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Properties of pure neutron matter at low and high densities

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Abstract

We report a new microscopic equation of state (EoS) of pure neutron matter (PNM) at zero temperature using the recent realistic two-body interaction derived in the framework of chiral perturbation theory (ChPT). The EoS is derived using the Brueckner–Bethe–Goldstone quantum many-body theory in the Brueckner–Hartree–Fock approach. We have calculated the EoS of PNM at low and high densities using LO, NLO, N\(^{2}\)LO, N\(^{3}\)LO, N\(^{4}\)LO potentials at three different values of the momentum-space cut-off \(\Lambda \) = 450, 500 and 550 MeV. It is found that the EoS is not much affected by the cut-off variations at low densities. Also the binding energy of PNM has been computed within the framework of the Brueckner–Hartree–Fock (BHF) approach plus two-body density-dependent Skyrme potential which is equivalent to three-body forces. The effect of the two-body density-dependent Skyrme potential is to produce a stiffer EoS. This is actually needed to improve the saturation point of symmetric nuclear matter obtained using the two-body NN interaction. The results of several microscopic approaches are compared. It is found that the EoS is sensitive to the momentum-space cut-off \(\Lambda \). Also the partial wave contributions to potential energy at the empirical saturation density \(\rho = 0.16\) fm\(^{-3}\) for different potentials are listed from \(^{1}S_{0}\) to \(^{3}F_{3}\) states. It is found that all contributions are nearly cut-off independent except the ones from \(^{3}P_{1}\), \(^{3}P_{2}, ^{3}\!H_{4}\) and \(^{3}F_{4}\) states, which are increasing with the cut-off \(\Lambda \). Actually, the size of these contributions is strongly dependent on the central and tensor components in the NN potential. The larger cut-off \(\Lambda \) corresponds to harder interactions and gives more repulsive contribution to the NN potential at short distance. It leads to smaller binding energy.

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Acknowledgements

The author is grateful to Deanship of Scientific Research at Islamic University of Madinah for funding this work through the research Project No. (23/40) of the 10th (Takamul) programs of academic year 1440-1441 AH. The author would like to thank Professor R Machleidt for providing potential code.

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Authors and Affiliations

  1. Physics Department, Faculty of Science, Islamic University of Madinah, Madinah, Kingdom of Saudi Arabia

    Kh Gad

  2. Physics Department, Faculty of Science, Sohag University, Sohâg, 82524, Egypt

    Kh Gad

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Correspondence to Kh Gad.

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Gad, K. Properties of pure neutron matter at low and high densities. Pramana - J Phys 95, 108 (2021). https://doi.org/10.1007/s12043-021-02144-7

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