Application of a time-dependent density-matrix formalism

Gong, Mengyuan; Tohyama, Mitsuru

doi:10.1007/bf01294470

Cited by 46 publications

(112 citation statements)

References 29 publications

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“…In any case, the present results by TDHF+GEMINI suggest that, in order to fully reproduce experimental cross sections for MNT processes, one should extend the theoretical framework that goes beyond the TDHF theory: e.g. a variational method of Balian and Vénéroni [54,58], stochastic mean-field theory (SMF) [86,87], time-dependent density matrix theory (TDDM) [88][89][90][91], time-dependent generator coordinate method (TDGCM) [92,93], multiconfiguration TDHF (MCTDHF) [94,95], and so forth.…”

Section: Resultsmentioning

confidence: 99%

Microscopic description of production cross sections including deexcitation effects

Sekizawa

2017

Phys. Rev. C

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Background: At the forefront of the nuclear science, production of new neutron-rich isotopes is continuously pursued at accelerator laboratories all over the world. To explore the currently-unknown territories in the nuclear chart far away from the stability, reliable theoretical predictions are inevitable.Purpose: To provide a reliable prediction of production cross sections taking into account secondary deexcitation processes, both particle evaporation and fission, a new method called TDHF+GEMINI is proposed, which combines the microscopic time-dependent Hartree-Fock (TDHF) theory with a sophisticated statistical compoundnucleus deexcitation model, GEMINI++.Methods: Low-energy heavy ion reactions are described based on three-dimensional Skyrme-TDHF calculations. Using particle-number projection method, production probabilities, total angular momenta, and excitation energies of primary reaction products are extracted from the TDHF wavefunction after collision. Production cross sections for secondary reaction products are evaluated employing GEMINI++. Results are compared with available experimental data and widely-used GRAZING calculations. Results:The method is applied to describe cross sections for multinucleon transfer processes in MeV) reactions at energies close to the Coulomb barrier. It is shown that the inclusion of secondary deexcitation processes, which are dominated by neutron evaporation in the present systems, substantially improves agreement with the experimental data. The magnitude of the evaporation effects is very similar to the one observed in GRAZING calculations. TDHF+GEMINI provides better description of the absolute value of the cross sections for channels involving transfer of more than one protons, compared to the GRAZING results. However, there remain discrepancies between the measurements and the calculated cross sections, indicating a limit of the theoretical framework that works with a single mean-field potential. Possible causes of the discrepancies are discussed. Conclusions:In order to perfectly reproduce experimental cross sections for multinucleon transfer processes, one should go beyond the standard self-consistent mean-field description. Nevertheless, the proposed method will provide valuable information to optimize production mechanisms of new neutron-rich nuclei through its microscopic, non-empirical predictions.

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Section: Resultsmentioning

confidence: 99%

Microscopic description of production cross sections including deexcitation effects

Sekizawa

2017

Phys. Rev. C

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“…(7) are given in Appendix A. The equation for C αβα ′ β ′ without S αβα ′ β ′ and T αβα ′ β ′ are the same as that in TDDM [14]. Since the total wavefunction |Φ(t) is not an eigenstate of the number operator, the couplings to κ αβ and K αβγ:α ′ appear in Eq.…”

Section: Formulation a Etdhfb Equationsmentioning

confidence: 99%

“…We formulate the extended TDHFB (ETDHFB) using a truncation scheme similar to that used in the time-dependent density-matrix theory (TDDM) in the normal-fluid regime [13,14], where higher-order reduced density matrices are approximated by lower-order density matrices to truncate the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for reduced density matrices. TDDM has in the past demonstrated its effectiveness in various applications [14][15][16] and it can reasonably be assumed that its extension to the superfluid case will show equally good performance. The advantages of ETDHFB are that it has a direct connection to TDHFB and that various correction terms are expressed explicitly, contrary to Monte Carlo approaches.…”

Section: Introductionmentioning

confidence: 99%

Extension of time-dependent Hartree-Fock-Bogoliubov equations

Tohyama

Schuck

2015

Phys. Rev. C

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An extension of the time-dependent Hartree-Fock-Bogoliubov theory (ETDHFB) which includes higher-order effects such as screening of the pairing correlation is proposed. ETDHFB is applied to a fermion system trapped in a harmonic potential to test its feasability by comparison with the exact solution. With the use of perturbative expressions for the pairing tensor and the two-body density matrix derived from ETDHFB, the screening effect is investigated for atomic fermion systems and isotopes of tin nuclei. It is found that the screening effect on the pairing correlation is not significant.

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“…TDDM gives the time-evolution of the one-body density-matrix ρ and the correlated part C 2 of a two-body densitymatrix [4,15], and STDDM has been formulated by linearizing the equations of motion for ρ and C 2 [9]. The equations of STDDM for the one-body amplitude x αα ′ (µ) and the two-body amplitude X α1α2α ′ 1 α ′ 2 (µ) can be written in matrix form [10] a c b d…”

Section: Small Amplitude Limit Of Tddmmentioning

confidence: 99%

“…Introducing a pairing field, HFB and QRPA deal with pairing correlations in the framework of a mean field theory. In contrast to HFB and QRPA, the time-dependent density-matrix theory (TDDM) [4], which is one of extended time-dependent Hartree-Fock theories, deals with groundstate correlations as genuine two-body correlations. TDDM has been applied to giant resonances in stable nuclei [5,6] and also to low-lying collective states in unstable nuclei [7,8].…”

Section: Introductionmentioning

confidence: 99%

Extended RPA with ground-state correlations

2004

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We propose a time-independent method for finding a correlated ground state of an extended timedependent Hartree-Fock theory, known as the time-dependent density-matrix theory (TDDM). The correlated ground state is used to formulate the small amplitude limit of TDDM (STDDM) which is a version of extended RPA theories with ground-state correlations. To demonstrate the feasibility of the method, we calculate the ground state of 22 O and study the first 2 + state and its two-phonon states using STDDM.

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Application of a time-dependent density-matrix formalism

Cited by 46 publications

References 29 publications

Microscopic description of production cross sections including deexcitation effects

Microscopic description of production cross sections including deexcitation effects

Extension of time-dependent Hartree-Fock-Bogoliubov equations

Extended RPA with ground-state correlations

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