### Abstract

A nonuniform system of fermions in superfluid state is treated starting from the equations for the one-particle Green's function in the framework of the generalized Hartree-Fock method taking into account pairing correlation. Equations for determining the self-consistent pairing potential and expressions for the phase space density of tractable form are deduced with the aid of an approximation method which to the lowest order gives formulas of similar form to those of infinite systems, but the one-particle effective potential, and therefore all the other quantities too depend on the position. In that approximation the phase space density goes over into that of the Thomas-Fermi model if the pairing correlation is neglected. By taking into account first- and second-order terms we derived inhomogeneity corrections both to the phase space density and the equations determining the pair correlation. The presence of the pair correlation plays an intrinsic role in the evaluation of the correction terms to the phase space density from the Green's function. Thus the pairing correlation may have considerable effect on the density distribution.

Original language | English |
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Pages (from-to) | 229-239 |

Number of pages | 11 |

Journal | Acta Physica Academiae Scientiarum Hungaricae |

Volume | 17 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Apr 1964 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Parnaya korryelyatsiya v povyerkhnostnom sloye yadra.** / Szépfalusy, P.

Research output: Contribution to journal › Article

*Acta Physica Academiae Scientiarum Hungaricae*, vol. 17, no. 1-2, pp. 229-239. https://doi.org/10.1007/BF03156906

}

TY - JOUR

T1 - Parnaya korryelyatsiya v povyerkhnostnom sloye yadra

AU - Szépfalusy, P.

PY - 1964/4

Y1 - 1964/4

N2 - A nonuniform system of fermions in superfluid state is treated starting from the equations for the one-particle Green's function in the framework of the generalized Hartree-Fock method taking into account pairing correlation. Equations for determining the self-consistent pairing potential and expressions for the phase space density of tractable form are deduced with the aid of an approximation method which to the lowest order gives formulas of similar form to those of infinite systems, but the one-particle effective potential, and therefore all the other quantities too depend on the position. In that approximation the phase space density goes over into that of the Thomas-Fermi model if the pairing correlation is neglected. By taking into account first- and second-order terms we derived inhomogeneity corrections both to the phase space density and the equations determining the pair correlation. The presence of the pair correlation plays an intrinsic role in the evaluation of the correction terms to the phase space density from the Green's function. Thus the pairing correlation may have considerable effect on the density distribution.

AB - A nonuniform system of fermions in superfluid state is treated starting from the equations for the one-particle Green's function in the framework of the generalized Hartree-Fock method taking into account pairing correlation. Equations for determining the self-consistent pairing potential and expressions for the phase space density of tractable form are deduced with the aid of an approximation method which to the lowest order gives formulas of similar form to those of infinite systems, but the one-particle effective potential, and therefore all the other quantities too depend on the position. In that approximation the phase space density goes over into that of the Thomas-Fermi model if the pairing correlation is neglected. By taking into account first- and second-order terms we derived inhomogeneity corrections both to the phase space density and the equations determining the pair correlation. The presence of the pair correlation plays an intrinsic role in the evaluation of the correction terms to the phase space density from the Green's function. Thus the pairing correlation may have considerable effect on the density distribution.

UR - http://www.scopus.com/inward/record.url?scp=36148953273&partnerID=8YFLogxK

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U2 - 10.1007/BF03156906

DO - 10.1007/BF03156906

M3 - Article

VL - 17

SP - 229

EP - 239

JO - Acta Physica Academiae Scientiarum Hungaricae

JF - Acta Physica Academiae Scientiarum Hungaricae

SN - 0001-6705

IS - 1-2

ER -