Tensor Potential Research Articles

Theoretical Foundation of the Nuclear Force in QCD and Its Applications to Central and Tensor Forces in Quenched Lattice QCD Simulations

We present full accounts of a method to extract nucleon-nucleon (NN) potentials from the Bethe-Salpter amplitude in lattice QCD. The method is applied to two nucleons on the lattice with quenched QCD simulations. By disentangling the mixing between the S-state and the D-state, we obtain central and tensor potentials in the leading order of the velocity expansion of the non-local NN potential. The spatial structure and the quark mass dependence of the potentials are analyzed in detail.

Pseudospin and spin symmetry in the Dirac equation with Woods-Saxon potential and tensor potential

The Dirac equation is solved approximately for the Woods-Saxon potential and a tensor potential with the arbitrary spin-orbit coupling quantum number \( \kappa\) under pseudospin and spin symmetry. The energy eigenvalues and the Dirac spinors are obtained in terms of hypergeometric functions. The energy eigenvalues are calculated numerically.

Some details of the description of a disordered condensed system using the theory of defect states of orientational order

Using the theory of defect states of orientational order, we describe a disordered condensed system as an elastic medium with linear topological singularities. We show that elastic stress fields produced by linear disclinations are Abelian. In the quasistationary linear approximation, we obtain expressions for linear dislocation and disclination tensor potentials. We show that using the theory of defect states of orientational order, we can describe the α and β relaxations in a supercooled liquid as relaxation processes in the respective disclination and dislocation subsystems.

EXACT SOLUTIONS OF THE DIRAC EQUATION WITH HARMONIC OSCILLATOR POTENTIAL INCLUDING A COULOMB-LIKE TENSOR POTENTIAL

In this work, we study the Dirac equation with scalar, vector, and tensor interactions. The Dirac Hamiltonian contains quadratic scalar and vector potentials, as well as a tensor potential. The tensor potential is taken as a sum of a linear term and a Coulomb-like term. It is shown that the tensor potential preserves the form of the harmonic oscillator potential and generates spin-orbit terms. The energy eigenvalues and the corresponding eigenfunctions are obtained for different alternatives.

Dirac equation with scalar and vector quadratic potentials and Coulomb-like tensor potential

It is shown that the Dirac equation with scalar and vector quadratic potentials and a Coulomb-like tensor potential can be solved exactly. The bound state solutions for equal vector and scalar potentials are obtained. The limit of zero tensor coupling is investigated. The case of equal vector and scalar potentials with opposite sign is also studied. The pseudospin symmetry and its breaking by the tensor interaction are discussed.

Core Polarization and Tensor Coupling Effects on Magnetic Moments of Hypernuclei

Effects of core polarization and tensor coupling on the magnetic moments in Λ13C, Λ17O, and Λ41Ca Λ-hypernuclei are studied by employing the Dirac equation with scalar, vector and tensor potentials. It is found that the effect of core polarization on the magnetic moments is suppressed by Λ tensor coupling. The Λ tensor potential reduces the spin-orbit splitting of pΛ states considerably. However, almost the same magnetic moments are obtained using the hyperon wavefunction obtained via the Dirac equation either with or without the A tensor potential in the electromagnetic current vertex. The deviations of magnetic moments for pΛ states from the Schmidt values are found to increase with nuclear mass number.

BBpotentials in quenched lattice QCD

The potentials between two B mesons are computed in the heavy-quark limit using quenched lattice QCD at m{sub {pi}}{approx}400 MeV. Nonzero central potentials are clearly evident in all four spin-isospin channels (I,s{sub l})=(0,0), (0, 1), (1, 0), (1, 1), where s{sub l} is the total spin of the light degrees of freedom. At short distance, we find repulsion in the I{ne}s{sub l} channels and attraction in the I=s{sub l} channels. Linear combinations of these potentials that have well-defined spin and isospin in the t-channel are found, in three of the four cases, to have substantially smaller uncertainties than the potentials defined with the s-channel (I,s{sub l}), and allow quenching artifacts from single hairpin exchange to be isolated. The BB*{pi} coupling extracted from the long-distance behavior of the finite-volume t-channel potential is found to be consistent with quenched calculations of the matrix element of the isovector axial-current. The tensor potentials in both of the s{sub l}=1 channels are found to be consistent with zero within calculational uncertainties.

