The many relationships between the IBM and the Bohr model

Rowe, D.J.; Thiamová, G.

doi:10.1016/j.nuclphysa.2005.06.001

Cited by 53 publications

(59 citation statements)

References 56 publications

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“…[15,[43][44][45][46] and has been used in the study of phase transitions. This concept is very useful for working with Hamiltonians that present two dynamical symmetries (depending on the value of a control parameter) as limits.…”

Section: Quasidynamical Symmetriesmentioning

confidence: 99%

Relation betweenE(5)models and the interacting boson model

García‐Ramos

Arias

2008

Phys. Rev. C

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The connections between the E(5) models [the original E(5) using an infinite square well, E(5)-β 4 , E(5)-β 6 , and E(5)-β 8 ], based on particular solutions of the geometrical Bohr Hamiltonian with γ -unstable potentials, and the interacting boson model (IBM) are explored. For that purpose, the general IBM Hamiltonian for the U(5)-O(6) transition line is used and a numerical fit to the different E(5) models energies is performed, later on the obtained wave functions are used to calculate B(E2) transition rates. It is shown that within the IBM one can reproduce very well all these E(5) models. The agreement is the best for E(5)-β 4 and reduces when passing through E(5)-β 6 , E(5)-β 8 , and E(5), where the worst agreement is obtained (although still very good for a restricted set of lowest-lying states). The fitted IBM Hamiltonians correspond to energy surfaces close to those expected for the critical point. A phenomenon similar to the quasidynamical symmetry is observed.

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Section: Quasidynamical Symmetriesmentioning

confidence: 99%

Relation betweenE(5)models and the interacting boson model

García‐Ramos

Arias

2008

Phys. Rev. C

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“…According to the concept of quasidynamical symmetry [22][23][24][25][26], the system described by the consistent-Q Hamiltonian (1) remains in the U(5) phase until the control parameter reaches the critical point. Since the EXT is only used to describe the phase transition from the U(5) phase to the E(5)-like critical point in the IBM, this is what we intend here as well.…”

Section: Fit To the E(5) Resultsmentioning

confidence: 99%

“…in which E (ζ ) τ,L is the ζ -th eigen-energy for given τ and L. To show that (24) and (25) are indeed consistent, one may directly apply the Hamiltonian (20) on the N-particle state (24) to establish the eigen-equationĤ c |N,…”

Section: A Solvable Hamiltonian Near the U(5)-o(6) Critical Pointmentioning

confidence: 99%

Alternative solvable description of the E(5) critical point symmetry in the interacting boson model

Pan

et al. 2015

Phys. Rev. C

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A solvable extended Hamiltonian that includes multi-pair interactions among s-and d-bosons up to infinite order within the framework of the interacting boson model is proposed to gain a better description of E(5) model results for finite-N systems. Numerical fits to low-lying energy levels and reduced E2 transition rates within this extended version of the theory are presented for various N values. It shows that the extended Hamiltonian within the IBM provides a better description of the E(5) model results for small N cases, while the results of the model in the large-N cases are close to those of the E(5)-β 2n type models studied previously.

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“…Algebraic collective model methods have already been applied [13] to calculation of collective states within the SO(6) limit of the IBM. The availability SO(5) ⊃ SO(3) Clebsch-Gordan coefficients enables such studies to be enhanced and extended.…”

Section: Resultsmentioning

confidence: 99%

Construction of spherical harmonics and Clebsch–Gordan coefficients

Caprio

Rowe

Welsh

2009

Computer Physics Communications

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The SO(5) ⊃ SO(3) spherical harmonics form a natural basis for expansion of nuclear collective model angular wave functions. They underlie the recently-proposed algebraic method for diagonalization of the nuclear collective model Hamiltonian in an SU(1, 1) × SO(5) basis. We present a computer code for explicit construction of the SO(5) ⊃ SO(3) spherical harmonics and use them to compute the Clebsch-Gordan coefficients needed for collective model calculations in an SO(3)-coupled basis. With these Clebsch-Gordan coefficients it becomes possible to compute the matrix elements of collective model observables by purely algebraic methods. Program Summary Title of program: GammaHarmonic

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The many relationships between the IBM and the Bohr model

Cited by 53 publications

References 56 publications

Relation betweenE(5)models and the interacting boson model

Relation betweenE(5)models and the interacting boson model

Alternative solvable description of the E(5) critical point symmetry in the interacting boson model

Construction of spherical harmonics and Clebsch–Gordan coefficients

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