Analytic descriptions for transitional nuclei near the critical point

Abstract

Exact solutions of the Bohr Hamiltonian with a five-dimensional square well potential, in isolation or coupled to a fermion by the five-dimensional spin-orbit interaction, are considered as examples of a new class of dynamical symmetry or Bose-Fermi dynamical symmetry. The solutions provide baselines for experimental studies of even-even [E(5)] and odd-mass [E(5|4)] nuclei near the critical point of the spherical to deformed gamma-unstable phase transition.

LaTeX (elsart), 53 pages; typographical correction to (3.15)

References in corpus (8)

• Temporally stable coherent states for infinite well and Pöschl-Teller potentials
• A computationally tractable version of the collective model
• Effects of beta-gamma coupling in transitional nuclei and the validity of the approximate separation of variables
• E(5), X(5), and Prolate to Oblate Shape Phase Transitions in Relativistic Hartree Bogoliubov Theory
• Sequence of Potentials Interpolating between the U(5) and E(5) Symmetries
• The U(5)-O(6) transition in the Interacting Boson Model and the E(5) critical point symmetry
• Consequences of wall stiffness for a beta-soft potential
• Phase transitions in the Interacting Boson Fermion Model: the gamma-unstable case

Cited by in corpus (13)

• Quantum phase transitions in the interacting boson model
• Critical point symmetries in boson-fermion systems. The case of shape transition in odd nuclei in a multi-orbit model
• Dual algebraic structures for the two-level pairing model
• Construction of SO(5)>SO(3) spherical harmonics and Clebsch-Gordan coefficients
• The emergent dynamical symmetry at the triple point of nuclear deformations
• Algebraic Solutions for $U^{BF}(5)-O^{BF}(6)$ Quantum Phase Transition in Odd Mass Number Nuclei
• Euclidean Dynamical Symmetry in Nuclear Shape Phase Transitions
• Racah's method for general subalgebra chains: Coupling coefficients of SO(5) in canonical and physical bases
• Bohr space in six dimensions
• Interplay of quadrupole and octupole degrees of freedom in the Gd isotopes
• Bohr-Mottelson Hamiltonian with octic potential applied to the ${}^{106-116}$Cd isotopes
• Symmetry and Supersymmetry in Nuclear Physics
• Rotation and vibration in tetraquarks