Physical Review Letters

Dispersion Effect in the Iwamoto-Yamada Cluster Expansion

Chun Wa Wong

Published Mar 29, 1971• 19 citations

Abstract

The use of auxiliary single-particle potentials permits the inclusion of the dispersion effect in the energy of a many-Fermion system calculated in the independent-pair approximation of the Iwamoto-Yamada cluster expansion.

DOI: 10.1103/physrevlett.26.783

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Physical Review Letters

Dispersion Effect in the Iwamoto-Yamada Cluster Expansion

Chun Wa Wong

Published Mar 29, 1971• 19 citations

Publisher

Abstract

DOI: 10.1103/physrevlett.26.783

Related papers

Simple Derivation of Cluster Expansions for Many-Fermion Systems

J. W. Clark, Dennis A. Chakkalakal, Paul A. Westhaus

A simple alternative derivation of conventional cluster expansion formulas of Iwamoto and Yamada and others for the expectation value ≪H > of the energy of a many-Fermion system is offered. The assumed trial function is of the general form FΦp/(FΦp, FΦp)1/2, where Φp is a Slater determinant of appropriate single-particle functions and the factor F is attached to account for the possibility of strong interparticle correlations. The proposed scheme is applicable to finite as well as infinite systems and is easily generalized to the calculation of non-diagonal as well as diagonal matrix elements, with respect to the members of the set {FΦp/(FΦp, FΦp)1/2}. Explicit results for ≪H > are displayed to second cluster order, contributions being classified according to their assigned order of magnitude in a correlation parameter ξ=|Nω/Ω| of the sort introduced by Iwamoto and Yamada and Clark and Westhaus.A simple alternative derivation of conventional cluster expansion formulas of Iwamoto and Yamada and others for the expectation value ≪H > of the energy of a many-Fermion system is offered. The assumed trial function is of the general form FΦp/(FΦp, FΦp)1/2, where Φp is a Slater determinant of appropriate single-particle functions and the factor F is attached to account for the possibility of strong interparticle correlations. The proposed scheme is applicable to finite as well as infinite systems and is easily generalized to the calculation of non-diagonal as well as diagonal matrix elements, with respect to the members of the set {FΦp/(FΦp, FΦp)1/2}. Explicit results for ≪H > are displayed to second cluster order, contributions being classified according to their assigned order of magnitude in a correlation parameter ξ=|Nω/Ω| of the sort introduced by Iwamoto and Yamada and Clark and Westhaus.

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Certain physical mechanisms contributing to the Brueckner pair dispersion energy

{W}_{2}^{D}

are reviewed. This

{W}_{2}^{D}

is found to appear also in the Iwamoto-Yamada cluster expansion if the same Brueckner state- and momentum-dependent correlation operators are used. It does not appear in the two-body Iwamoto-Yamada energy, however, but in the three-body energy. Up to this point, a Brueckner triplet dispersion energy

{W}_{3}^{D}

has not yet appeared. This

{W}_{3}^{D}

depends on a triplet excitation parameter ${\ensuremath{\kappa}}_{3}$, which is calculated using Jastrow correlation functions. We find that ${\ensuremath{\kappa}}_{3}$ is small when ${\ensuremath{\kappa}}_{2}$ is small (\ensuremath{\lesssim} 0.1), and large when ${\ensuremath{\kappa}}_{2}$ is large (\ensuremath{\gtrsim} 0.4). Since ${\ensuremath{\kappa}}_{2}\ensuremath{\approx}0.2$ in nuclear matter, there is hope that both Brueckner and Iwamoto-Yamada expansions converge to the same answer at fairly low orders.NUCLEAR STRUCTURE Fermion fluids, nuclear matter; compared Brueckner and IY expansions; calculated triplet excitation parameter.