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Title: Coupled-Cluster Theory for Three-Body Hamiltonians

Abstract

We derive coupled-cluster equations for three-body Hamiltonians. The equations for the one- and two-body cluster amplitudes are presented in a factorized form that leads to an efficient numeerical implementation. We employ low-momentum two- and three-nucleon interactions and calculate the binding energy of 4He. The results show that the main contribution of the three-nucleon interaction stems from its density-dependent zero-, one-, and two-body terms that result from the normal ordering of the Hamiltonian in coupled-cluster theory. The residual three-body terms that remain after normal ordering can be neglected.

Authors:
 [1];  [1];  [1];  [2];  [3];  [4];  [4]
  1. ORNL
  2. TRIUMF, Canada
  3. Forschungszentrum Julich, Julich, Germany
  4. Michigan State University, East Lansing
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC)
OSTI Identifier:
932045
DOE Contract Number:
DE-AC05-00OR22725
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review C; Journal Volume: 76; Journal Issue: 3
Country of Publication:
United States
Language:
English

Citation Formats

Hagen, Gaute, Papenbrock, Thomas F, Dean, David Jarvis, Schwenk, A., Nogga, A., Wloch, M., and Piecuch, P. Coupled-Cluster Theory for Three-Body Hamiltonians. United States: N. p., 2007. Web. doi:10.1103/PhysRevC.76.034302.
Hagen, Gaute, Papenbrock, Thomas F, Dean, David Jarvis, Schwenk, A., Nogga, A., Wloch, M., & Piecuch, P. Coupled-Cluster Theory for Three-Body Hamiltonians. United States. doi:10.1103/PhysRevC.76.034302.
Hagen, Gaute, Papenbrock, Thomas F, Dean, David Jarvis, Schwenk, A., Nogga, A., Wloch, M., and Piecuch, P. Mon . "Coupled-Cluster Theory for Three-Body Hamiltonians". United States. doi:10.1103/PhysRevC.76.034302.
@article{osti_932045,
title = {Coupled-Cluster Theory for Three-Body Hamiltonians},
author = {Hagen, Gaute and Papenbrock, Thomas F and Dean, David Jarvis and Schwenk, A. and Nogga, A. and Wloch, M. and Piecuch, P.},
abstractNote = {We derive coupled-cluster equations for three-body Hamiltonians. The equations for the one- and two-body cluster amplitudes are presented in a factorized form that leads to an efficient numeerical implementation. We employ low-momentum two- and three-nucleon interactions and calculate the binding energy of 4He. The results show that the main contribution of the three-nucleon interaction stems from its density-dependent zero-, one-, and two-body terms that result from the normal ordering of the Hamiltonian in coupled-cluster theory. The residual three-body terms that remain after normal ordering can be neglected.},
doi = {10.1103/PhysRevC.76.034302},
journal = {Physical Review C},
number = 3,
volume = 76,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}
  • We derive coupled-cluster equations for three-body Hamiltonians. The equations for the one- and two-body cluster amplitudes are presented in a factorized form that leads to an efficient numerical implementation. We employ low-momentum two- and three-nucleon interactions and calculate the binding energy of {sup 4}He. The results show that the main contribution of the three-nucleon interaction stems from its density-dependent zero-, one-, and two-body terms that result from the normal ordering of the Hamiltonian in coupled-cluster theory. The residual three-body terms that remain after normal ordering can be neglected.
  • We construct eigenstates of the (phi/sup 4/)/sub 3/ quantum field theory in the framework of the coupled cluster method (CCM). Therefore the principle of coherence is stressed leading to a description of these states by an infinite set of correlation amplitudes. In the standard form of the CCM the amplitudes obey a hierarchy of coupled nonlinear integral equations containing some poorly defined terms because of ultraviolet divergences. We remove these divergences by a systematic transformation to an equivalent set of amplitudes. No expansion in the coupling constant is therefore required to make the hierarchy well defined. It is possible tomore » find truncation schemes for the transformed amplitudes which are compatible with the requirement of renormalizability. We conclude that the CCM is helpful to analyze the structure of the vacuum and to make precise statements about the mass spectrum of superrenormalizable quantum field theories.« less
  • In this paper we discuss a new formalism for producing an analytic coupled-cluster (CC) Green's function for an N-electron system by shifting the poles of similarity transformed Hamiltonians represented in N - 1 and N + 1 electron Hilbert spaces. Simple criteria are derived for the states in N - 1 and N + 1 electron spaces that are then corrected in the spectral resolution of the corresponding matrix representations of the similarity transformed Hamiltonian. The accurate description of excited state processes within a Green's function formalism would be of significant importance to a number of scientific communities ranging frommore » physics and chemistry to engineering and the biological sciences. This is because the Green's function methodology provides a direct path for not only calculating properties whose underlying origins come from coupled many-body interactions but also provides a straightforward path for calculating electron transport, response, and correlation functions that allows for a direct link with experiment. Finally, as a special case of this general formulation, we discuss the application of this technique for Green's function defined by the CC with singles and doubles representation of the ground-state wave function.« less
  • In this paper we discuss a new formalism for producing an analytic coupled-cluster (CC) Green's function for an N-electron system by shifting the poles of similarity transformed Hamiltonians represented in N − 1 and N + 1 electron Hilbert spaces. Simple criteria are derived for the states in N − 1 and N + 1 electron spaces that are then corrected in the spectral resolution of the corresponding matrix representations of the similarity transformed Hamiltonian. The accurate description of excited state processes within a Green's function formalism would be of significant importance to a number of scientific communities ranging frommore » physics and chemistry to engineering and the biological sciences. This is because the Green's function methodology provides a direct path for not only calculating properties whose underlying origins come from coupled many-body interactions but also provides a straightforward path for calculating electron transport, response, and correlation functions that allows for a direct link with experiment. As a special case of this general formulation, we discuss the application of this technique for Green's function defined by the CC with singles and doubles representation of the ground-state wave function.« less
  • K-shell charge-transfer cross sections are calculated for swift fully stripped ions impinging on target atoms in a post-interaction distorted-wave formalism. The projectile interaction with the residual target atom is part of the unperturbed Hamiltonian and is approximated by its asymptotic form while the consequent projectile distortion is approximated by an eikonal wave function. The results are compared to experiment and to other theoretical calculations and are used to shed light on some aspects of the three-body Coulombic rearrangement process and in particular on the significance of asymptotic properties of interactions and wave functions on the results of simple approximation schemes.more » (AIP)« less