Exactly separable version of the Bohr Hamiltonian with the Davidson potential

An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form u({beta})+u({gamma})/{beta}{sup 2}, with the Davidson potential u({beta})={beta}{sup 2}+{beta}{sub 0}{sup 4}/{beta}{sup 2} (where {beta}{sub 0} is the position of the minimum) and a stiff harmonic oscilla...

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Bibliographic Details
Published in:Physical review. C, Nuclear physics Nuclear physics, 2007-12, Vol.76 (6), Article 064312
Main Authors: Bonatsos, Dennis, McCutchan, E. A., Minkov, N., Casten, R. F., Yotov, P., Lenis, D., Petrellis, D., Yigitoglu, I.
Format: Article
Language:English
Subjects:
ACTINIDE NUCLEI
APPROXIMATIONS
CORRELATIONS
E2-TRANSITIONS
GROUND STATES
HAMILTONIANS
HARMONIC OSCILLATORS
INTERACTING BOSON MODEL
MATHEMATICAL SOLUTIONS
NUCLEAR PHYSICS AND RADIATION PHYSICS
NUCLEAR POTENTIAL
NUCLEAR STRUCTURE
RARE EARTHS
SU-3 GROUPS
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Summary:An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form u({beta})+u({gamma})/{beta}{sup 2}, with the Davidson potential u({beta})={beta}{sup 2}+{beta}{sub 0}{sup 4}/{beta}{sup 2} (where {beta}{sub 0} is the position of the minimum) and a stiff harmonic oscillator for u({gamma}) centered at {gamma}=0 deg. In the resulting solution, called the exactly separable Davidson (ES-D) solution, the ground-state, {gamma}, and 0{sub 2}{sup +} bands are all treated on an equal footing. The bandheads, energy spacings within bands, and a number of interband and intraband B(E2) transition rates are well reproduced for almost all well-deformed rare-earth and actinide nuclei using two parameters ({beta}{sub 0},{gamma} stiffness). Insights are also obtained regarding the recently found correlation between {gamma} stiffness and the {gamma}-bandhead energy, as well as the long-standing problem of producing a level scheme with interacting boson approximation SU(3) degeneracies from the Bohr Hamiltonian.
ISSN:0556-2813
1089-490X
DOI:10.1103/PhysRevC.76.064312