Deconstructing triplet nucleon-nucleon scattering

Nucleon-nucleon scattering in spin-triplet channels is analyzed within an effective field theory where one-pion exchange is treated nonperturbatively. Justifying this requires the identification of an additional low-energy scale in the strength of that potential. Short-range interactions are organized according to the resulting power counting, in which the leading term is promoted to significantly lower order than in the usual perturbative counting. In each channel there is a critical momentum above which the waves probe the singular core of the tensor potential and the new counting is necessary. When the effects of one- and two-pion exchange have been removed using a distorted-wave Born approximation, the residual scattering in waves with L{ =}3 is consistent with the perturbative counting, at least for energies up to 300 MeV. This pattern is in agreement with estimates of the critical momenta in these channels.

Negative parity bands in 238U

We describe the low-lying negative parity states of 238U in terms of a Pb–Ne cluster model. The Pb core is in an excited 3− state and the relative orbital motion has angular momentum values L = 0, 2, 4, …. The two bodies interact through central and second rank tensor potentials, leading to four bands loosely labelled by the rotational model notation of Kπ = 0−, 1−, 2−, 3−. However, the coupling between core and cluster is of intermediate strength, leading to an irregular pattern of energy differences, in particular inverted doublets in the Kπ = 1− band. Remarkably, the main features of the predicted spectrum are borne out by experiment.

Evolution of nuclear shells with the Skyrme density dependent interaction

We present the evolution of the shell structure of nuclei in Hartree-Fock calculations using Skyrme's density-dependent effective nucleon-nucleon interaction. The role of the tensor part of the Skyrme interaction to the Hartree-Fock spin-orbit splitting in spherical spin unsaturated nuclei is reanalyzed. The contribution of a finite range tensor force to the spin-orbit splitting in closed shell nuclei is calculated. It is found that the exact matrix elements of a Gaussian and of a one-pion exchange tensor potential could be written as a product Skyrme's short range expression times a suppression factor which is almost constant for closed shell nuclei with mass number $A\ensuremath{\geqslant}48$. The suppression factor is $\ensuremath{\sim}0.15$ for the one-pion exchange potential.

Finding fields and self-force in a gauge appropriate to separable wave equations

Gravitational waves from the inspiral of a stellar-size black hole to a supermassive black hole can be accurately approximated by a point particle moving in a Kerr background. This paper presents progress on finding the electromagnetic and gravitational field of a point particle in a black-hole spacetime and on computing the self-force in a ``radiation gauge.'' The gauge is chosen to allow one to compute the perturbed metric from a gauge-invariant component ${\ensuremath{\psi}}_{0}$ (or ${\ensuremath{\psi}}_{4}$) of the Weyl tensor and follows earlier work by Chrzanowski, Cohen, and Kegeles (we correct a minor, but propagating, error in the Cohen-Kegeles formalism). The electromagnetic field tensor and vector potential of a static point charge and the perturbed gravitational field of a static point mass in a Schwarzschild geometry are found, surprisingly, to have closed-form expressions. The gravitational field of a static point charge in the Schwarzschild background must have a strut, but ${\ensuremath{\psi}}_{0}$ and ${\ensuremath{\psi}}_{4}$ are smooth except at the particle, and one can find local radiation gauges for which the corresponding spin $\ifmmode\pm\else\textpm\fi{}2$ parts of the perturbed metric are smooth. Finally a method for finding the renormalized self-force from the Teukolsky equation is presented. The method is related to the Mino, Sasaki, Tanaka and Quinn and Wald (MiSaTaQuWa) renormalization and to the Detweiler-Whiting construction of the singular field. It relies on the fact that the renormalized ${\ensuremath{\psi}}_{0}$ (or ${\ensuremath{\psi}}_{4}$) is a source-free solution to the Teukolsky equation; and one can therefore reconstruct a nonsingular renormalized metric in a radiation gauge.

