Approach to the relativistic extended Thomas-Fermi expansion for Green’s functions, phase-space densities, and densities

Von-Eiff, D.; Haddad, S.; Weigel, M. K.

doi:10.1103/physrevc.46.230

Cited by 12 publications

(10 citation statements)

References 12 publications

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“…will later be used to determine the value of the constituent mass m as a function of the cut-off Λ. The semi-classical, relativistic particle and energy densities for fermions in the background of a scalar field are derived within the Wigner-Kirkwood (WK) expansion up to order h2 [13,14,15] ρ = ρ (0) + ρ (2) , E = E (meson) + E (0) + E (2) .…”

Section: Thomas-fermi Methods and Wigner-kirkwood Expansionmentioning

confidence: 99%

Soliton formation in the Nambu–Jona-Lasinio model

2000

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The soliton formation is considered in the Nambu-Jona-Lasinio model with local four quark interaction and various schemes to regularize the energy contribution of the polarized vacuum. No additional constraints are admitted in order to stabilize the soliton. While solitons are unstable in the proper-time regularized version the three momentum cut-off regularization apparently is more appropriate. Using a semi-classical approach multi-quark solitons obtained from that scheme are discussed. However, no self-consistent non-trivial unit baryon number configuration has been found. We also study a renormalizable extension of the model. In this case no stable multi-quark solitons are obtained within the semi-classical approach.

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Section: Thomas-fermi Methods and Wigner-kirkwood Expansionmentioning

confidence: 99%

Soliton formation in the Nambu–Jona-Lasinio model

2000

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“…v' '(rr') represents the static meson propagator (Yukawa potential), while G ( r, q) is the In Ref. [16]we derived the WK corrections to the relativistic phase-space densities and densities up to second order in A. The explicit expressions for the second-order terms of the particle, scalar, energy, and kinetic-energy densities of each kind of nucleons "feeling" the action of a scalar and a timelike potential, Xz and Xo, respectively, are given in the Appendix.…”

Section: Quantum Correci'ionsmentioning

confidence: 99%

“…Equations (2.16},(2.26}, (2.14), and (2.29) represent the corresponding zeroth-order expressions of the A expansion of Ref. [16], with the energy density erF depending on the definition of the interaction. With the dynamics of the system specified by the I-agrangian (2.1), the scalar and timelike parts of the nucleon self-energy are given in each order by and equal to Eqs.…”

Section: Quantum Correci'ionsmentioning

confidence: 99%

“…Swiatecki In this appendix we give the explicit expressions for the second-order WK corrections to the particle, scalar, energy, and kinetic-energy densities of each kind of nucleon "feeling" the action of a scalar and a timelike potential Xs and Xo, respectively (see Ref. [16]): In Eq. (A3), A, =0 corresponds to a purely external potential, while A, =l describes the case of a self-consistent two-particle interaction.…”

Section: And 6mentioning

confidence: 99%

“…(2.14}yields Equations (2.20) -(2.27) constitute a nonlinear system for the nuclear densities, meson, and electromagnetic fields in the RTFA, which has to be solved self-consistently. At each iteration step, the chemical potentials can be adjust- For the kinetic-energy density, one obtains in the RTFA the expression [16] 'rrp( r) = g 2 2pr( r)cr( r) -M' (r) 5 -4, pF( r)cF( r) …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Relativistic Thomas-Fermi calculations of finite nuclei including quantum corrections

Von-Eiff

Weigel

1992

Phys. Rev. C

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Semiclassical expansions of the relativistic nuclear Hartree-Fock theory at finite temperature

Haddad¹,

Weigel²

1994

J. Phys. G: Nucl. Part. Phys.

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The Wigner-Kirkwood semiclassical expansion of the relativistic nuclear Hartree-Fock theory is generalized for finite temperatures by utilizing the spectral representation of the Green function for non-zero temperatures. The expansion is described in greater detail up to second order and the thermostatic properties of nuclear systems are discussed in the same order. For finite nuclear systems static Hartree-Fock calculations at finite temperature describe a hot nucleus in equilibrium with an external vapour. A subtraction scheme is needed to extract the properties of the hot nucleus from those of the system 'gas+hot nucleus'. In the spectral representation method we achieve this goal by subtracting the parts of the occupation probabilities which are related solely to the external gas (vapour phase).

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Approach to the relativistic extended Thomas-Fermi expansion for Green’s functions, phase-space densities, and densities

Cited by 12 publications

References 12 publications

Soliton formation in the Nambu–Jona-Lasinio model

Soliton formation in the Nambu–Jona-Lasinio model

Relativistic Thomas-Fermi calculations of finite nuclei including quantum corrections

Semiclassical expansions of the relativistic nuclear Hartree-Fock theory at finite temperature

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