Relativistic Potentials Research Articles

Relativistic treatment of the decay constants of light and heavy mesons

Novel relativistic expressions are used to calculate the weak decay constants of pseudoscalar and vector mesons within the constituent quark model. Meson wave functions satisfy the quasipotential equation with the complete relativistic potential. New contributions, coming from the negative-energy quark states, are substantial for the light mesons, significantly decrease the values of their decay constants and, thus, bring them into agreement with experiment. For heavy-light mesons these contribution are much less pronounced, but permit to reduce uncertainties of the predicted decay constants. Their values agree with the results of lattice calculations and experimental data.

Relativistic models for quasielastic neutrino scattering

We present quasielastic neutrino-nucleus cross sections in the energy range from 150 MeV to 5 GeV for the target nuclei {sup 12}C and {sup 56}Fe. A relativistic description of the nuclear dynamics and the neutrino-nucleus coupling is adopted. For the treatment of final-state interactions we rely on two frameworks successfully applied to exclusive electron-nucleus scattering: a relativistic optical potential and a relativistic multiple-scattering Glauber approximation. At lower energies, the optical-potential approach is considered to be the optimum choice, whereas at high energies a Glauber approach is more natural. Comparing the results of both calculations, it is found that the Glauber approach yields valid results down to the remarkably small nucleon kinetic energies of 200 MeV. We argue that the nuclear transparencies extracted from A(e,e{sup '}p) measurements can be used to obtain realistic estimates of the effect of FSI mechanisms on quasielastic neutrino-nucleus cross sections. We present two independent relativistic plane-wave impulse approximation (RPWIA) calculations of quasielastic neutrino-nucleus cross sections. They agree at the percentage level, showing the reliability of the numerical techniques adopted and providing benchmark RPWIA results.

Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport

Supernova models with a full spectral treatment of the neutrino transport are presented, employing the PROMETHEUS/VERTEX neutrinohydrodynamics code with a variable Eddington factor closure of the O(v/c) moments equations of neutrino number, energy, and momentum. Our ray-by-ray plus approximation developed for two- (or three-) dimensional problems assumes that the local neutrino distribution function is azimuthally symmetric around the radial direction, which implies that the nonradial flux components disappear. Other terms containing the angular velocity components are retained in the moments equations and establish a coupling of the transport at different latitudes by lateral derivatives. Also lateral components of the neutrino pressure gradients are included in the hydrodynamics equations. This approximative approach for neutrino transport in multi-dimensional environments is motivated and critically assessed with respect to its capabilities, limitations, and inaccuracies in the context of supernova simulations. In this first paper of a series, one- (1D) and two-dimensional (2D) core-collapse calculations for a (nonrotating) 15 M ○. star are discussed, uncertainties in the treatment of the equation of state - numerical and physical - are tested, Newtonian results are compared with simulations using a general relativistic potential, bremsstrahlung and interactions of neutrinos of different flavors are investigated, and the standard approximation in neutrino-nucleon interactions with zero energy transfer is replaced by rates that include corrections due to nucleon recoil, thermal motions, weak magnetism, and nucleon correlations. Models with the full implementation of the ray-by-ray plus spectral transport were found not to explode, neither in spherical symmetry nor in 2D when the computational grid is constrained to a lateral wedge (<±45°) around the equator. The success of previous two-dimensional simulations with grey, flux-limited neutrino diffusion can therefore not be confirmed. An explosion is obtained in 2D for the considered 15 M ○. progenitor, when the radial velocity terms in the neutrino momentum equation are omitted. This manipulation increases the neutrino energy density in the convective gain layer by about 20-30% and thus the integral neutrino energy deposition in this region by about a factor of two compared to the non-exploding 2D model with the full transport. The spectral treatment of the transport and detailed description of charged-current processes leads to proton-rich neutrino-heated ejecta, removing the problem that previous explosion models with approximate neutrino treatment overproduced N = 50 closed neutron shell nuclei by large factors.