The Dirac oscillator with a Coulomb-like tensor potential

We study the Dirac equation with a tensor potential which contains a term linear in r and a Coulomb-like term. The eigenstates and eigenvalues are obtained exactly. We found that the energy spectrum and the degeneracy of the levels depend on the alignment of spin with the orbital angular momentum. For parallel alignment, the second term in the potential makes no contribution to the energy levels.

Dominant2πγ-exchange nucleon-nucleon interaction: Spin-spin and tensor potentials

We calculate at two-loop order in chiral perturbation theory the electromagnetic corrections to the two-pion exchange nucleon-nucleon interaction that is generated by the isovector spin-flip $\pi\pi NN$ contact-vertex proportional to the large low-energy constant $c_4\simeq 3.4 $GeV$^{-1}$. We find that the respective $2\pi\gamma$-exchange potentials contain sizeable isospin-breaking components which reach up to -4% of corresponding isovector $2\pi$-exchange potentials. The typical values of these novel charge-independence breaking spin-spin and tensor potentials are $-0.11 $MeV and $0.09 $MeV, at a nucleon distance of $r=m_\pi^{-1}=1.4 $fm. The charge-symmetry breaking spin-spin and tensor potentials come out a factor of 2.4 smaller. Our analytical results for these presumably dominant isospin-violating spin-spin and tensor NN-forces are in a form such that they can be easily implemented into phase-shift analyses and few-body calculations.

Volume-preserving maps, source-free systems and their local structures

In this paper, we study local structures of volume-preserving maps and source-free vector fields, which are defined in the Euclidean n-space Rn with n ≥ 3. First, we prove that any volume-preserving map, defined in some neighbourhood of the origin, can be represented as a composition of n − 1 essentially two-dimensional area-preserving maps. This result can be viewed as an analogue of the following known fact (Feng and Shang 1995 Volume-preserving algorithms for source-free dynamical systems Numer. Math. 71 451–63): any source-free vector field on Rn can be represented as a sum of n − 1 essentially two-dimensional Hamiltonian vector fields. Then, we present a local representation of source-free vector fields under volume-preserving coordinate changes. Finally, we construct a Lie algebra of skew-symmetric tensor potentials of second order associated with source-free vector fields. The Lie algebra turns out to be isomorphic to the Lie algebra of source-free vector fields.

Pion-photon exchange nucleon-nucleon potentials

In chiral perturbation theory, the dominant next-to-leading-order correction to the {pi}{gamma}-exchange NN-potential proportional to the large isovector magnetic moment {kappa}{sub v}=4.7 of the nucleon is calculated. The corresponding spin-spin and tensor potentials V{sup {approx}}{sub S,T}(r) in coordinate space have a very simple analytical form. At long distances, r{approx_equal}2 fm, these potentials are of similar size (but opposite in sign) as the leading-order {pi}{gamma}-exchange potentials. Effects from virtual {delta}-isobar excitation are also considered, as well as other isospin-breaking contributions to the 2{pi}-exchange NN potential induced by additional one-photon exchange.

Evolution of Nuclear Shells due to the Tensor Force

The monopole effect of the tensor force is presented, exhibiting how spherical single-particle energies are shifted as protons or neutrons occupy certain orbits. An analytic relation for such shifts is shown, and their general features are explained intuitively. Single-particle levels are shown to change in a systematic and robust way, by using the pi + rho meson exchange tensor potential, consistently with the chiral perturbation idea. Several examples are compared with experiments.

