Deformation and cluster structures in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mrow /><mml:mn>12</mml:mn></mml:msup></mml:math>C studied with configuration mixing using Skyrme interactions

Fukuoka, Yoshiyuki; Shinohara, Shuichi; Funaki, Y.; Nakatsukasa, Takashi; Yabana, Kazuhiro

doi:10.1103/physrevc.88.014321

Cited by 36 publications

(43 citation statements)

References 45 publications

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“…A similar discrepancy was found in Ref. [68] in the case of 12 C. There, it has been argued that the spreading of the collective wave function on many deformations creates a too large smoothing of the one-body density and decreases the weights of the large-q components of the transition density. In the case of 12 C, the pure HF form factor was slightly in better agreement with the data.…”

Section: Illustrative Application To 24 Mgsupporting

confidence: 79%

“…For a better description of low-lying excited states in spherical even-even nuclei, it would be desirable to add noncollective timereversal-breaking n-quasiparticle states to the GCM basis. [58][59][60][61][62][63][64][65][66][67][68] Ni, in comparison with available data [9]. [58][59][60][61][62][63][64][65][66][67][68] Ni, in comparison with available data, taken from Ref.…”

Section: Discussionmentioning

confidence: 96%

“…Similar developments based on an angular-momentum and parity-projected GCM with (nonpaired) HF states, also using Skyrme interactions, have been recently reported in Ref. [68], but the calculations were limited to the simple case of elastic and inelastic transitions between 0 + states.…”

Section: Introductionmentioning

confidence: 84%

“…The shell-model description of this Ni isotope, and also of all others up to 68 Ni, shows that a correct reproduction of both energies and B(E2) values of the low-lying states requires the inclusion of the full fp shell (see the discussion in Ref. [93]).…”

Section: Application To Even-mass 58-68 Nimentioning

confidence: 94%

“…III, we present an illustrative calculation of both elastic and inelastic scattering form factors for 24 Mg. Section IV details an application to the transition densities in even-mass [58][59][60][61][62][63][64][65][66][67][68] Ni. The static and dynamic deformation effects on nuclear charge densities, transition charge densities, and form factors will be discussed in detail.…”

Section: Introductionmentioning

confidence: 99%

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Beyond-mean-field study of elastic and inelastic electron scattering off nuclei

2015

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Background: Electron scattering provides a powerful tool to determine charge distributions and transition densities of nuclei. This tool will soon be available for short-lived neutron-rich nuclei. Purpose: Beyond-mean-field methods have been successfully applied to the study of excitation spectra of nuclei in the whole nuclear chart. These methods permit determination of energies and transition probabilities starting from an effective in-medium nucleon-nucleon interaction but without other phenomenological ingredients. Such a method has recently been extended to calculate the charge density of nuclei deformed at the mean-field level of approximation [J. M. Yao et al., Phys. Rev. C 86, 014310 (2012)]. The aim of this work is to further extend the method to the determination of transition densities between low-lying excited states. Method: The starting point of our method is a set of Hartree-Fock-Bogoliubov wave functions generated with a constraint on the axial quadrupole moment and using a Skyrme energy density functional. Correlations beyond the mean field are introduced by projecting mean-field wave functions on angular momentum and particle number and by mixing the symmetry-restored wave functions. Results: We give in this paper detailed formulas derived for the calculation of densities and form factors. These formulas are rather easy to obtain when both initial and final states are 0 + states but are far from being trivial when one of the states has a finite J value. Illustrative applications to 24 Mg and to the even-mass 58-68 Ni have permitted an analysis of the main features of our method, in particular the effect of deformation on densities and form factors. An illustrative calculation of both elastic and inelastic scattering form factors is presented. Conclusions: We present a very general framework to calculate densities of and transition densities between low-lying states that can be applied to any nucleus. Achieving better agreement with the experimental data will require improving the energy density functionals that are currently used and also introducing quasiparticle excitations in the mean-field wave functions.The reduced transition density ρ J f μ f J i μ i ,L (r) with angular momentum transfer L is therefore given byBy substituting the expression for ρ α f α i (r) into Eqs. (A8)-(A10), one finds as an expression for the reduced transition density024301-14 BEYOND-MEAN-FIELD STUDY OF ELASTIC AND . . . PHYSICAL REVIEW C 91, 024301 (2015) With the help of the orthogonality relation of spherical harmonics, dr Y LM (r) Y λν (r) = (−1) −M δ Lλ δ M−ν , and the symmetry relation J f M f L − M|J i M i = (−1) 2L−M+J i −J f J î J f J i M i LM|J f M f of the Clebsch-Gordan coefficients, the reduced transition density can be simplified to ρ J f μ f J i μ i ,L (r) = (−1) J i −J fĴ 2 f J 2

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Section: Illustrative Application To 24 Mgsupporting

confidence: 79%

Section: Discussionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 84%

Section: Application To Even-mass 58-68 Nimentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

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Beyond-mean-field study of elastic and inelastic electron scattering off nuclei

2015

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Collective-subspace requantization for sub-barrier fusion reactions: Inertial functions for collective motions

Ruike,

Wen,

Hinohara

et al. 2024

EPJ Web Conf.

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The adiabatic self-consistent collective coordinate (ASCC) method is used to determine the optimum reaction path and to calculate the potential and the inertial functions of the reaction model. The properties of the inertial functions are investigated with the ASCC method, in comparison with those of the cranking formulae. In addition, the properties of the pair rotation are investigated in the BCS pair model. The moments of inertia for rotation in both the real and the gauge spaces may decrease as the deformation develops.

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Non-empirical description of nuclear collective motion with optimized basis for multi-reference density functional theory

Matsumoto,

Tanimura,

Hagino

2024

EPJ Web Conf.

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The generator coordinate method (GCM) has been a well-known method to describe nuclear collective motions. In this method, one a priori specifies collective degrees of freedom as inputs of the method based on empirical and/or phenomenological assumptions. We here present an extension of the GCM, in which both the basis Slater determinants and weight factors are optimized in a non-empirical manner. The result for 16O nucleus with the Skyrme functional suggests that a collective coordinate should be determined in a more complex way than what has been assumed so far.

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Deformation and cluster structures in12C studied with configuration mixing using Skyrme interactions

Cited by 36 publications

References 45 publications

Beyond-mean-field study of elastic and inelastic electron scattering off nuclei

Beyond-mean-field study of elastic and inelastic electron scattering off nuclei

Collective-subspace requantization for sub-barrier fusion reactions: Inertial functions for collective motions

Non-empirical description of nuclear collective motion with optimized basis for multi-reference density functional theory

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