Generator coordinate calculations on 28Si

Pelet, J.; Letourneux, J.

doi:10.1016/0375-9474(77)90026-4

Cited by 17 publications

(10 citation statements)

References 17 publications

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“…In turn, given this basis, the local harmonic equation determines f ph . If we neglect the affine connection we obtain a set of equations that is very close to the set derived in the Holzwarth-Yukawa formalism [71] by Pelet and Letourneux, [69,70], the only difference being that we use RPA where they use a further approximation, the TDA (Tamm-Dancoff approximation) [6].…”

Section: Equations Of the Local Harmonic Formulationsupporting

confidence: 55%

“…Furthermore, following Pelet [69,70] we impose "ellipsoidal" symmetry, i.e., we require the intrinsic nuclear shape to be invariant under a rotation of 180 degrees about any of the three symmetry axes. It is well known [72] that such a symmetry requires that K, the projection of the angular momentum on the intrinsic z-axis is even and also relates wavefunction components with positive K to those with negative K. In the latter regard, it duplicates the function of time reversal invariance, which for static solutions of the Hartree-Fock problem for even nuclei already implies that any pair of time-reversed orbits is either occupied or unoccupied.…”

Section: Symmetriesmentioning

confidence: 99%

“…Unfortunately this appears to rule out simple separable interactions (such as the quadrupole-quadrupole interaction), at least for 28 Si. Furthermore, for this nucleus we can compare our calculation with the only existing application to a bound system [69,70] of a "competing" self-consistent theory of large amplitude collective motion [71].…”

Section: Introductionmentioning

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: Equations Of the Local Harmonic Formulationsupporting

confidence: 55%

Section: Symmetriesmentioning

confidence: 99%

Section: Introductionmentioning

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 low-lying K = 2 band built on top of the 2 + 2 state suggests that the triaxial degree of freedom is activated in the collective dynamics. In 28 Si, importance of triaxiality has been suggested in connection with the large-amplitude collective dynamics of the oblate-prolate shape coexistence [10,11].…”

Section: Introductionmentioning

confidence: 99%

Triaxial quadrupole deformation dynamics insd-shell nuclei aroundMg26

Hinohara

Kanada-En’yo

2011

Phys. Rev. C

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Large-amplitude dynamics of axial and triaxial quadrupole deformation in 24,26 Mg, 24 Ne, and 28 Si is investigated on the basis of the quadrupole collective Hamiltonian constructed with use of the constrained Hartree-Fock-Bogoliubov plus the local quasiparticle random-phase approximation method. The calculation reproduces well properties of the ground rotational bands, and β and γ vibrations in 24 Mg and 28 Si. The γ-softness in the collective states of 26 Mg and 24 Ne are discussed. Contributions of the neutrons and protons to the transition properties are also analyzed in connection with the large-amplitude quadrupole dynamics.

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“…This means that we can restrict the RPA diagonalisation to this small space, rather than deal with the full millions-by-millions RPA matrix. Such a scenario has been examined in reference [4] and in reference [5] for the HF problem in 28 Si, and a strong radial and spin dependence of self-consistent cranking operators was found. However, since the model space had only six degrees of freedom and the pairing degrees of freedom were neglected, the results can not be directly generalised to heavy nuclei.…”

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confidence: 99%

A basis of cranking operators for the pairing-plus-quadrupole model

Nakatsukasa

Walet

Dang

1999

J. Phys. G: Nucl. Part. Phys.

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Abstract. We investigate the RPA normal-mode coordinates in the pairingplus-quadrupole model, with an eye on simplifying the application of large amplitude collective motion techniques. At the Hartree-Bogoliubov minimum, the RPA modes are exactly the cranking operators of the collective coordinate approach. We examine the possibility of representing the self-consistent cranking operator by linear combinations of a limited number of one-body operators. We study the Sm nuclei as an example, and find that such representations exist in terms of operators that are state-dependent in a characteristic manner. The selection of proper collective variables is an important problem in the study of large amplitude collective motion. In the usual Constrained Hartree-Fock (CHF) or Hartree-Fock-Bogoliubov (CHFB) calculations, the collective subspaces are generated by a small number of one-body constraint (also called cranking) operators which are most commonly taken to be of the multipole form (r L Y LK ). In realistic calculations of processes such as fission, the number of coordinates to describe the full nuclear dynamics can easily become larger than can be dealt with in satisfactory manner, and a method to determine the optimal combination needs to be devised. Even assuming that such a method exists, there is no a priori reason to limit oneself to multipole operators, and the cranking operators should be determined by the nuclear collective dynamics itself, from the set of all one-body operators. This is clearly a difficult task, and one would like to be able to select a small group of operators, and find the optimal combination of these operators at each point of the collective surface.In our past work, we have investigated a theory of adiabatic large amplitude collective motion as a method to generate self-consistent collective subspaces (see reference [1] and references therein). The key ingredient of the method is the selfconsistent determination of the constraint operator, and as such it may provide an answer to the selection question discussed above. Using the local harmonic version (LHA) of the theory [1], we have recently embarked on a study of the properties of large amplitude collective motion in systems with pairing. We have dealt with two simple models: a semi-microscopic model of nucleons interacting through a pairing force, coupled to a single harmonic variable [2] and a fully microscopic O(4) model which may § Electronic address: T.Nakatsukasa@umist.ac.ukElectronic address: Niels.Walet@umist.ac.uk ¶ Electronic address: Giu.Dodang@th.u-psud.fr

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Generator coordinate calculations on 28Si

Cited by 17 publications

References 17 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

Triaxial quadrupole deformation dynamics insd-shell nuclei aroundMg26

A basis of cranking operators for the pairing-plus-quadrupole model

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