A simple Gaussian approximation for the one-body density matrix

doi:10.1016/0370-2693(86)90820-8

Physics Letters B

Volume 172, Issue 2, 15 May 1986, Pages 122-128

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Abstract

A simple form of the nonlocal one-body density matrix ϱ(r, r′) is proposed whose parameters are determined by imposing the correct local semiclassical kinetic energy density and the projector character of ϱ in an integrated form. The validity of this approach is assessed for physical quantities sensitive to the nonlocal nature of the density matrix such as the momentum distribution in the nucleus, the exchange energies of the Gogny and the Coulomb force and the two-body center-of-mass correction for various nuclei,

References (25)

Y.M. Engel et al.
Nucl. Phys.
(1975)
D.J. Thouless et al.
Nucl. Phys.
(1962)
C. Guet et al.
Nucl. Phys.
(1984)
C. Gregoire et al.
Nucl. Phys.
(1985)
J. Martorell et al.
Ann. Phys.
(1984)
R.K. Bhaduri et al.
Can. J. Phys.
(1979)
N.L. Balazs et al.
Ann. Phys. (NY)
(1973)
B.K. Jennings
Phys. Lett. B
(1978)
B. Grammaticos et al.
Ann. Phys. (NY)
(1979)
M. Durand et al.
Phys. Lett. B
(1982)
M. Prakash et al.
Nucl. Phys.
(1981)
J. Bartel et al.
Phys. Lett. B
(1982)
J. Bartel
C. Titin-Schneider et al.
Phys. Lett. B
(1974)
P. Quentin et al.
Annu. Rev. Nucl. Part. Sci.
(1978)

C.M. Ko et al.

Nucl. Phys.

(1974)

S. Aicher and M. Brack, to be...

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A simple Gaussian approximation for the one-body density matrix

Abstract

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Ann. Phys.

Can. J. Phys.

Ann. Phys. (NY)

Phys. Lett. B

Ann. Phys. (NY)

Phys. Lett. B

Nucl. Phys.

Phys. Lett. B

Phys. Lett. B

Annu. Rev. Nucl. Part. Sci.

Nucl. Phys.