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Register a new userQuantitative analysis of tensor effects in the relativistic Hartree-Fock theory
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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.
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With the relativistic representation of the nuclear tensor force that is included automatically by the Fock diagrams, we explored the self-consistent tensor effects on the properties of nuclear matter system. The analysis were performed within the density-dependent relativistic Hartree-Fock (DDRHF) theory. The tensor force is found to notably influence the saturation mechanism, the equation of state and the symmetry energy of nuclear matter, as well as the neutron star properties. Without introducing any additional free parameters, the DDRHF approach paves a natural way to reveal the tensor effects on the nuclear matter system.
Time-dependent Hartree-Fock (TDHF) theory has achieved a remarkable success in describing and understanding nuclear many-body dynamics from nucleons degrees of freedom. We here report our investigation of multinucleon transfer (MNT) processes employing the TDHF theory. To calculate transfer probabilities for channels specified by the number of protons and neutrons included in reaction products, a particle-number projection (PNP) method has been developed. The PNP method is also used to calculate excitation energies of reaction products. Combined use of the PNP method with a statistical model, we can evaluate MNT cross sections taking account of effects of particle evaporation. Using these methods, we evaluate MNT cross sections for $^{40,48}$Ca+$^{124}$Sn, $^{40}$Ca+$^{208}$Pb, and $^{58}$Ni+$^{208}$Pb reactions. From systematic analyses, we find that cross sections for channels with a large reaction probability are in good agreement with experimental data. However, the agreement becomes less accurate as the number of transferred nucleons increases. Possible directions to improve the description are discussed.
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.
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.
Background: The time-dependent Hartree-Fock (TDHF) theory has been successful in describing low-energy heavy ion collisions. Recently, we have shown that multinucleon transfer processes can be reasonably described in the TDHF theory combined with the particle-number projection technique. Purpose: In this work, we propose a theoretical framework to analyze properties of reaction products in TDHF calculations. Methods: TDHF calculation in three-dimensional Cartesian grid representation combined with particle number projection method. Results: We develop a theoretical framework to calculate expectation values of operators in the TDHF wave function after collision with the particle-number projection. To show how our method works in practice, the method is applied to $^{24}$O+$^{16}$O collisions for two quantities, angular momentum and excitation energy. The analyses revealed following features of the reaction: The nucleon removal proceeds gently, leaving small values of angular momentum and excitation energy in nucleon removed nuclei. Contrarily, nuclei receiving nucleons show expectation values of angular momentum and excitation energy which increase as the incident energy increases. Conclusions: We have developed a formalism to analyze properties of fragment nuclei in the TDHF theory combined with the particle-number projection technique. The method will be useful for microscopic investigations of reaction mechanisms in low-energy heavy ion collisions as well as for evaluating effects of particle evaporation on multinucleon transfer cross sections.
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