Isospin-dependent optical potentials in Dirac-Brueckner-Hartree-Fock approach

The relativistic microscopic optical potential (RMOP) is studied within the framework of the Dirac-Brueckner-Hartree-Fock (DBHF) approach. A new decomposition of the Dirac structure of nuclear self-energy in the DBHF is extended to asymmetric nuclear matter calculations. A nucleon effective interaction is introduced to reproduce the results of the G matrix. The real part of nucleon self-energy in asymmetric nuclear matter is calculated with the G matrix in the Hartree-Fock approach, while the imaginary part is obtained from the polarization diagram. Nuclear optical potentials in finite nuclei are derived from the self-energies in asymmetric matter through a local-density approximation. The differential cross sections and the analyzing powers in p+Ca-40 and p+Pb-208 elastic scattering at E-p<= 200 MeV are studied with these RMOPs. A satisfactory agreement with the experimental data is found. This is achieved without readjusting phenomenologically the RMOP derived from the DBHF plus polarization diagram.

Model-independent study of the Dirac structure of the nucleon-nucleon interaction

Relativistic and non-relativistic modern nucleon-nucleon potentials are mapped on a relativistic operator basis using projection techniques. This allows to compare the various potentials at the level of covariant amplitudes were a remarkable agreement is found. In nuclear matter large scalar and vector mean fields of several hundred MeV magnitude are generated at tree level. This is found to be a model independent feature of the nucleon-nucleon interaction.

Exploring the relativistic regime with Newtonian hydrodynamics: an improved effective gravitational potential for supernova simulations

We investigate the possibility approximating relativistic effects in hydrodynamical simulations of stellar core collapse and post-bounce evolution by using a modified gravitational potential in an otherwise standard Newtonian hydrodynamic code. Different modifications of a previously introduced effective relativistic potential are discussed. Corresponding hydrostatic solutions are compared with solutions of the TOV equations, and hydrodynamic simulations with two different codes are compared with fully relativistic results. One code is applied for one- and two-dimensional calculations with a simple equation of state and employs either the modified effective relativistic potential in a Newtonian framework or solves the general relativistic field equations under the assumption of the conformal flatness condition (CFC) for the three-metric. The second code allows for full-scale supernova runs including a microphysical equation of state and neutrino transport based on the solution of the Boltzmann equation and its moments equations. We present prescriptions for the effective relativistic potential for self-gravitating fluids to he used in Newtonian codes, which produce excellent agreement with fully relativistic solutions in spherical symmetry, leading to significant improvements compared to previously published approximations. Moreover, they also approximate qualitatively well relativistic solutions for models with rotation.

Cartan–Weyl Dirac and Laplacian Operators, Brownian Motions: The Quantum Potential and Scalar Curvature, Maxwell’s and Dirac-Hestenes Equations, and Supersymmetric Systems

