Relativistic Hartree-Fock Approximation Research Articles

Decomposition of nuclear symmetry energy based on Lorentz-covariant nucleon self-energies in relativistic Hartree-Fock approximation

Using the Lorentz-covariant decomposition of nucleon self-energies based on the Hugenholtz–Van Hove theorem, we study the effect of Fock terms on the nuclear symmetry energy and its slope parameter within relativistic Hartree-Fock approximation. It is found that the exchange contribution suppresses the nuclear symmetry energy and prevents the slope parameter from increasing monotonically at high densities. Furthermore, not only the isovector-vector (ρ) meson but also the isoscalar mesons (σ,ω) and pion give significant influence on the potential term of nuclear symmetry energy through the exchange diagrams.

Tensor force effect on the evolution of single-particle energies in some isotopic chains in the relativistic Hartree–Fock approximation

Within a nonlinear relativistic Hartree–Fock approximation combined with the BCS method, we study the effect of the nucleon–nucleon tensor force of the π-exchange potential on the spin- and pseudospin–orbit doublets along the Ca and Sn isotopic chains.We show how the self-consistent tensor force effect modifies the splitting of both kinds of doublets in an interdependent form, leading, quite generally, to opposite effects in the accomplishment of the spin and pseudospin symmetries (the one is restored, the other one deteriorates and vice versa). The ordering of the single-particle energy levels is crucial to this respect.Also, we observe a mutual dependence on the evolution of the shell closure gap Z = 50 and the energy band outside the core, along the Sn chain, as due to the tensor force. In fact, when the shell gap is quenched the outside energy band is enlarged, and vice versa. A reduction of the strength of the pion tensor force with respect to its experimental value from the nucleon–nucleon scattering is needed to get results closer to the experiment. Pairing correlations act to some extent in the opposite direction of the tensor term of the one-pion-exchange force.

Effects of Tensor Couplings on Nucleonic Direct URCA Processes in Neutron Star Matter**Supported by the National Natural Science Foundation of China under Grant Nos 11447165, 11373047 and 11265009, and the Youth Innovation Promotion Association of Chinese Academy of Sciences under Grant No 2016056.

The relativistic neutrino emissivity of the nucleonic direct URCA processes in neutron star matter is investigated within the relativistic Hartree—Fock approximation. We particularly study the influences of the tensor couplings of vector mesons ω and ρ on the nucleonic direct URCA processes. It is found that the inclusion of the tensor couplings of vector mesons ω and ρ can slightly increase the maximum mass of neutron stars. In addition, the results indicate that the tensor couplings of vector mesons ω and ρ lead to obvious enhancement of the total neutrino emissivity for the nucleonic direct URCA processes, which must accelerate the cooling rate of the non-superfluid neutron star matter. However, when considering only the tensor coupling of vector meson ρ, the neutrino emissivity for the nucleonic direct URCA processes slightly declines at low densities and significantly increases at high densities. That is, the tensor coupling of vector meson ρ leads to the slow cooling rate of a low-mass neutron star and rapid cooling rate of a massive neutron star.

Ionization potentials and polarizabilities of superheavy elements from Db to Cn(Z=105–112)

Relativistic Hartree-Fock and random phase approximation methods for open shells are used to calculate ionization potentials and static scalar polarizabilities of eight superheavy elements with open $6d$-shell, which include Db, Sg, Bh, Hs, Mt, Ds, Rg and Cn ($Z$=105 to 112). Inter-electron correlations are taken into account with the use of the semi-empirical polarization potential. Its parameters are chosen to fit the known ionization potentials of lighter atoms. Calculations for lighter atoms are also used to illustrate the accuracy of the approach.

