Velocity-dependent Potential Research Articles

Derivation of the Lee-Yang term via stochastic quantization.

We derive the so called Lee-Yang term for velocity-dependent potentials via stochastic quantization. The derivation shows that there is a subtlety in choosing the appropriate Langevin equation, i.e., the Langevin equation must have a positive-definite Fokker-Planck Hamiltonian. In the derivation, we also make use of the Stratonovic calculus to transform a stochastic equation with an additive white noise to a stochastic equation with multiplicative white noise.

Reply to "Bound states in pion-nucleus velocity-dependent potentials: Finite or infinite number"

The discrepancy between the results obtained by Gal and Mandelzweig and those published by us is shown to be due to an ambiguity in the definition of the radial wave function occurring whenever the velocity-dependent potential satisfies the criticality condition of Ericson and Myhrer. The non-Hermitian solutions predicted by these authors are closely related to that ambiguity.

Nonlocal potentials and their exact and approximate local and velocity-dependent equivalents

We show that good approximations to the exact equivalent local potential (ELP) and damping factor of a nonlocal Perey-Buck potential can be calculated in the partial wave WKB approximation of Horiuchi. The exact ELP and damping factor are obtained by means of a method previously given by one of us. We also confirm that an approximate ELP proposed by Bauhoff et al. is of comparable accuracy as the Horiuchi approximation. Thesel-dependent ELP's exhibit reduced attraction in the interior and provide a test for higher order WKB approximations. We subsequently obtain an equivalent velocity dependent potential (EVDP) which is even exactly wave function equivalent to the original nonlocal potential. This almost local potential, unlike the trivial equivalent local potential, is smooth and well-behaved and is therefore particularly useful in nuclear reactions where the off-shell behaviour of the potential is important.

Bound states in the pion-nucleus velocity-dependent potential

The possibility of bound states in a velocity-dependent potential of the Kisslinger type, such as that used to describe the low-energy pion-nucleus interaction, is discussed. It is shown in a specific example that, for a real potential, the number of bound states is finite and their binding energies are real, in contradiction with general results claimed by other authors.NUCLEAR REACTIONS Pion-nucleus optical potential; nuclear bound states of pions in nuclei; velocity-dependent potential.

Generalization of Szebehely's equation

Szebehely's partial differential equation for the force functionU=U(x,y) which gives rise to a given family of planar orbitsf(x,y)=Constant is generalized to account for velocity-dependent potentials V*=V*(x,y, $$\dot x,\dot y$$ ). The new partial differential equation is quasi-linear and of the first order. An example is given and a comparison is made of the two equations.

Path integration for velocity-dependent potentials

We extent the prodistribution definition of path integrals to include Lagrangians with velocity-dependent potentials. We use Cameron-Martin transformations to evaluate a large part of a path integral exactly and give techniques for evaluating the remaining terms of the semi-classical expansion of the path integral. The Fredholm determinants, associated with these transformations, are evaluated explicitly in terms of Jacobi matrices defined by the classical system.

Two-body effects in the sum rules for thed(γ, p)nreaction

The integrated and bremsstrahlung-weighted cross sections have been calculated including the one-pion-exchange contributions to the charge density for the Paris, super-soft-core, Yale, Hamada-Johnston, and modified Hamada-Johnston potentials. The contribution of the two-meson exchange to the integrated cross section has been estimated. For velocity independent potentials the change in the enhancement factor due to the meson exchange is found to be approximately the same, but it is a little larger for the velocity dependent (Paris) potential. It is found that contrary to the claim made in the literature the integrated cross section cannot distinguish between the various two-nucleon potentials.NUCLEAR REACTIONS $d(\ensuremath{\gamma}, p)n$, calculated integrated and bremsstrahlung-weighted cross sections; included one- and two-pion exchange contribution.

Analytic velocity-dependent potential for bound and scattering states of electrons and atoms

In this work we represent the static potential of an electron interacting with an atom by a sum of two Debye-H\"uckel or Yukawa functions. We approximate the nonlocal exchange term by an attractive, velocity-dependent potential using the effective-mass approximation with a regularized Yukawa form factor. This is transformed to an approximate local but energy-dependent potential. We also include an imaginary term with a regularized Yukawa form factor in the static potential. We apply this framework to a description of the bound and scattering states of electrons interacting with atomic oxygen and electrons interacting with neon. The results suggest that a small degree of velocity or energy dependence yields improvements with respect to the use of strictly static electron-atom potentials. In applications to atomic physics the formalism which is economical in parameters should serve as a simple parametrization of experimental data and as a means of extrapolation and interpolation of experimental observations.

Correlations between potentials and observables in the NN interaction

We study the effects of the components of the soft-core and velocity-dependent Paris nucleon-nucleon potential on the scattering observables for laboratory energies, T L, between 10 and 350 MeV. Knowledge of these correlations is useful to indicate constraints on components of the nucléon-nucléon force. The velocity-dependent component, attractive at low energy and repulsive at high energy, plays a role at all energies. The polarisation P, the depolarisation D and the parameters D t, A, R, C KP and C NN are good tests for the tensor, spin-orbit and, to a smaller extent, quadratic spin-orbit forces. The isovector tensor force contribution is important at low energy and that of the isovector spin-orbit at high energy. The isoscalar tensor force effect is large at all energies and that of the isoscalar spin-orbit force rather small. The potential without quadratic spin-orbit term reproduces well the experimental data for T L < 150 MeV.