We present the Dirac and Laplacian operators on Clifford bundles over space–time, associated to metric compatible linear connections of Cartan–Weyl, with trace-torsion, Q. In the case of nondegenerate metrics, we obtain a theory of generalized Brownian motions whose drift is the metric conjugate of Q. We give the constitutive equations for Q. We find that it contains Maxwell’s equations, characterized by two potentials, an harmonic one which has a zero field (Bohm-Aharonov potential) and a coexact term that generalizes the Hertz potential of Maxwell’s equations in Minkowski space.We develop the theory of the Hertz potential for a general Riemannian manifold. We study the invariant state for the theory, and determine the decomposition of Q in this state which has an invariant Born measure. In addition to the logarithmic potential derivative term, we have the previous Maxwellian potentials normalized by the invariant density. We characterize the time-evolution irreversibility of the Brownian motions generated by the Cartan–Weyl laplacians, in terms of these normalized Maxwell’s potentials. We prove the equivalence of the sourceless Maxwell equation on Minkowski space, and the Dirac-Hestenes equation for a Dirac-Hestenes spinor field written on Minkowski space provided with a Cartan–Weyl connection. If Q is characterized by the invariant state of the diffusion process generated on Euclidean space, then the Maxwell’s potentials appearing in Q can be seen alternatively as derived from the internal rotational degrees of freedom of the Dirac-Hestenes spinor field, yet the equivalence between Maxwell’s equation and Dirac-Hestenes equations is valid if we have that these potentials have only two components corresponding to the spin-plane. We present Lorentz-invariant diffusion representations for the Cartan–Weyl connections that sustain the equivalence of these equations, and furthermore, the diffusion of differential forms along these Brownian motions. We prove that the construction of the relativistic Brownian motion theory for the flat Minkowski metric, follows from the choices of the degenerate Clifford structure and the Oron and Horwitz relativistic Gaussian, instead of the Euclidean structure and the orthogonal invariant Gaussian. We further indicate the random Poincare–Cartan invariants of phase-space provided with the canonical symplectic structure. We introduce the energy-form of the exact terms of Q and derive the relativistic quantum potential from the groundstate representation. We derive the field equations corresponding to these exact terms from an average on the invariant state Cartan scalar curvature, and find that the quantum potential can be identified with 1 / 12R(g), where R(g) is the metric scalar curvature. We establish a link between an anisotropic noise tensor and the genesis of a gravitational field in terms of the generalized Brownian motions. Thus, when we have a nontrivial curvature, we can identify the quantum nonlocal correlations with the gravitational field. We discuss the relations of this work with the heat kernel approach in quantum gravity. We finally present for the case of Q restricted to this exact term a supersymmetric system, in the classical sense due to E.Witten, and discuss the possible extensions to include the electromagnetic potential terms of Q

A Computational Study of the Thermochemistry of Bromine- and Iodine-Containing Methanes and Methyl Radicals

Bromo- and iodomethanes and the corresponding halogenated methyl radicals have been investigated by ab initio methods. Geometries and vibrational frequencies were derived with quadratic configuration interaction methods at the QCISD/6-311G(d,p) level of theory, and energies via QCISD(T)/6-311+G(3df,2p). Core electrons were represented with relativistic effective potentials. Anharmonicity of the out-of-plane bending modes in the methyl radicals was taken into account by numerical integration of the Schrödinger equation with potentials derived from relaxed scans of these modes. The results are in good accord with experimental data where available. Thermochemistry derived via isodesmic reactions referenced to CH3, CH4, and monohalomethanes yields excellent accord with new experiments on dihalomethanes and provides recommendations for the more poorly characterized tri- and tetrahalomethanes and halomethyl radicals. For the methanes CH2Br2, CHBr3, CBr4, CH2I2, CHI3, CI4, CH2BrI, CHBr2I, and CHBrI2 we compute DeltafH degrees (298) values of 4.3, 51.6, 110.6, 108.1, 208.5, 321.3, 56.8, 104.8, and 157.1 kJ mol(-1), respectively. For the methyl radicals CH2Br, CHBr2, CBr3, CH2I, CHI2, CI3, CHBrI, CBr2I, and CBrI2 we compute DeltafH degrees (298) values of 166.6, 191.7, 224.0, 217.2, 290.4, 369.1, 241.6, 320.8, and 272.3 kJ mol(-1), respectively. Recommended confidence limits are +/-3 kJ mol(-1) per Br or I atom. Trends in these values and the corresponding C-H bond strengths are discussed and compared with prior experiments, empirical estimation schemes, and ab initio calculations.

