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

Abstract

Davidson potentials of the form ${\beta }^2+{\beta }_0^4/{\beta }^2$, when used in the E(5) framework, bridge the U(5) and O(6) symmetries, while they bridge the U(5) and SU(3) symmetries when used in the X(5) framework. Using a variational procedure, we determine for each value of angular momentum $L$ thevalue of ${\beta }_0$ at which the rate of change of various physical quantities (energy ratios, intraband B(E2) ratios, quadrupole moment ratios) has a maximum, the collection of the values of the physical quantity formed in this way being a candidate for describing its behavior at the relevant critical point. Energy ratios lead to the E(5) and X(5) results (whice correspond to an infinite well potential in $\beta$), while intraband B(E2) ratios and quadrupole moments lead to the E(5)-${\beta }^4$ and X(5)-${\beta }^4$ results, which correspond to the use of a ${\beta }^4$ potential in the relevant framework. A new derivation of the Holmberg-Lipas formula for nuclear energy spectra is obtained as a by-product.

LaTeX, 29 pages plus 17 postscript figures

References in corpus (8)

• Analytically solvable potentials for $\gamma$-unstable nuclei
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• Sequence of Potentials Interpolating between the U(5) and E(5) Symmetries
• Ground State Bands of the E(5) and X(5) Critical Symmetries Obtained from Davidson Potentials through a Variational Procedure
• The sextic oscillator as a $\gamma$-independent potential
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• A test of X(5) for the gamma degree of freedom
• New analytic solutions of the collective Bohr hamiltonian for a beta-soft, gamma-soft axial rotor

Cited by in corpus (11)

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• First order shape transition and critical point nuclei in Sm isotopes from relativistic mean field approach
• Bohr Hamiltonian with Davidson potential for triaxial nuclei
• Description of nuclear octupole and quadrupole deformation close to the axial symmetry and phase transitions in the octupole mode
• Collective motion in prolate γ-rigid nuclei within minimal length concept via a quantum perturbation method
• Conformable Fractional Bohr Hamiltonian with Bonatsos and Double-Well Sextic Potentials
• Triaxial nuclei and analytical solutions of the conformable fractional Bohr Hamiltonian with some exponential-type potentials
• Isovector pair correlations in analytically solvable models
• Evidence of the Excited X(5)-like Critical-Point Symmetry Structures in 152Sm