Bohr Hamiltonian for $\gamma = 30^{\circ}$ γ = 30 ∘ with Davidson potential

Yigitoglu, I.; Gökbulut, Melek

doi:10.1140/epjp/i2018-11969-0

Cited by 4 publications

(8 citation statements)

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“…corresponds to the Z(4) solutions obtained in [16,23]. Equation (32) and equation (33) suggest that these two critical point symmetries (CPSs) are the two limit cases of this model: the Z(4) corresponds to the upper limit while the X(4) corresponds to the lower limit.…”

Section: γ-Variation Solutions Methodsmentioning

confidence: 70%

“…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.…”

Section: Introductionmentioning

confidence: 63%

“…The Z(4) CPSM [11,[13][14][15][16][17] of the geometry Bohr Hamiltonian and Bohr-Mottelson Hamiltonian [18][19][20][21] is a γ-rigid solution obtained by freezing γ at exactly π/6. With respect to the γ-vibrations, the Z(4) candidate isotopes are considered to be rigid, consequently, their Hamiltonian coordinate systems are restricted to a four degree of freedom, taking into account the β and the Euler angles, θ i=1,2,3 .…”

Section: Introductionmentioning

confidence: 99%

“…With respect to the γ-vibrations, the Z(4) candidate isotopes are considered to be rigid, consequently, their Hamiltonian coordinate systems are restricted to a four degree of freedom, taking into account the β and the Euler angles, θ i=1,2,3 . [15,16,22,23]. On the other hand, the X(4) CPSM [10] is a four dimensional critical point symmetry (CPS) in the context of Bohr Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Ajulo,

Oyewumi,

Orosun

et al. 2024

Phys. Scr.

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In this paper, four degree of freedom γ-rigid solutions of the Bohr Hamiltonian at γ0 = π/6 areobtained. The relative variation between γ and the potential of the Hamiltonian is employed to retrieve X(4) from Z(4). γ is varied in the interval 0 ≤ γ0 ≤ π/6 while the potential minimum, β0, is varied in the interval 0 ≤ β0 ≤ ∞. Very small value of β0 yields Z(4) while a large value of β0 produces X(4) and SU(3) is realized at β0 ≈ ∞. The solutions at γ0 = 0 correspond to X(4) while the solutions at γ0 = π/6 yield Z(4): a dynamic link between Z(4) and X(4) critical point symmetries (CPSs) has been provided. The fact that γ and β0 of the potential play the same role in the dynamical link between Z(4) and X(4) shows that β0 also measures the departure from axial symmetry to other shapes as γ does. In the experimental realization of the model, the conformation of 192Pt and 194Pt isotopes to the present Z(4) model shows that the present model can be employed in the description of triaxial rotors and γ-soft isotopes. 194Pt is shown to be the best choice for triaxial rigid rotor candidacy. 130Xe, a critical point isotope, which belongs to the class of γ-soft nuclei, reproduces this present model very well in all the states. Consequently, this present model can serve as a critical point model. 40,0 - β0 distribution for Z(4) and X(4) candidate isotopes shows a significant interval between the two models where the T (4) CPS lies.

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