EQUATION OF STATE FOR NEUTRON STARS WITH HYPERONS AND QUARKS IN THE RELATIVISTIC HARTREE–FOCK APPROXIMATION

We construct the equation of state (EoS) for neutron stars explicitly including hyperons and quarks. Using the quark-meson coupling model with relativistic Hartree-Fock approximation, the EoS for hadronic matter is derived by taking into account the strange ($\sigma^{\ast}$ and $\phi$) mesons as well as the light non-strange ($\sigma$, $\omega$, $\vec{\pi}$ and $\vec{\rho}$) mesons. Relevant coupling constants are determined to reproduce the experimental data of nuclear matter and hypernuclei in SU(3) flavor symmetry. For quark matter, we employ the MIT bag model with one-gluon-exchange interaction, and Gibbs criteria for chemical equilibrium in the phase transition from hadrons to quarks. We find that the strange vector ($\phi$) meson and the Fock contribution make the hadronic EoS stiff, and that the maximum mass of a neutron star can be consistent with the observed mass of heavy neutron stars even if the coexistence of hadrons and quarks takes place in the core. However, in the present calculation the transition to pure quark matter does not occur in stable neutron stars. Furthermore, the lower bound of the critical chemical potential of the quark-hadron transition at zero temperature turns out to be around 1.5 GeV in order to be consistent with the recent observed neutron star data.

Atomic Ionization by Dark Matter Particles

SynopsisUsing the relativistic Hartree-Fock approximation, we calculate the rates of atomic ionization by absorption of axions and other Dark matter candidates. We also calculate atomic ionization by scattering of heavy Dark matter particles on electrons. The results are used to interpret possible detection of Dark matter by DAMA collaboration.

Pion tensor force and nuclear binding energy in the relativistic Hartree-Fock formalism

The binding energies of several isotopic families are studied within the relativistic Hartree-Fock approximation with the pseudovector coupling for the πN vertex, to find out a suitable strength for the effective pion tensor force (EPTF). An approximation for determining separately the contributions of the central and tensor forces generated by pion is considered. The results for heavy nuclei indicate that a realistic strength for the EPTF is smaller than a half of that appearing in the OPEP. This conclusion also applies to the results for the single-particle energies. Besides, it has been found that there is a genuine relativistic contribution of the EPTF in nuclear matter which is small but significant.

Nuclear Tensor Force and Effective Pions in the Relativistic Hartree-Fock Formalism

In the framework of nonlinear nuclear models based on the relativistic Hartree-Fock approximation, we have isolated the contribution of the tensor force of pions in the effective NN interaction, by means of two different approximate methods, recently developed by us, in order to dilucidate its role in a variety of nuclear properties. Results show that a reduction of the contribution of this tensor force considerably influences the spin-orbit splittings and magic gaps in the spin-unsaturated midweight 56Ni nucleus as well as the behaviour of the total binding energies with A in heavy nuclei. Both methods give similar results. We also study the evolution of the splitting of the proton 1d spin-orbit doublet in the chain Z=14, from N=20 to N=28, and the neutron 2p − 1f shell in the chain N=28, from the 48Ca nucleus to the 42Si nucleus. Whereas, in the first case, the pion tensor force (PTF) plays an important role and its reduction is needed to reproduce the corresponding experimental results; in the second case, the quenching of the neutron 2p3/2 − 1f7/2 gap in the mentioned isotonic chain N=28 is hardly affected by the PTF.

A NEW EQUATION OF STATE FOR NEUTRON STAR MATTER WITH NUCLEI IN THE CRUST AND HYPERONS IN THE CORE

The equation of state for neutron stars in a wide-density range at zero temperature is constructed. The chiral quark-meson coupling model within relativistic Hartree-Fock approximation is adopted for uniform nuclear matter. The coupling constants are determined so as to reproduce the experimental data of atomic nuclei and hypernuclei. In the crust region, nuclei are taken into account within the Thomas-Fermi calculation. All octet baryons are considered in the core region, while only $\Xi^{-}$ appears in neutron stars. The resultant maximum mass of neutron stars is $1.95M_\odot$, which is consistent with the constraint from the recently observed massive pulsar, PSR J1614-2230.

Nuclear relativistic Hartree-Fock approximation with weakened pion tensor force

Properties linked to the single-particle energies, as nuclear spectra, spin-orbit splittings and shell gaps are investigated in the framework of the relativistic Hartree-Fock approximation with pseudovector coupling for the πN vertex. The role of an effective mass of pions moving in the nuclear medium and its relationship with the strength of pion tensor force is discussed. A simple method to reduce the contribution of this tensor force that considerably improves the single-particle spectrum of nuclei is proposed.

