## Abstract

Relativistic Hartree-Fock equations are solved for an infinite system of nucleons and mesons. At high densities there exists a phase transition from a Fermi "sphere" to a Fermi "shell", characterized by a discontinuity in the heat capacity. The precise value of the critical density is sensitive to the approximations.

Original language | English |
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Pages (from-to) | 341-346 |

Number of pages | 6 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 109 |

Issue number | 5 |

DOIs | |

State | Published - 4 Mar 1982 |

Externally published | Yes |

### Bibliographical note

Funding Information:To overcome some of the approximations inherent in the conventional approach to nuclear structure, a model relativistic qfiantum field theory has been proposed by Walecka \[1\].T his theory avoids introducing static nucleon-nucleon potentials by explicitly including mesons. Furthermore, the model correctly treats the relativistic propagation and retardation of both the nucleons and the mesons generating the interactions. The model has been solved in the mean-field approximation by replacing the meson field operators with their classical expectation values. This mean-field theory (MFT) provides a reasonable equation of state for high-density matter and a natural framework for describing the saturation properties of normal nuclear matter \[1\]. Recent Hartree calculations \[2\] have found excellent agreement with experimental data on the bulk properties of doubly magic nuclei. Furthermore, since the quantum field model is tenor-realizable, there is a well-defined procedure for calculating corrections to these MFT results. Calculations of vacuum fluctuation and second-order exchange corrections by Chin \[3\]a nd of correlation corrections by Brittan \[4\]i ndicate that the MFT becomes more accurate as the nuclear density increases. In this letter, exchange corrections to the MFT are calculated selfconsistently using a relativistic Itartree-Fock (HF) approach. Several authors have reported Work supported in part by NSF grant NSF PHY 79-18046. 1 NSF Predoctoral t-ellow.

### Funding

To overcome some of the approximations inherent in the conventional approach to nuclear structure, a model relativistic qfiantum field theory has been proposed by Walecka \[1\].T his theory avoids introducing static nucleon-nucleon potentials by explicitly including mesons. Furthermore, the model correctly treats the relativistic propagation and retardation of both the nucleons and the mesons generating the interactions. The model has been solved in the mean-field approximation by replacing the meson field operators with their classical expectation values. This mean-field theory (MFT) provides a reasonable equation of state for high-density matter and a natural framework for describing the saturation properties of normal nuclear matter \[1\]. Recent Hartree calculations \[2\] have found excellent agreement with experimental data on the bulk properties of doubly magic nuclei. Furthermore, since the quantum field model is tenor-realizable, there is a well-defined procedure for calculating corrections to these MFT results. Calculations of vacuum fluctuation and second-order exchange corrections by Chin \[3\]a nd of correlation corrections by Brittan \[4\]i ndicate that the MFT becomes more accurate as the nuclear density increases. In this letter, exchange corrections to the MFT are calculated selfconsistently using a relativistic Itartree-Fock (HF) approach. Several authors have reported Work supported in part by NSF grant NSF PHY 79-18046. 1 NSF Predoctoral t-ellow.

Funders | Funder number |
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National Science Foundation | PHY 79-18046 |