs, if this present method must be used, requires that a potential with a minimum or a free parameter potential such as Davidson potential used in [16], inverse square potential in [24,33,34], etc., must be used. In this present paper, the minimum of the potential, serves as an entity that can change the axial symmetry between the two CPSs.…”