Effects of velocity dependent potentials in the low-lying octupole vibration

The low-lying octupole state is investigated in the framework of the schematic model. It is shown that the inclusion of the spin - orbit interaction is responsible for the fragmentation of the octupole strength in the low-lying region. An explicit expression for the vibrational energy which satisfactorily reproduces the average behaviour of experimental data is derived. The role of effective mass is also discussed.

Ermakov systems, velocity dependent potentials, and nonlinear superposition

We derive new Ermakov systems with velocity-dependent potentials. The extended Ermakov system presented contains all known one-dimensional cases and many new systems. These Ermakov systems lead to a nonlinear superposition law for the solutions.

Considerations about equivalent models in a classical one-dimensional system

A series of equivalent models for a classical, conservative, one-dimensional system is developed. Next, with respect to such models, we obtain a set of related results about some specific, interesting, and outwardly unconnected subjects in mechanics. For instance, dissipative functions, variable mass, generalized velocity-dependent potentials, ’’hidden motions’’, and noninertial situations. A comparative analysis allows us to deduce certain formal analogies with particular relativistic statements.

Existence of strongly bound states of pions in nuclei

References are given to mostly unknown work on velocity-dependent potentials of the kind used in optical pion-nucleus models for which the possibility of an infinity of strongly bound states has been recently suggested.NUCLEAR REACTIONS Pion-nucleus optical potential; nuclear bound states of pions in nuclei; complex velocity-dependent potential.

Binding in velocity dependent potentials and pion-nuclear systems

Properties of bound states in velocity-dependent potentials are discussed and the WKB approximation is established and used to derive quantization conditions for such states. The most updated zero-range optical potential for pionic atoms is reviewed and employed for the calculation of strongly bound π − nuclear states. Some of the several physical mechanisms, in particular the πN finite interaction range, which affect the whole issue of binding and critically determine the number of bound states expected, are qualitatively discussed. Unless dynamical suppression of π − nuclear absorption occurs below threshold, the calculated states are too wide to be considered as well-defined physical states.

Alpha Cluster in Hartree‐Fock Calculations

AbstractHartree‐Fock (HF) calculations have been performed fcr 12C nucleus assuming a trigonal D3h equilibrium configuration. Different aspects including symmetry, kinds of two‐body interactions are investigated. The HF calculations have been carried out using a velocity dependent effective potential of s‐wave interaction. The results are compared with previous calculations. In all HF calculations no deviation from axial symmetry is obtained.

Binding in velocity dependent potentials and pion-nuclear systems: V. B. Mandelzweig, A. Gal, and E. Friedman. Racah Institute of Physics, The Hebrew University, Jerusalem, Israel

Binding in velocity dependent potentials and pion-nuclear systems: V. B. Mandelzweig, A. Gal, and E. Friedman. Racah Institute of Physics, The Hebrew University, Jerusalem, Israel

Properties of nuclear matter using the velocity-dependent effective potential ofs-wave interaction

Two forms of a velocity-dependent effective potential are used. The binding energy and the incompressibility of the nuclear matter are calculated. These are found to be in a good agreement with those obtained by others and with the experimental results. The single-particle potential, the effective massM* and the nuclear surface energy are also discussed and compared with those obtained by the others.

Newtonian limit for a geodesic in a Schwarzschild field

In the 19th century there were many attempts to explain the advance of the perihelion of Mercury by modifying the Newtonian potential by the addition of velocity-dependent terms. That such potentials did not give better results was due to the wrong choice of sign of the velocity term. This is demonstrated by showing that in a simple Newtonian limit for near-circular orbits the geodesic of a mass point in a Schwarzschild field may be expressed as motion in a velocity-dependent central potential. The sign of the velocity term is opposite to that arbitrarily assigned in the past.

Grain boundary drag in alloys

The extrinsic component of the drag force on a grain boundary in an alloy of arbitrary composition and appreciable atomic size disparity is studied in a model in which the boundary is simulated by an externally imposed two-dimensional distortion field. Extrinsic boundary properties arise from processes occurring near, but not in the boundary, so the present study may also be viewed as a study of the coupled concentration and strain fields near a boundary. The results of this paper may be interpreted qualitatively in terms of a velocity and temperature dependent solute-boundary interaction potential. In the limit of small concentrations, this potential becomes velocity and temperature independent so we recover essentially the grain boundary drag theory of Cahn and Lücke and Stüwe. We find that for temperatures close to the coherent spinodal, the grain boundary mobility decreases rapidly with increasing velocity at low velocity, and that this behavior corresponds to a composition profile which is very sensitive to velocity. These effects are less pronounced at higher temperatures. The results apply to velocities less than the breakaway velocity, but the way to extend the theory to higher velocities is indicated.

On the low-energy scattering by velocity-dependent potentials

On the low-energy scattering by velocity-dependent potentials