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Register a new userHypernuclear stars from relativistic Hartree-Fock density functional theory
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Jia Jie Li ITPn Frankfurt
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The hypernuclear matter is studied within the relativistic Hartree-Fock theory employing several parametrizations of the hypernuclear density functional with density-dependent couplings. The equations of state and compositions of hypernuclear matter are determined for each parametrization and compact stars are constructed by solving their structure equations in spherical symmetry. We quantify the softening effect of Fock terms on the equation of state, as well as discuss the impact of tensor interactions, which are absent in the Hartree theories. Starting from models of density functionals which are fixed in the nuclear sector to the nuclear phenomenology, we vary the couplings in the hyperonic sector around the central values which are fitted to the hyperon potentials in nuclear matter. We use the SU(6) spin-flavor and SU(3) flavor symmetric quark models to relate the hyperonic couplings to the nucleonic ones. We find, consistent with previous Hartree studies, that for the SU(6) model the maximal masses of compact stars are below the two-solar mass limit. In the SU(3) model we find sufficiently massive compact stars with cores composed predominantly of $Lambda$ and $Xi$ hyperons and a low fraction of leptons (mostly electrons). The parameter space of the SU(3) model is identified where simultaneously hypernuclear compact stars obey the astrophysical limits on pulsar masses and the empirical hypernuclear potentials in nuclear matter are reproduced.
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A new relativistic Hartree-Fock approach with density-dependent $sigma$, $omega$, $rho$ and $pi$ meson-nucleon couplings for finite nuclei and nuclear matter is presented. Good description for finite nuclei and nuclear matter is achieved with a number of adjustable parameters comparable to that of the relativistic mean field approach. With the Fock terms, the contribution of the $pi$-meson is included and the description for the nucleon effective mass and its isospin and energy dependence is improved.
On the way of a microscopic derivation of covariant density functionals, the first complete solution of the relativistic Brueckner-Hartree-Fock (RBHF) equations is presented for symmetric nuclear matter. In most of the earlier investigations, the $G$-matrix is calculated only in the space of positive energy solutions. On the other side, for the solution of the relativistic Hartree-Fock (RHF) equations, also the elements of this matrix connecting positive and negative energy solutions are required. So far, in the literature, these matrix elements are derived in various approximations. We discuss solutions of the Thompson equation for the full Dirac space and compare the resulting equation of state with those of earlier attempts in this direction.
Tensor force is identified in each meson-nucleon coupling in the relativistic Hartree-Fock theory. It is found that all the meson-nucleon couplings, except the $sigma$-scalar one, give rise to the tensor force. The effects of tensor force on various nuclear properties can now be investigated quantitatively, which allows fair and direct comparisons with the corresponding results in the non-relativistic framework. The tensor effects on nuclear binding energies and the evolutions of the $Z,,N = 8,,20$, and $28$ magic gaps are studied. The tensor contributions to the binding energies are shown to be tiny in general. The $Z,,N = 8$ and $20$ gaps are sensitive to the tensor force, but the $Z,,N = 28$ gaps are not.
Background: The Density-constraint Time-dependent Hartree-Fock method is currently the tool of choice to predict fusion cross-sections. However, it does not include pairing correlations, which have been found recently to play an important role. Purpose: To describe the fusion cross-section with a method that includes the superfluidity and to understand the impact of pairing on both the fusion barrier and cross-section. Method: The density-constraint method is tested first on the following reactions without pairing, $^{16}$O+$^{16}$O and $^{40}$Ca+$^{40}$Ca. A new method is developed, the Density-constraint Time-dependent Hartree-Fock-Bogoliubov method. Using the Gogny-TDHFB code, it is applied to the reactions $^{20}$O+$^{20}$O and $^{44}$Ca+$^{44}$Ca. Results: The Gogny approach for systems without pairing reproduces the experimental data well. The DC-TDHFB method is coherent with the TDHFB fusion threshold. The effect of the phase-lock mechanism is shown for those reactions. Conclusions: The DC-TDHFB method is a useful new tool to determine the fusion potential between superfluid systems and to deduce their fusion cross-sections.
We have explored the occurrence of the spherical shell closures for superheavy nuclei in the framework of the relativistic Hartree-Fock-Bogoliubov (RHFB) theory. Shell effects are characterized in terms of two-nucleon gaps $delta_{2n(p)}$. Although the results depend slightly on the effective Lagrangians used, the general set of magic numbers beyond $^{208}$Pb are predicted to be $Z = 120$, $138$ for protons and $N = 172$, 184, 228 and 258 for neutrons, respectively. Specifically the RHFB calculations favor the nuclide $^{304}$120 as the next spherical doubly magic one beyond $^{208}$Pb. Shell effects are sensitive to various terms of the mean-field, such as the spin-orbit coupling, the scalar and effective masses.
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