Classical theory of collective motion in the large amplitude, small velocity regime

Klein, Abraham; Walet, Niels R.; Dang, G. Do

doi:10.1016/0003-4916(91)90343-7

Cited by 47 publications

(96 citation statements)

References 78 publications

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“…II B, the collective coordinate q is mapped onto the relative distance R ≡ ψ(q)|R|ψ(q) with Eq. (18). Figure 4 shows the obtained potential energy along the ASCC collective path.…”

Section: Collective Path Potential and Inertial Massmentioning

confidence: 99%

“…The ASCC provides an alternative practical solution to the SCC [19]: The state is determined at each value of q by solving the equation expanded up to the second order in p. The ASCC method has been successfully applied to nuclear structure problems with large-amplitude shape fluctuations/oscillations for the Hamiltonian of the separable interactions [3,[22][23][24][25][26][27][28]. It should be noted that a solution to the non-uniqueness problem of the ATDHF was given by higher-order equations with respect to momenta [17,18], which are similar to the ASCC equations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Self-consistent collective coordinate for reaction path and inertial mass

Wen¹,

Nakatsukasa²

2016

Phys. Rev. C

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We propose a numerical method to determine the optimal collective reaction path for the nucleusnucleus collision, based on the adiabatic self-consistent collective coordinate (ASCC) method. We use an iterative method combining the imaginary-time evolution and the finite amplitude method, for the solution of the ASCC coupled equations. It is applied to the simplest case, the α − α scattering. We determine the collective path, the potential, and the inertial mass. The results are compared with other methods, such as the constrained Hartree-Fock method, the Inglis's cranking formula, and the adiabatic time-dependent Hartree-Fock (ATDHF) method.

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“…II B, the collective coordinate q is mapped onto the relative distance R ≡ ψ(q)|R|ψ(q) with Eq. (18). Figure 4 shows the obtained potential energy along the ASCC collective path.…”

Section: Collective Path Potential and Inertial Massmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Self-consistent collective coordinate for reaction path and inertial mass

Wen¹,

Nakatsukasa²

2016

Phys. Rev. C

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“…A systematic theory for an optimized collective path is provided by adiabatic TDHF (ATDHF) [32,33,34]. The overwhelming majority of practical applications simplifies the construction by using a simple quadrupole constraint Hartree-Fock to produce the |Φ q .…”

Section: B Deduced Collective Dynamicsmentioning

confidence: 99%

“…The positive aspect is that the theoretical results come so close at all in view of the fact that the transition strengths are always much more demanding. The remaining mismatch can have various origins: 1) We use simply a quadrupole constraint to generate the collective path instead of the variationally optimized ATDHF prescription [32,33,34]. 2) We use the raw quadrupole expectation value rather than the fully mapped collective image (see appendix A 6).…”

Section: Variation Of Forcesmentioning

confidence: 99%

Skyrme energy functional and low lying2+states in Sn, Cd, and Te isotopes

et al. 2004

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We study the predictive power of Skyrme forces with respect to low lying quadrupole spectra along the chains of Sn, Cd, and Te isotopes. Excitation energies and B(E2) values for the lowest quadrupole states are computed from a collective Schrödinger equation which as deduced through collective path generated by constraint Skyrme-Hartree-Fock (SHF) plus self-consistent cranking for the dynamical response. We compare the results from four different Skyrme forces, all treated with two different pairing forces (volume versus density-dependent pairing). The region around the neutron shell closure N = 82 is very sensitive to changes in the Skyrme while the mid-shell isotopes in the region N < 82 depend mainly on the adjustment of pairing. The neutron rich isotopes are most sensitive and depend on both aspects.

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“…In the case of a single collective coordinate (K = 1), the equations can be written as [2] V ,α = λf…”

Section: Theorymentioning

confidence: 99%