1990
DOI: 10.1007/bf01294470
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Application of a time-dependent density-matrix formalism

Abstract: An extended time-dependent Hartree-Fock theory which includes the effects of nucleonnucleon collisions is presented and applied to the small-amplitude quadrupole motions of 160 and 4~The collision term of the theory includes not only the Born term but also higher-order terms. It is found that the higher-order terms are essential to the damping of the motions.

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Cited by 47 publications
(112 citation statements)
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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%
“…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%
“…(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%
“…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%