scholarly journals UBF(5)toSUBF(3)shape phase transition in odd nuclei forj=1/2,3/2, and5/2orbits: The role of the odd particle at the critical point

2009 ◽  
Vol 79 (1) ◽  
Author(s):  
C. E. Alonso ◽  
J. M. Arias ◽  
L. Fortunato ◽  
A. Vitturi
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
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.

scholarly journals Generalized Independence in the q-Voter Model: How Do Parameters Influence the Phase Transition?

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 120 ◽  
Author(s):  
Angelika Abramiuk ◽  
Katarzyna Sznajd-Weron
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Broad Spectrum ◽  
Order Parameter ◽  
Analytical Formula ◽  
Voter Model ◽  
Pair Approximation ◽  
Scaling Relation ◽  
Independent Behavior

We study the q-voter model with flexibility, which allows for describing a broad spectrum of independence from zealots, inflexibility, or stubbornness through noisy voters to self-anticonformity. Analyzing the model within the pair approximation allows us to derive the analytical formula for the critical point, below which an ordered (agreement) phase is stable. We determine the role of flexibility, which can be understood as an amount of variability associated with an independent behavior, as well as the role of the average network degree in shaping the character of the phase transition. We check the existence of the scaling relation, which previously was derived for the Sznajd model. We show that the scaling is universal, in a sense that it does not depend neither on the size of the group of influence nor on the average network degree. Analyzing the model in terms of the rescaled parameter, we determine the critical point, the jump of the order parameter, as well as the width of the hysteresis as a function of the average network degree ⟨ k ⟩ and the size of the group of influence q.

scholarly journals Low- Z boundary of the N=88 –90 shape phase transition: Ce148 near the critical point

2020 ◽  
Vol 101 (1) ◽  
Author(s):  
P. Koseoglou ◽  
V. Werner ◽  
N. Pietralla ◽  
S. Ilieva ◽  
T. Nikšić ◽  
...  
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Shape Phase Transition

Study of Grodzins relation of B(E2) with E(21+) in A = 130, 100 and 80 regions

2018 ◽  
Vol 27 (11) ◽  
pp. 1850100
Author(s):  
J. B. Gupta ◽  
Vikas Katoch
Keyword(s):  
Phase Transition ◽  
Magic Number ◽  
Product Rule ◽  
Effective Number ◽  
Microscopic Calculation ◽  
Cd Isotopes ◽  
Nuclear Structures ◽  
Shape Phase Transition ◽  
Stability Line

The nuclei in the [Formula: see text] [Formula: see text] and [Formula: see text] regions, lying on both sides of the [Formula: see text]-stability line, continue to be of interest for their complex nuclear structures. The Grodzins product rule (GPR) viz. [Formula: see text], for the ground bands of even-[Formula: see text] even-[Formula: see text] nuclei provides a useful approach to study these structures. The utility of our method, displaying the linear relation of [Formula: see text] to [Formula: see text], is illustrated for the [Formula: see text] Zn to [Formula: see text] Cd series of isotopes. The spread of the data on the linear plots enables a quick view of the shape phase transitions. The role of the shells and the subshells, at spherical and deformed shell gaps for neutrons and protons, with their mutual re-inforcement and the shape phase transition are vividly visible on our plots. The development of collectivity in this region is also linked to the effective number of valence nucleons above the magic number of [Formula: see text], and 28 rather than [Formula: see text], for Mo to Cd isotopes for a microscopic calculation.

Quasi-exact description of the γ-unstable shape phase transition

2020 ◽  
Vol 35 (12) ◽  
pp. 2050085 ◽  
Author(s):  
A. Lahbas ◽  
P. Buganu ◽  
R. Budaca
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Transition Probabilities ◽  
Spectral Characteristics ◽  
Exact Solvability ◽  
Exactly Solvable Potential ◽  
Exactly Solvable ◽  
Shape Phase Transition ◽  
Critical Nuclei ◽  
Point Parameter

The equation of the [Formula: see text]-unstable Bohr Hamiltonian, with particular forms of the sextic potential in the [Formula: see text] shape variable, is exactly solved for a finite number of states. The shape of the quasi-exactly solvable potential is then defined by the number of exactly determined states. The effect of exact solvability order on the spectral characteristics of the model is closely investigated, especially, concerning the critical point of the phase transition from spherical to deformed shapes. The energy spectra and the [Formula: see text] transition probabilities, up to a scaling factor, depend only on a single-free parameter, while for the critical point, parameter-free results are available. Several numerical applications are done for nuclei undergoing a [Formula: see text]-unstable shape phase transition in order to identify critical nuclei based on the most suitable exact solvability order.

STATISTICAL MECHANICS AND TOPOLOGY OF SURFACES IN ${\mathcal Z}^d$

1994 ◽  
Vol 03 (03) ◽  
pp. 365-378 ◽  
Author(s):  
E. J. JANSE VAN RENSBURG
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Free Energy ◽  
Statistical Mechanics ◽  
Critical Point ◽  
And Topology

The role of topology in the statistical mechanics of surfaces in the lattice [Formula: see text] is considered. The possibility that a phase transition driven by the number of boundary components occurs is investigated. Bounds on the limiting free energy is derived and conditions for the existence of a critical point in the phase diagram are presented.

scholarly journals Phenomenological implications of Bohr space in six dimensions

2019 ◽  
Vol 21 ◽  
pp. 75
Author(s):  
P. Georgoudis
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Mass Parameter ◽  
Structural Evolution ◽  
Second Order ◽  
Irrotational Flow ◽  
Atomic Nuclei ◽  
Six Dimensions ◽  
Shape Phase Transition

The critical point for a second order shape/phase transition in the structural evolution of atomic nuclei, the consequences on the mass parameter and its irrotational flow are discussed after the embedding of Bohr space in six dimensions.

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