scholarly journals Z(5): Critical Point Symmetry for the Prolate to Oblate Nuclear Shape Phase Transition

2020 ◽  
Vol 13 ◽  
pp. 73
Author(s):  
Dennis Bonatsos ◽  
D. Lenis ◽  
D. Petrellis ◽  
P. A. Terziev
Keyword(s):  
Experimental Data ◽  
Phase Transition ◽  
Critical Point ◽  
Point Symmetry ◽  
Transition Rates ◽  
Oblate Shape ◽  
Scale Factors ◽  
Shape Phase Transition ◽  
Nuclear Shape Phase Transition ◽  
Good Agreement

A critical point symmetry for the prolate to oblate shape phase transition is intro­ duced, starting from the Bohr Hamiltonian and approximately separating variables for γ=30°. Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are found to be in good agreement with experimental data for 194Pt, which is supposed to be located very close to the prolate to oblate critical point, as well as for its neighbours (192Pt, 196Pt).

scholarly journals X(3): an exactly separable γ-rigid version of the X(5) critical point symmetry

2020 ◽  
Vol 15 ◽  
pp. 157
Author(s):  
D. Bonatsos ◽  
D. Lenis ◽  
D. Petrellis ◽  
P. A. Terziev ◽  
I. Yiyitoglou
Keyword(s):  
Experimental Data ◽  
Critical Point ◽  
Degrees Of Freedom ◽  
Separation Of Variables ◽  
Point Symmetry ◽  
Transition Rates ◽  
Scale Factors ◽  
Exact Separation ◽  
Three Degrees Of Freedom ◽  
Good Agreement

A γ-rigid version (with γ = 0) of the X(5) critical point symmetry is constructed. The model, to be called X(3) since it is proved to contain three degrees of freedom, utilizes an infinite well potential, is based on exact separation of variables, and leads to parameter free (up to overall scale factors) predictions for spectra and B(E2) transition rates, which are in good agreement with existing experimental data for 172Os and 186Pt. An unexpected similarity of the β1-bands of the X(5) nuclei 150Nd, 152Sm, 154Gd, and 156Dy to the X(3) predictions is observed.

scholarly journals Z(5): critical point symmetry for the prolate to oblate nuclear shape phase transition

2004 ◽  
Vol 588 (3-4) ◽  
pp. 172-179 ◽  
Author(s):  
Dennis Bonatsos ◽  
D. Lenis ◽  
D. Petrellis ◽  
P.A. Terziev
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Nuclear Shape ◽  
Point Symmetry ◽  
Shape Phase Transition ◽  
Nuclear Shape Phase Transition

scholarly journals γ-rigid solution of the Bohr Hamiltonian compared to the E(5) critical point symmetry

2019 ◽  
Vol 14 ◽  
pp. 71
Author(s):  
Dennis Bonatsos ◽  
D. Lenis ◽  
D. Petrellis ◽  
P. Terziev ◽  
I. Yigitoglu
Keyword(s):  
Critical Point ◽  
Ground State ◽  
Close Agreement ◽  
Point Symmetry ◽  
Transition Rates ◽  
Ground State Band ◽  
Scale Factors ◽  
State Band ◽  
Euclidean Algebra ◽  
Rigid Solution

A γ-rigid solution of the Bohr Hamiltonian for 7 = 30° is derived, its ground state band being related to the second order Casimir operator of the Euclidean algebra E(4). Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are in close agreement to the E (5) critical point symmetry, as well as to experimental data in the Xe region around A = 130.

A theoretical study of energy spectra and transition probabilities of 200–204Hg isotopes in transitional region of IBM

2014 ◽  
Vol 23 (10) ◽  
pp. 1450056 ◽  
Author(s):  
H. Sabri
Keyword(s):  
Experimental Data ◽  
Theoretical Study ◽  
Transition Probabilities ◽  
Energy Spectra ◽  
Interacting Boson Model ◽  
Transitional Region ◽  
Transition Rates ◽  
Scale Factors ◽  
Boson Model ◽  
Good Agreement

In this paper, by using the SO(6) representation of eigenstates and transitional Interacting Boson Model (IBM) Hamiltonian, the evolution from prolate to oblate shapes along the chain of Hg isotopes is studied. Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are found to be in good agreement with experimental data for 200–204 Hg isotopes which are supported to be located in this transitional region.

scholarly journals Critical point symmetry for the spherical to triaxially deformed shape phase transition

2015 ◽  
Vol 751 ◽  
pp. 423-429 ◽  
Author(s):  
Yu Zhang ◽  
Feng Pan ◽  
Yan-An Luo ◽  
J.P. Draayer
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Point Symmetry ◽  
Shape Phase Transition

scholarly journals Variational procedure leading from Davidson potentials to the E(5)and X(5) critical point symmetries

2020 ◽  
Vol 13 ◽  
pp. 10
Author(s):  
Dennis Bonatsos ◽  
D. Lenis ◽  
N. Minkov ◽  
D. Petrellis ◽  
P. P. Raychev ◽  
...  
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Ground State ◽  
Nuclear Energy ◽  
Energy Spectra ◽  
Variational Procedure ◽  
Ground State Band ◽  
Sharp Maximum ◽  
State Band ◽  
Shape Phase Transition

Davidson potentials of the form β^2 + β0^4/β^2, when used in the original Bohr Hamiltonian for γ-independent potentials bridge the U(5) and 0(6) symmetries. Using a variational procedure, we determine for each value of angular momentum L the value of β0 at which the derivative of the energy ratio RL = E(L)/E(2) with respect to β0 has a sharp maximum, the collection of RL values at these points forming a band which practically coincides with the ground state band of the E(5) model, corresponding to the critical point in the shape phase transition from U(5) to Ο(6). The same potentials, when used in the Bohr Hamiltonian after separating variables as in the X(5) model, bridge the U(5) and SU(3) symmetries, the same variational procedure leading to a band which practically coincides with the ground state band of the X(5) model, corresponding to the critical point of the U(5) to SU(3) shape phase transition. A new derivation of the Holmberg-Lipas formula for nuclear energy spectra is obtained as a by-product.

Extended study on the application of the sextic potential in the frame of X(3)-Sextic

2021 ◽  
Author(s):  
Mostafa Oulne ◽  
Imad Tagdamte
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Electromagnetic Properties ◽  
Shape Evolution ◽  
Isotopic Chain ◽  
Oscillator Potential ◽  
Extended Study ◽  
Deformed Nuclei ◽  
Exact Solvability ◽  
Shape Phase Transition

Abstract The main aim of the present paper is to study extensively the γ-rigid Bohr Hamiltonian with anharmonic sextic oscillator potential for the variable β and γ = 0. For the corresponding spectral problem, a finite number of eigenvalues are found explicitly, by algebraic means, so-called Quasi-Exact Solvability (QES). The evolution of the spectral and electromagnetic properties by considering higher exact solvability orders is investigated, especially the approximate degeneracy of the ground and first two β bands in the critical point of the shape phase transition from a harmonic to an anharmonic prolate β-soft, also the shape evolution within an isotopic chain. Numerical results are given for 39 nuclei, namely, 98-108Ru, 100-102Mo, 116-130Xe, 180-196Pt, 172Os, 146-150Nd, 132-134Ce, 152-154Gd, 154-156Dy, 150-152Sm, 190Hg and 222Ra. Across this study, it seems that the higher quasi-exact solvability order improves our results by decreasing the rms, mostly for deformed nuclei. The nuclei 100,104Ru, 118,120,126,128Xe, 148Nd and 172Os fall exactly in the critical point.

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