Smooth relativistic Hartree–Fock pseudopotentials for H to Ba and Lu to Hg

We report smooth relativistic Hartree-Fock pseudopotentials (also known as averaged relativistic effective potentials) and spin-orbit operators for the atoms H to Ba and Lu to Hg. We remove the unphysical extremely nonlocal behavior resulting from the exchange interaction in a controlled manner, and represent the resulting pseudopotentials in an analytic form suitable for use within standard quantum chemistry codes. These pseudopotentials are suitable for use within Hartree-Fock and correlated wave function methods, including diffusion quantum Monte Carlo calculations.

Relativistic microscopic description of proton-nucleus scattering at energies u p to 200MeV

A new decomposition of the Dirac Brückner-Hartree-Fock (DBHF) G matrix is used to study the isospin-dependent relativistic microscopic optical potential (RMOP). The optical potential of finite nuclei can be obtained in the local den sity approximation. The energy dependence of proton-nucleus scattering for the optical potentials of finite nuclei is discussed. The differential cross section s and the resolution power in the p+4040Ca and p+208208Pb at Epp less than 200MeV are also calculated using the above RMOP. I t is found that the calculated results agree with the experimental results. It should be e mphasized that the ROMP obtained from DBHF G matrix without any free parameter s could well describe the proton elastic scattering. This RMOP can also be used for unstable nuclei. From the results of the Ca isotopes, it is found that the i sospin dependence is more important for the exotic nuclei.

Final state interaction effects in neutrino-nucleus quasielastic scattering

We consider the charged-current quasielastic scattering of muon neutrinos on an Oxygen 16 target, described within a relativistic shell model and, for comparison, the relativistic Fermi gas. Final state interactions are described in the distorted wave impulse approximation, using both a relativistic mean field potential and a relativistic optical potential, with and without imaginary part. We present results for inclusive cross sections at fixed neutrino energies in the range $E_\nu =$ 200 MeV - 1 GeV, showing that final state interaction effects can remain sizable even at large energies.

Some Aspects of Nuclear Structure in Relativistic Approach**The project supported by National Natural Science Foundation of China under Grant Nos. 10235020 and 10275094 and The State Key Research Development Program under Grant No. G200077407

The nucleon effective interaction in the nuclear medium is investigated in the framework of the Dirac–Brueckner–Hartree–Fock (DBHF) approach. A new decomposition of the Dirac structure of nucleon self-energy in the DBHF is adopted for asymmetric nuclear matter. The properties of finite nuclei are investigated with the nucleon effective interaction. The agreement with the experimental data is satisfactory. The relativistic microscopic optical potential in asymmetric nuclear matter is investigated in the DBHF approach. The proton scattering from nuclei is calculated and compared with the experimental data. A proper treatment of the resonant continuum for exotic nuclei is studied. The width effect of the resonant continuum on the pairing correlation is discussed. The quasiparticle relativistic random phase approximation based on the relativistic mean-field ground state in the response function formalism is also addressed.

On the Survival of Short‐Period Terrestrial Planets

The currently feasible method of detecting Earth-mass planets is transit photometry, with detection probability decreasing with a planet's distance from the star. The existence or otherwise of short-period terrestrial planets will tell us much about the planet-formation process, and such planets are likely to be detected first, if they exist. Tidal forces are intense for short-period planets and result in decay of the orbit on a timescale that depends on properties of the star as long as the orbit is circular. However, if an eccentric companion planet exists, orbital eccentricity (ei, where i is the inner orbit) is induced, and the decay timescale depends on properties of the short-period planet, reduced by a factor of the order of 105e if it is terrestrial. Here we examine the influence companion planets have on the tidal and dynamical evolution of short-period planets with terrestrial structure, and we show that the relativistic potential of the star is fundamental to their survival.

P+6,8He elastic scattering at intermediate energies

Using a relativistic nuclear optical potential consisting of a Lorentz scalar, Vs, and the time-like component of a four-vector potential, V0, with a Gaussian form factor, we have calculated elastic scattering differential sections and polarizations for p+ 6,8He at intermediate energies. We compare our results with those of the Relativisitic Impulse Approximation (RIA) and with the available experimental data in the range of 0 < t < 0.22 (GeV/c)2.

