Nuclear ground states in the random phase approximation

Sanderson, E.A.

doi:10.1016/0031-9163(65)90751-1

Cited by 92 publications

(28 citation statements)

References 9 publications

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“…[112], 84) where N is a real normalization factor, whose value we shall not need, a i |0] = 0, and Z ij is a generally complex array whose role will be considered in more detail below. Using the constancy of the norm of the correlated ground state as a function of the values of Q, we can rewrite (5.83) as 85) which shows that the derivative of the (real) normalization factor N does not contribute.…”

Section: Model With Berry Phase In Excited Statesmentioning

confidence: 99%

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

2000

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The goal of the present account is to review our efforts to obtain and apply a "collective" Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of freedom. The approach is based on an analysis of the classical limit of quantum-mechanical problems. Initially, we study the classical problem within the framework of Hamiltonian dynamics and derive a fully self-consistent theory of large amplitude collective motion with small velocities. We derive a measure for the quality of decoupling of the collective degree of freedom. We show for several simple examples, where the classical limit is obvious, that when decoupling is good, a quantization of the collective Hamiltonian leads to accurate descriptions of the low energy properties of the systems studied. In nuclear physics problems we construct the classical Hamiltonian by means of time-dependent mean-field theory, and we transcribe our formalism to this case. We report studies of a model for monopole vibrations, of 28 Si with a realistic interaction, several qualitative models of heavier nuclei, and preliminary results for a more realistic approach to heavy nuclei. Other * Email: Giu.Dodang@th.u-psud.fr † Email: aklein@walet.physics.upenn.edu ‡ Email: Niels.Walet@umist.ac.uk 1 topics included are a nuclear Born-Oppenheimer approximation for an ab initio quantum theory and a theory of the transfer of energy between collective and non-collective degrees of freedom when the decoupling is not exact. The explicit account is based on the work of the authors, but a thorough survey of other work is included. PACS number(s): 21.60.-n, 21.60.Jz, 21.60.Ev

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Section: Model With Berry Phase In Excited Statesmentioning

confidence: 99%

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

2000

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“…The amplitudes defined as T = YX −1 can alternatively to the solution of Eq. (51) be obtained from the solution of the Riccati equation [101] B + Tε + εT + TA + AT + TBT = 0 (63) and it can be shown that the RPA correlation energy defined in Eq. (62) can be calculated in terms of a sum over the differences of the RPA and SCI (singles configuration interaction) respectively (TDA) Tamm-Dancoff approximation excitation energies:…”

Section: Overview Of Rpa Methods Including Exchange Interactionsmentioning

confidence: 99%

Random-phase approximation correlation methods for molecules and solids

2011

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“…Finally, there are approaches which avoid numerical integration altogether, like (3) the plasmon formula, obtained after a double analytical integration on both the frequency and the interaction strength [7]. An elegant way to obtain the plasmon expression consists in solving the algebraic Riccati-equations of the RPA problem [28,29]. This method has been shown to be strictly equivalent to a coupled cluster doubles approach in the ring-approximation (rCCD) [30,31].…”

Section: Introductionmentioning

confidence: 99%

Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects

Mussard¹,

Rocca²,

Jansen

et al. 2016

J. Chem. Theory Comput.

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Starting from the general expression for the ground state correlation energy in the adiabatic connection fluctuation dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this famework, the ACFDT analog of the second order screened exchange (SOSEX) approximation leads to a logarithmic formula for the correlation energy similar to the direct RPA expression. Alternatively, the contribution of the exchange can be included in the kernel used to evaluate the response functions. In this case the use of an approximate kernel is crucial to simplify the formalism and to obtain a correlation energy in logarithmic form. Technical details of the implementation of these methods are discussed and it is shown that one can take advantage of density fitting or Cholesky decomposition techniques to improve the computational efficiency; a discussion on the numerical quadrature made on the frequency variable is also provided. A series of test calculations on atomic correlation energies and molecular reaction energies shows that exchange effects are instrumental to improve over direct RPA results.

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Nuclear ground states in the random phase approximation

Cited by 92 publications

References 9 publications

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

Random-phase approximation correlation methods for molecules and solids

Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects

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