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Register a new userRevisiting the Hugenholtz-Van Hove theorem in nuclear matter
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An assessment of the magnitude of the rearrangement contribution to the Fermi energy and to the binding energy per particle is carried out in symmetric nuclear matter by extending the G-matrix framework. The restoration of the thermodynamic consistency or, equivalently, the fulfillment of the Hugenholtz-Van Hove theorem, is discussed.
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We prove that there does not exist a nontrivial quantization of the Poisson algebra of the symplectic manifold S^2 which is irreducible on the subalgebra generated by the components {S_1,S_2,S_3} of the spin vector. We also show that there does not exist such a quantization of the Poisson subalgebra P consisting of polynomials in {S_1,S_2,S_3}. Furthermore, we show that the maximal Poisson subalgebra of P containing {1,S_1,S_2,S_3} that can be so quantized is just that generated by {1,S_1,S_2,S_3}.
The existence of phase transitions from liquid to gas phases in asymmetric nuclear matter (ANM) is related with the instability regions which are limited by the spinodals. In this work we investigate the instabilities in ANM described within relativistic mean field hadron models, both with constant and density dependent couplings at zero and finite temperatures. In calculating the proton and neutron chemical potentials we have used an expansion in terms of Bessel functions that is convenient at low densities. The role of the isovector scalar $delta$-meson is also investigated in the framework of relativistic mean field models and density dependent hadronic models. It is shown that the main differences occur at finite temperature and large isospin asymmetry close to the boundary of the instability regions.
In most nuclear many-body methods, observables are calculated using many-body wave functions explicitly. The variational two-particle reduced density matrix method is one of the few exceptions to the rule. Ground-state energies of both closed-shell and open-shell nuclear systems can indeed be evaluated by minimizing a constrained linear functional of the two-particle reduced density matrix. However, it has virtually never been used in nuclear theory, because nuclear ground states were found to be well overbound, contrary to those of atoms and molecules. Consequently, we introduced new constraints in the nuclear variational two-particle reduced density matrix method, developed recently for atomic and molecular systems. Our calculations then show that this approach can provide a proper description of nuclear systems where only valence neutrons are included. For the nuclear systems where both neutrons and protons are active, however, the energies obtained with the variational two-particle reduced density matrix method are still overbound. The possible reasons for the noticed discrepancies and solutions to this problem will be discussed.
The self-energy effect on the neutron-proton (np) pairing gap is investigated up to the third order within the framework of the extend Bruecker-Hartree-Fock (BHF) approach combined with the BCS theory. The self-energy up to the second-order contribution turns out to reduce strongly the effective energy gap, while the emph{renormalization} term enhances it significantly. In addition, the effect of the three-body force on the np pairing gap is shown to be negligible. To connect the present results with the np pairing in finite nuclei, an effective density-dependent zero-range pairing force is established with the parameters calibrated to the microscopically calculated energy gap.
The effective field theory of NN interactions in nuclear matter is considered. Due to the Pauli principle the effective NN amplitude is not affected by the shallow bound states. We show that the next-to-leading order terms in the chiral expansion of the effective NN potential can be interpreted as corrections so the expansion is systematic. The value of potential energy per particle is calculated and some issues concerning the chiral effective theory of nuclear matter are outlined.
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