Exact solution of the quadrupole surface vibration Hamiltonian in body-fixed coordinates

Corrigan, Thomas Michael; Margetan, F. J.; Williams, S. J.

doi:10.1103/physrevc.14.2279

Cited by 54 publications

(70 citation statements)

References 16 publications

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“…The results of that investigation are contained in Reference (60), and have served as the foundation for both this thesis, and the dissertation work of one of our co-authors in Reference (60), F. Margetan.…”

Section: Discussionmentioning

confidence: 99%

Unified Model Studies of N = 84 and N = 80 Nuclei

Corrigan

1977

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Section: Discussionmentioning

confidence: 99%

Unified Model Studies of N = 84 and N = 80 Nuclei

Corrigan

1977

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“…The functions g, that have the property g K = g −K , are given explicitely by Bés [12] and in addition to L and M , are also labeled by other two quantum numbers τ and ν. The former is the quantum number that comes from the solution of the eigenvalue equation of the Casimir operator of the SO(5) group (also called SO(5) seniority), while the latter is an empirical label needed in order to distinguish between the occurrence of multiple set of the same L, M within a given SO(5) IR and takes the values [13] :…”

Section: γ−Unstable Casesmentioning

confidence: 99%

Solutions of the Bohr Hamiltonian, a compendium

2005

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The Bohr hamiltonian, also called collective hamiltonian, is one of the cornerstone of nuclear physics and a wealth of solutions (analytic or approximated) of the associated eigenvalue equation have been proposed over more than half a century (confining ourselves to the quadrupole degree of freedom). Each particular solution is associated with a peculiar form for the V (β, γ) potential. The large number and the different details of the mathematical derivation of these solutions, as well as their increased and renewed importance for nuclear structure and spectroscopy, demand a thorough discussion. It is the aim of the present monograph to present in detail all the known solutions in γ−unstable and γ−stable cases, in a taxonomic and didactical way. In pursuing this task we especially stressed the mathematical side leaving the discussion of the physics to already published comprehensive material.The paper contains also a new approximate solution for the linear potential, and a new solution for prolate and oblate soft axial rotors, as well as some new formulae and comments, and an appendix on the analysis of a few interesting numerical sequences appearing in this context. The quasi-dynamical SO(2) symmetry is proposed in connection with the labeling of bands in triaxial nuclei.

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“…A non-trivial simplest case is to construct symmetric irreducible representations (irreps) of the O(5) group in the O(3) basis for identical d-bosons useful in the nuclear collective model [4,5] and the interacting boson model for nuclei [6]. Because of its physical importance, there have been a lot of attempts to construct the O(5) ⊃ O(3) basis vectors [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Most notably, Rowe, Hecht, and many others in a series of papers [23][24][25][26] established the vector-coherent-state (VCS) representations of O(5) ⊃ O(3) and constructed the O(5) spherical harmonics [27].…”

Section: Introductionmentioning

confidence: 99%

Construction of basis vectors for symmetric irreducible representations of O(5) $ \supset$ O(3)

et al. 2014

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A recursive method for construction of symmetric irreducible representations of O(2l + 1) in the O(2l + 1) ⊃ O(3) basis for identical boson systems is proposed. The formalism is realized based on the group chain U (2l + 1) ⊃ U (2l − 1) ⊗ U (2), of which the symmetric irreducible representations are simply reducible. The basis vectors of the O(2l + 1) ⊃ O(2l − 1) ⊗ U (1) can easily be constructed from those of 0) with resultant angular momentum quantum number L = 2τ + 2 − k for k = 0, 2, 3, · · · , 6 with a multiplicity 2 case for k = 6 are presented.

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Exact solution of the quadrupole surface vibration Hamiltonian in body-fixed coordinates

Cited by 54 publications

References 16 publications

Unified Model Studies of N = 84 and N = 80 Nuclei

Unified Model Studies of N = 84 and N = 80 Nuclei

Solutions of the Bohr Hamiltonian, a compendium

Construction of basis vectors for symmetric irreducible representations of O(5) $ \supset$ O(3)

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