Relativistic many-body calculations of excitation energies, oscillator strengths, transition rates, and lifetimes in samariumlike ions

The unique atomic properties of samariumlike ions, not yet measured experimentally, are theoretically predicted and studied in this paper. Excitation energies, oscillator strengths, transition probabilities, and lifetimes are calculated for $(5{s}^{2}+5{p}^{2}+5{d}^{2}+5s5d+5s5g+5p5f)$--$(5s5p+5s5f+5p5d+5p5g)$ electric dipole transitions in Sm-like ions with nuclear charge $Z$ ranging from 74 to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate retarded $E1$ matrix elements in length and velocity forms. The calculations start from a $1{s}^{2}2{s}^{2}2{p}^{6}3{s}^{2}3{p}^{6}3{d}^{10}4{s}^{2}4{p}^{6}4{d}^{10}4{f}^{14}$ Dirac-Fock potential. First-order perturbation theory is used to obtain intermediate coupling coefficients, and the second-order RMBPT is used to determine the matrix elements. The contributions from negative-energy states are included in the second-order $E1$ matrix elements to achieve agreement between length-form and velocity-form amplitudes. The resulting transition energies and transition probabilities, and lifetimes for Sm-like W${}^{12+}$ are compared with results obtained by the relativistic Hartree-Fock approximation (cowan code) to estimate contributions of the $4f$-core-excited states. Trends of excitation energies and oscillator strengths as the function of nuclear charge $Z$ are shown graphically for selected states and transitions. This work provides a number of yet unmeasured atomic properties of these samariumlike ions for various applications and as a benchmark for testing theory.

Nuclear Relativistic Hartree–Fock Approximation with Weakened Pion Tensor Force

Nuclear Relativistic Hartree–Fock Approximation with Weakened Pion Tensor Force

Nuclear relativistic hartree-fock approximation with effective pions

The effect of an interaction between the σ- and π-meson fields, as well as that of the mixture of pseudoscalar (PS) and pseudovector (PV) couplings for the πN vertex on the shell structure of finite nuclei are analyzed in the framework of different nonlinear nuclearmodels based on the relativistic Hartree-Fock approximation. For the case of a dominant πN PV coupling, it is found that if the σ-π interaction generates an effective pion mass increasing with the nuclear density, the unrealistic effect of pions on the shell structure can be strongly reduced, keeping, roughly, the contribution of pions to the total binding energy. The πN PS coupling increases slightly the spin-orbit splittings and the binding energy of the single-particle levels.

EQUATION OF STATE FOR MASSIVE NEUTRON STARS

Using relativistic Hartree-Fock approximation, we investigate the properties of the neutron-star matter in detail. In the present calculation, we consider not only the tensor coupling of vector mesons to octet baryons and the form factors at interaction vertexes but also the internal (quark) structure change of baryons in dense matter. The relativistic Hartree-Fock calculations are performed in two ways: one is the calculation with the coupling constants determined by SU(6) (quark model) symmetry, the other is with the coupling constants based on SU(3) (flavor) symmetry. For the latter case, we use the latest Nijmegen (ESC08) model. Then, it is very remarkable that the particle composition of the core matter in SU(3) symmetry is completely different from that in SU(6) symmetry. In SU(6) symmetry, all octet baryons appear in the density region below $\sim 1.2$ fm$^{-3}$, while, in the ESC08 model, only the \Xi^- hyperon is produced. Furthermore, the medium modification of the internal baryon structure hardens the equation of state for the core matter. Taking all these effects into account, we can obtain the maximum neutron-star mass which is consistent with the recently observed mass, 1.97 \pm 0.04 M_\sun (PSR J1614-2230). We therefore conclude that the extension from SU(6) symmetry to SU(3) symmetry in the meson-baryon couplings and the internal baryon-structure variation in matter certainly enhance the mass of neutron star. Furthermore, the effects of the form factor at vertex and the Fock contribution including the tensor coupling due to the vector mesons are indispensable to describe the core matter. In particular, the Fock term is very vital in reproducing the preferable value of symmetry energy, a_4 (\simeq 30 - 40 MeV), in nuclear matter.