Mergers of binary stars: the ultimate heavy-ion experience

The mergers of black-hole neutron star binaries are calculated using a pseudo-general relativistic potential that incorporates post-Newtonian corrections. Both normal matter neutron stars and self-bound strange quark matter stars are considered as black-hole partners. As long as the neutron stars are not too massive relative to the black-hole mass, orbital decay terminates in stable mass transfer rather than an actual merger. For a normal neutron star, mass transfer results in a widening of the orbit but the stable transfer ends before the minimum neutron star mass is reached. For a strange star, mass transfer does not result in an appreciable enlargement of the orbital separation, and the stable transfer continues until the strange star essentially disappears. These differences might be observable through their respective gravitational wave signatures.

Relativistic correlating basis sets for the sixth-period d-block atoms from Lu to Hg.

Contracted Gaussian-type function sets to describe valence correlation are developed for the sixth-period d-block atoms Lu through Hg. A segmented contraction scheme is employed for their compactness and efficiency. Contraction coefficients and exponents are determined by minimizing the deviation from accurate natural orbitals generated from configuration interaction calculations, in which relativistic effects are incorporated through the third-order Douglas-Kroll approximation. The present basis sets yield more than 99% of atomic correlation energies predicted by accurate natural orbital sets of the same size. Relativistic model core potential calculations with the present correlating sets give the spectroscopic constants of the AuH molecule in excellent agreement with experimental results.

Isospin-dependent relativistic microscopic optical potential in the Dirac Brueckner-Hartree-Fock method

The relativistic microscopic optical potential in the asymmetric nuclear matter is studied in the framework of the Dirac Brueckner-Hartree-Fock method. A new decomposition of the Dirac structure of the nuclear self-energy in nuclear matter is adopted. The self-energy of a nucleon with E > 0 in nuclear matter is calculated with the G matrix in the Hartree-Fock approach. The optical potential of a nucleon in the nuclear medium is identified with the nucleon self-energy. The energy and asymmetric parameter dependence of the relativistic optical potentials for proton and neutron are discussed. The resulting Schroedinger equivalent potentials have reasonable behaviors of the energy dependence. The asymmetric parameter dependence of relativistic optical potentials and Schroedinger potentials are emphasized.

Nuclear model effects in charged-current neutrino-nucleus quasielastic scattering

The quasielastic scattering of muon neutrinos on oxygen 16 is studied for neutrino energies between 200 MeV and 1 GeV using a relativistic shell model. Final state interactions are included within the distorted wave impulse approximation, by means of a relativistic optical potential, with and without imaginary part, and of a relativistic mean field potential. For comparison with experimental data the inclusive charged--current quasielastic cross section for $\nu_\mu$--$^{12}C$ scattering in the kinematical conditions of the LSND experiment at Los Alamos is also presented and briefly discussed.

A relativistic separable potential to describe pairing in nuclear matter

Using the Dirac–Hartree–Fock–Bogoliubov approximation to study nuclear pairing, we have found the short-range correlations of the Dirac 1 S 0 pairing fields to be essentially identical to those of the two-nucleon virtual state at all values of the baryon density. We make use of this fact to develop a relativistic separable potential that correctly describes the pairing fields.

Elastic scattering of electrons from krypton

We present differential cross sections for elastic scattering of electrons from krypton andcompare our results with experimental measurements for differential and integrated crosssections including recent experiments which extend the measurements to larger scatteringangles. Our calculations are based upon the relativistic polarized-orbital method andinclude both static and dynamic polarization potentials as well as an absorption potentialto simulate the loss of flux into other channels. The inclusion of these absorption effectssignificantly improves upon our previous calculations, bringing them into very good toexcellent agreement with experimental measurements of the differential cross sections aswell as the total and momentum transfer cross sections over the energy range from 10 to200 eV.