Nuclear deformations in the pairing-plus-quadrupole model

Kumar, Krishna; Baranger, Michel

doi:10.1016/0375-9474(68)90045-6

Cited by 353 publications

(76 citation statements)

References 25 publications

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“…Baranger and Kumar analyzed in great detail the (adiabatic) collective motion in the P+Q model assuming that the collective variables are the mass quadrupole operators [1][2][3][4][5]. Thus, they reduced the large number of two-quasiparticle (2qp) degrees of freedom (of the order of thousands) into only two collective coordinates, β and γ.…”

Section: Cranking Operators In the Pairing-plus-quadrupole Modelmentioning

confidence: 99%

“…To be specific, consider the quadrupole degrees of freedom studied in the Kumar-Baranger theory [1][2][3][4][5]. For this and for more modern applications, the latter has been replaced by a two-step procedure [88,89].…”

Section: A Survey Of Literaturementioning

confidence: 99%

“…Historically, it was the first of the problems cited that called attention to the need for a deeper theory than the one that was first applied (successfully) to its solution. We refer here to the work of Kumar and Baranger [1][2][3][4][5], that we judge to be the first successful calculations, starting from a many-body Hamiltonian, of the low-energy rotations and quadrupole vibrations of deformed nuclei. The main features of this work are:…”

Section: Introduction a Why Was This Review Written?mentioning

confidence: 99%

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Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

2000

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The goal of the present account is to review our efforts to obtain and apply a "collective" Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of freedom. The approach is based on an analysis of the classical limit of quantum-mechanical problems. Initially, we study the classical problem within the framework of Hamiltonian dynamics and derive a fully self-consistent theory of large amplitude collective motion with small velocities. We derive a measure for the quality of decoupling of the collective degree of freedom. We show for several simple examples, where the classical limit is obvious, that when decoupling is good, a quantization of the collective Hamiltonian leads to accurate descriptions of the low energy properties of the systems studied. In nuclear physics problems we construct the classical Hamiltonian by means of time-dependent mean-field theory, and we transcribe our formalism to this case. We report studies of a model for monopole vibrations, of 28 Si with a realistic interaction, several qualitative models of heavier nuclei, and preliminary results for a more realistic approach to heavy nuclei. Other * Email: Giu.Dodang@th.u-psud.fr † Email: aklein@walet.physics.upenn.edu ‡ Email: Niels.Walet@umist.ac.uk 1 topics included are a nuclear Born-Oppenheimer approximation for an ab initio quantum theory and a theory of the transfer of energy between collective and non-collective degrees of freedom when the decoupling is not exact. The explicit account is based on the work of the authors, but a thorough survey of other work is included. PACS number(s): 21.60.-n, 21.60.Jz, 21.60.Ev

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Section: Cranking Operators In the Pairing-plus-quadrupole Modelmentioning

confidence: 99%

Section: A Survey Of Literaturementioning

confidence: 99%

Section: Introduction a Why Was This Review Written?mentioning

confidence: 99%

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Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

2000

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“…The prolate-to-oblate transition in Pt, as well as in Os and W nuclei, has been observed in a recent experiment [50], where a relatively moderate oblate-to-prolate shape/phase transition occurs in Pt as compared to Os and W nuclei. Spectroscopic calculations have been carried out for Pt isotopes in the framework of the five-dimensional collective Hamiltonian, derived from the pairing-plus-quadrupole model [51]. Evidence for γ vibrations and shape evolution in 184−190 Hg has been considered in Ref.…”

Section: Introductionmentioning

confidence: 99%

Structural evolution in Pt isotopes with the interacting boson model Hamiltonian derived from the Gogny energy density functional

et al. 2011

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Spectroscopic calculations are carried out for the description of the shape/phase transition in Pt nuclei in terms of the interacting boson model (IBM) Hamiltonian derived from (constrained) Hartree-Fock-Bogoliubov (HFB) calculations with the finite range and density-dependent Gogny-D1S energy density functional. Assuming that the many-nucleon driven dynamics of nuclear surface deformation can be simulated by effective bosonic degrees of freedom, the Gogny-D1S potential energy surface (PES) with quadrupole degrees of freedom is mapped onto the corresponding PES of the IBM. By using this mapping procedure, the parameters of the IBM Hamiltonian, relevant to the low-lying quadrupole collective states, are derived as functions of the number of valence nucleons. Merits of both Gogny-HFB and IBM approaches are utilized so that the spectra and the wave functions in the laboratory system are calculated precisely. The experimental low-lying spectra of both ground-state and sideband levels are well reproduced. From the systematics of the calculated spectra and the reduced E2 transition probabilities B(E2), the prolate-to-oblate shape/phase transition is shown to take place quite smoothly as a function of neutron number N in the considered Pt isotopic chain, for which the γ softness plays an essential role. All of these spectroscopic observables behave consistently with the relevant PES and the derived parameters of the IBM Hamiltonian as functions of N . Spectroscopic predictions are also made for those nuclei that do not have enough experimental E2 data.

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“…The GOA has often been used in the past to derive the ingredients of a collective Bohr Hamiltonian in the spirit of the work of Kumar and Baranger [12]. It is supplemented by several other approximations [2,13].…”

Section: Introductionmentioning

confidence: 99%

Correlation energies by the generator coordinate method: Computational aspects for quadrupolar deformations

2004

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We investigate truncation schemes to reduce the computational cost of calculating correlations by the generator coordinate method based on mean-field wave functions. As our test nuclei, we take examples for which accurate calculations are available. These include a strongly deformed nucleus, 156 Sm, a nucleus with strong pairing, 120 Sn, the krypton isotope chain which contains examples of soft deformations, and the lead isotope chain which includes the doubly magic 208 Pb. We find that the Gaussian overlap approximation for angular momentum projection is effective and reduces the computational cost by an order of magnitude. Cost savings in the deformation degrees of freedom are harder to realize. A straightforward Gaussian overlap approximation can be applied rather reliably to angular-momentum projected states based on configuration sets having the same sign deformation (prolate or oblate), but matrix elements between prolate and oblate deformations must be treated with more care. We propose a two-dimensional GOA using a triangulation procedure to treat the general case with both kinds of deformation. With the computational gains from these approximations, it should be feasible to carry out a systematic calculation of correlation energies for the nuclear mass table.

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Nuclear deformations in the pairing-plus-quadrupole model

Cited by 353 publications

References 25 publications

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

Structural evolution in Pt isotopes with the interacting boson model Hamiltonian derived from the Gogny energy density functional

Correlation energies by the generator coordinate method: Computational aspects for quadrupolar deformations

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