Crossing the phantom divide barrier with scalar tensor theories

There is accumulating observational evidence (based on SnIa data) that the dark energy equation of stateparameter w may be evolving with time and crossing the phantom divide barrierw = −1 at recent times. The confirmation of these indications by future data would indicate thatminimally coupled quintessence cannot reproduce the observed expansion rateH(z) for any scalar field potential. Here we explicitly demonstrate that scalar tensortheories of gravity (extended quintessence) can predict crossing of the phantomdivide barrier. We reconstruct phenomenologically viable scalar–tensor potentialsF(Φ) and U(Φ) that can reproduce a polynomial best fit expansion rateH(z) and the corresponding dark energy equation of state parameterw(z) crossingthe w = −1 line. The form of the reconstructed scalar tensor potentials is severely constrained but isnot uniquely determined. This is due to observational uncertainties in the form ofH(z) and also because asingle observed function H(z) does not suffice for the reconstruction of the two potential functionsF(Φ) and U(Φ).

PERTURBATIVE BREAKING OF THE PSEUDOSPIN SYMMETRY IN THE RELATIVISTIC HARMONIC OSCILLATOR

We show that relativistic mean fields theories with scalar S, and vector V, quadratic radial potentials can generate a harmonic oscillator with exact pseudospin symmetry and positive energy bound states when S=-V. The eigenenergies are quite different from those of the non-relativistic harmonic oscillator. We also discuss a mechanism for perturbatively breaking this symmetry by introducing a tensor potential. Our results shed light into the intrinsic relativistic nature of the pseudospin symmetry, which might be important in high density systems such as neutron stars.

The speed of gravity in general relativity and theoretical interpretation of the Jovian deflection experiment

According to Einstein, the notions of geodesic, parallel transport (affine connection) and curvature of the spacetime manifold have a pure geometric origin and do not correlate with any electromagnetic concepts. At the same time, curvature is generated by matter which is not affiliated with the spacetime geometric concepts. For this reason, the fundamental constant c entering the geometric and matter sectors of the general theory of relativity has different conceptual meanings. Specifically, the letter c on the left-hand side of the Einstein equations (geometric sector) entering the Christoffel symbols and its time derivatives is the ultimate speed of gravity characterizing the upper limit on the speed of its propagation as well as the maximal rate of change of time derivatives of the metric tensor, that is gravitational field. The letter c on the right-hand side of the Einstein equations (matter sector) is the maximal speed of propagation of any other field rather than gravity. Einstein's general principle of relativity extends his principle of special relativity and equates the numerical value of the ultimate speed of gravity to that of the speed of light in the special theory of relativity but this general principle must be tested experimentally. To this end, we work out the speed of gravity parametrization of the Einstein equations (cg-parametrization) to keep track of the time-dependent effects associated with the geometric sector of general relativity and to separate them from the time-dependent effects of the matter sector. Parametrized post-Newtonian (PPN) approximation of the Einstein equations is derived in order to explain the gravitational physics of the Jovian deflection VLBI experiment conducted on 8 September 2002. The post-Newtonian series expansion in the cg-parametrized general relativity is with respect to a small parameter that is proportional to the ratio of the characteristic velocity of the bodies to the speed of propagation of the gravitational interaction cg. The Einstein equations are solved in terms of the Liénard–Wiechert tensor potentials which are used for integrating the light-ray propagation equations. An exact analytic expression for the relativistic time delay in the propagation of a radio wave from a quasar to an observer is calculated under the assumption that the light-ray deflecting bodies move with constant velocities. A post-Newtonian expansion of the time delay proves that in general relativity the time delay is affected by the speed of gravity already to the first order in 1/cg beyond the leading (static) Shapiro term. We conclude that recent measurements of the propagation of the quasar's radio signal past Jupiter are directly sensitive to the time-dependent effect from the geometric sector of general relativity which is proportional to the speed of propagation of gravity cg but not the speed of light. It provides a first confirmative measurement of the fundamental speed c of the Einstein general principle of relativity for gravitational field. A comparative analysis of our formulation with the alternative interpretations of the experiment given by other authors is provided.

Lanczos tensor potential for conformally flat space-times

A sufficient condition is derived for the Lanczos tensor potential such that the Weyl tensor remains conformal. This condition is then applied to the metric of a conformally flat space-time, and the corresponding Lanczos tensor potential is obtained.