scholarly journals Critical point for the Deformation Dependent Mass model through a variational procedure

2019 ◽  
Vol 21 ◽  
pp. 65
Author(s):  
D. Petrellis
Keyword(s):  
Critical Point ◽  
Variational Approach ◽  
Variational Procedure ◽  
Mass Model ◽  
Dependent Mass

The recently introduced Deformation-Dependent Mass model is combined with a variational approach to the Bohr Hamiltonian in order to describe transitional nuclei. The results of this procedure are demon- strated for the ‘spherical to γ-unstable’ and the ‘spherical to deformed’ transitional classes, which corre- spond to the E(5) and X(5) solutions.

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.

scholarly journals A Variational Approach to Perturbed Discrete Anisotropic Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Amjad Salari ◽  
Giuseppe Caristi ◽  
David Barilla ◽  
Alfio Puglisi
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Critical Point ◽  
Critical Point Theory ◽  
Variational Approach ◽  
Boundary Value ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Multiplicity Results ◽  
Anisotropic Equation

We continue the study of discrete anisotropic equations and we will provide new multiplicity results of the solutions for a discrete anisotropic equation. We investigate the existence of infinitely many solutions for a perturbed discrete anisotropic boundary value problem. The approach is based on variational methods and critical point theory.

VARIATIONAL PROCEDURE LEADING FROM DAVIDSON POTENTIALS TO THE E(5) AND X(5) CRITICAL POINT SYMMETRIES

2005 ◽  
Author(s):  
DENNIS BONATSOS ◽  
D. LENIS ◽  
D. PETRELLIS ◽  
N. MINKOV ◽  
P. P. RAYCHEV ◽  
...  
Keyword(s):  
Critical Point ◽  
Variational Procedure

Analytical description of odd-A nuclei around the critical point of shape phase transition within a conjunction of γ-rigid and γ-stable in the presence of deformation-dependent mass formalism

2020 ◽  
Vol 98 (7) ◽  
pp. 675-682
Author(s):  
N. Soheibi ◽  
M. Eshghi ◽  
M. Bigdeli
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Collective Motion ◽  
Level Structure ◽  
Analytical Description ◽  
Dynamical Symmetry ◽  
Mass Term ◽  
Stable Part ◽  
Dependent Mass ◽  
Shape Phase Transition

We have investigated a conjunction of γ-rigid and γ-stable collective motion of odd-A nuclei around the critical point of spherical to axially deformed shape phase transition. Our model is made on even–even nuclei with the [Formula: see text] critical point symmetry that is coupled to a single nucleon in a j orbit. The Davidson potential for the β part is applied to the γ-rigid and γ-stable part of a Bohr–Hamiltonian in the presence of a deformation-dependent mass term and spin-orbit interaction. The solutions provide baselines for odd-mass nuclei with the [Formula: see text] symmetry as Bose–Fermi dynamical symmetry. The level structure and transition patterns for some special j is estimated in detail.

A position-dependent mass model for the Thomas–Fermi potential: Exact solvability and relation to -doped semiconductors

2013 ◽  
Vol 333 ◽  
pp. 323-334 ◽  
Author(s):  
Axel Schulze-Halberg ◽  
Jesús García-Ravelo ◽  
Christian Pacheco-García ◽  
José Juan Peña Gil
Keyword(s):  
Mass Model ◽  
Doped Semiconductors ◽  
Exact Solvability ◽  
Thomas Fermi ◽  
Dependent Mass ◽  
Position Dependent Mass

scholarly journals E(5) and X(5) critical point symmetries obtained from Davidson potentials through a variational procedure

2004 ◽  
Vol 70 (2) ◽  
Author(s):  
Dennis Bonatsos ◽  
D. Lenis ◽  
N. Minkov ◽  
D. Petrellis ◽  
P. P. Raychev ◽  
...  
Keyword(s):  
Critical Point ◽  
Variational Procedure
Sign in / Sign up

Export Citation Format

Share Document