Effects of Fock term, tensor coupling and baryon structure variation on a neutron star

The equation of state for neutron matter is calculated within relativistic Hartree–Fock approximation. The tensor couplings of vector mesons to baryons are included, and the change of baryon internal structure in matter is also considered using the quark–meson coupling model. We obtain the maximum neutron-star mass of ∼2.0M⊙, which is consistent with the recently observed, precise mass, 1.97±0.04M⊙. The Fock contribution is very important and, in particular, the inclusion of tensor coupling is vital to obtain such large mass. The baryon structure variation in matter also enhances the mass of a neutron star.

Off-Mass-Shell Behaviors of Nucleon Self-Energies and the Gamow-Teller Sum Rule in the Relativistic Hartree-Fock Approach

The relativistic Hartree approximation predicts a deep attractive potential for antinucleon, which largely reduces the threshold energies of the nucleon-antinucleon (NN) production. This effect has played an important role in explaining the quenching of the GamowTeller (GT) strength because the quenched strength in the particle-hole excitation is partially taken by the NN production. On the other hand antiproton experiments do not reveal a deep attractive potential for antinucleon. In this paper, we study the energy dependence of the nucleon self-energies in the relativistic Hartree-Fock (RHF) approximation in off-massshell states. Then, we demonstrate that the antinucleon appearing in low-energy observables is in the off-mass-shell energy region and its properties are quite different from those at the on-mass-shell state. Furthermore, we show that the quenched amount of the GT strength is taken by not only the NN production but also the meson production through the imaginary part of the nucleon self-energy in the RHF approximation.

Random phase approximation in a self-consistent covariant approach: recent applications

The relativistic Hartree-Fock (RHF) and Random Phase Approximation (RPA) methods are self-consistently applied to two issues of current interest. The first application is related to the isospin mixing corrections in the problem of super-allowed 0+ → 0+ β-transitions and the unitarity of the CKM matrix. The second application concerns the prediction of inclusive neutrino-nucleus cross-sections, where the results of the present model are compared with other approaches.

Axio-electric effect

Using the relativistic Hartree-Fock approximation, we calculate the rates of atomic ionization by absorption of axions of the energies up to 100 keV and for an arbitrary value of the axion mass. We present numerical results for atoms used in the low radioactive background searches of dark matter (e.g. Ar, Ge and Xe), as well as the analytical formula which fits numerical calculations for the absorption cross sections and can be applied for other atoms, molecules and condensed matter systems. Using the cross-sections for the axio-electric effect, we derive the counting rates induced by solar axions and set limits on the axion coupling constants.

RELATIVISTIC HARTREE-FOCK MODEL WITH SHORT RANGE CORRELATION IN NUCLEAR MATTER

We introduce the form factor and short range correlation in the relativistic Hartree-Fock approximation (RHFU) to study the properties of nuclear matter. We treat the short range correlation with the unitary correlation operator method (UCOM). In this framework, we can perfectly reproduce the equation of state of pure neutron matter obtained by the relativistic Brueckner-Hartree-Fock theory with the Bonn potential. We apply the RHFU model to symmetric nuclear matter. The contribution of ρ meson is cut down largely by the form factor of the size in the realistic nucleon-nucleon interaction. The short range correlation has a significant effect on the Fock energies of pion and ρ meson exchange interaction.

Atomic ionization by keV-scale pseudoscalar dark-matter particles

Using the relativistic Hartree-Fock approximation, we calculate the rates of atomic ionization by absorption of pseudoscalar particles in the mass range from 10 to $\sim$ 50 keV. We present numerical results for atoms relevant for the direct dark matter searches (e.g. Ar, Ge, I and Xe), as well as the analytical formula which fits numerical calculations with few per cent accuracy and may be used for multi-electron atoms, molecules and condensed matter systems.