Projected spectra of light nuclei with Skyrme interactions

Caurier, E.; Grammaticos, B.

doi:10.1016/0375-9474(77)90232-9

Cited by 26 publications

(6 citation statements)

References 12 publications

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“…Similarly good results are also attained for the p_ 12 C system in our treatment. Note that in this system, some portion of the flux outgoes to the inelastic channel from the elastic above the inelastic threshold E 1ab = 4.8 Me V. As our numerical results in Fig.…”

Section: Phase Shifts and Bound State Energiessupporting

confidence: 81%

“…4 ) Viewing this situation, we use the Skyrme potential in the analysis of elastic nucleon scattering from 12C. In this nucleon-12 C system (N _ 12 C), several resonances of positive parity have been well resolved experimentally in the low energy region, and in addition, properties of positive parity bound states have also been well determined experimentally in the neutron-12C system (n_ 12 …”

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confidence: 99%

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The Skyrme Potential and Elastic Nucleon Scattering from 12C

Kobayashi¹

1983

Progress of Theoretical Physics

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It is investigated whether the Skyrme potential is applicable for the microscopic coupled channels analysis of nucleon-12 C scattering in the resonance energy region. After studying carefully the conformity between our microscopic treatment and the phenomenological model, we carried out the numerical analysis of the nucleon-12 C system, replacing the phenomenological coupling potential form factor by the microscopic one in the phenomenological coupled channels equations. Satisfactory agreements were obtained between theory and experiment. It is concluded that the microscopic coupling potentia! form factor constructed from the Skyrme potential yields correct effects of the coupling between the target ground and excited states.*) This work is based on a

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Section: Phase Shifts and Bound State Energiessupporting

confidence: 81%

mentioning

confidence: 99%

The Skyrme Potential and Elastic Nucleon Scattering from 12C

Kobayashi¹

1983

Progress of Theoretical Physics

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“…Several methods have been developed for schematic nuclear interactions and a limited number of active valence nucleons (for recent references, see [12,13]). Methods based on effective interactions have been limited to either angular momentum [14][15][16] or particle number projection with mixing of configurations by the generator coordinate method (GCM) [17]. The present work generalizes this last work by the inclusion of a projection on angular momentum.…”

Section: Introductionmentioning

confidence: 95%

Configuration mixing of mean-field wave functions projected on angular momentum and particle number: Application to Mg

Valor¹,

Heenen²,

Bonche³

2000

Nuclear Physics A

114

148

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We present in this paper the general framework of a method which permits to restore the rotational and particle number symmetries of wave functions obtained in Skyrme HF+BCS calculations. This restoration is nothing but a projection of mean-field intrinsic wave functions onto good particle number and good angular momentum. The method allows also to mix projected wave functions. Such a configuration mixing is discussed for sets of HF+BCS intrinsic states generated in constrained calculations with suitable collective variables. This procedure gives collective states which are eigenstates of the particle number and the angular momentum operators and between which transition probabilities are calculated. An application to 24 Mg is presented, with mean-field wave functions generated by axial quadrupole constraints. Theoretical spectra and transition probabilities are compared to the experiment.

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“…The first application of symmetry restoration with an EDF possibly dates back to a work of Caurier and Grammaticos (Caurier and Grammaticos, 1977) where the projected spectrum of light nuclei was computed using several flavors of the Skyrme interaction. The limitation to light nuclei and small configuration spaces as well as the success of the mean-field approach over the whole nuclear periodic chart are the most likely reasons why this approach only become popular a couple of decades later.…”

Section: Non Relativistic Edfsmentioning

confidence: 99%

“…Angular momentum projection of triaxial intrinsic states was first carried out in an early work by Caurier and Grammaticos (Caurier and Grammaticos, 1977) with the Skyrme SIII interaction. A restricted variation after projection was used with the radii and quadrupole moments as variational quantities.…”

Section: Non Relativistic Edfsmentioning

confidence: 99%

Symmetry restoration in mean-field approaches

Sheikh,

Dobaczewski,

Ring

et al. 2019

Preprint

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The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Examples are strongly interacting atomic nuclei and mesoscopic condensed matter systems. In this approach, the linear Schrodinger equation for the exact many-body wave function is mapped onto a non-linear density-dependent one-body potential problem. This approximation, not only provides computationally very simple solutions even for systems with many particles, but due to the non-linearity, it also allows for obtaining solutions that break essential symmetries of the system, often connected with phase transitions. However, mean-field approach suffers from the drawback that the corresponding wave functions do not have sharp quantum numbers and, therefore, many results cannot be compared directly with experimental data. In this article, we discuss general group theoretical techniques to restore the broken symmetries, and provide detailed expressions on the restoration of translational, rotational, spin, isospin, parity and gauge symmetries, where the latter corresponds to the restoration of the particle number. In order to avoid the numerical complexity of exact projection techniques, various approximation methods available in the literature are examined. We present applications of the projection methods to simple nuclear models, realistic calculations in relatively small configuration spaces, nuclear energy density functional theory, as well as in other mesoscopic systems. We also discuss applications of projection techniques to quantum statistics in order to treat the averaging over restricted ensembles with fixed quantum numbers. Further, unresolved problems in the application of the symmetry restoration methods to the energy density functional theories are highlighted. CONTENTSL. Other electronic systems 60 M. Other emerging directions 60 VIII. Projected statistics 61 A. Symmetry restoration at finite temperature 62 B. Thermo-field dynamics 63 IX. Summary, conclusions, and perspectives 63 X. Acknowledgments 64 A. Overlaps and matrix elements between HFB states: the generalized Wick's theorem 65

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Projected spectra of light nuclei with Skyrme interactions

Cited by 26 publications

References 12 publications

The Skyrme Potential and Elastic Nucleon Scattering from 12C

The Skyrme Potential and Elastic Nucleon Scattering from 12C

Configuration mixing of mean-field wave functions projected on angular momentum and particle number: Application to Mg

Symmetry restoration in mean-field approaches

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