Reworking the Tucson-Melbourne Three-Nucleon Potential

 We introduce new values of the strength constants (i.e., a, b, c, and d coefficients) of the Tucson-Melbourne (TM) 2π-exchange three-nucleon potential. The new values come from contemporary dispersion-relation analyses of meson-factory πN-scattering data. We make variational Monte-Carlo calculations of the triton with the original and updated three-body forces to study the effects of this update. We remove a short-range–π-range part of the potential due to the c coefficient and discuss the effect on the triton binding energy. Received September 11, 1999; revised November 2, 1999; accepted February 23,     

An Algebraic Approach to the Generalized Symmetrical Double-Well Potential

We have obtained the energy eigenvalues and the corresponding eigenfunctions for the generalized double-well potential in the non-relativistic Schr?dinger equation. We have calculated the creation and annihilation operators directly from the eigenfunction and we have shown these operators satisfy the commutation relation of the SU(2) group. We have expressed the Hamiltonian in terms of the su(2) algebra. Some interesting result including the standard symmetrical double-well potential, reflectionless-type potential and V ₀tanh ²(r/d) potential are also discussed.     

On the Semiclassical Propagator for Any One-Dimensional Admissible Potential

This paper shows that by choosing suitably the general fundamental invariantI=f(I₁) as a new canonical momentum, we can find the semiclassical propagator for any one-dimensional admissible potential, whereIis a certain function of the fundamental invariantI₁. We apply this method to the case of quartic potential and point out few applications of the propagator for this potential.     

Continuity of the Lyapunov Exponent for Quasiperiodic Operators with Analytic Potential

We study regularity properties of the Lyapunov exponent L of one-frequency quasiperiodic operators with analytic potential, under no assumptions on the Diophantine class of the frequency. We prove joint continuity of L, in frequency and energy, at every irrational frequency.     

Born Reciprocity and the 1/r Potential

Many structures in nature are invariant under the transformation pair, (p,r)→(b  r,−p/b), where b is some scale factor. Born’s reciprocity hypothesis affirms that this invariance extends to the entire Hamiltonian and equations of motion. We investigate this idea for atomic physics and galactic motion, where one is basically dealing with a 1/r potential and the observations are very accurate, so as to determine the scale b≡mΩ. We find that an Ω∼1.5×10⁻¹⁵ s⁻¹ has essentially no effect on atomic physics but might possibly offer an explanation for galactic rotation, without invoking dark matter.     

Potential double layers in double plasma device

Results of the investigation on the formation of double layers in double plasma device are presented. By appropriate modifications in the biasing conditions, we have been able to obtain both weak (eΔφ<10KT _e ) and strong double layers (eΔφ>10kT _e ) in the device. Unlike previous experiments, we have not been limited to potential jumps equal to ionisation potential of the neutral gas. A detailed investigation has been carried out to find out why earlier experiments in similar devices were limited to only weak double layers. We have also investigated the phenomenon of the so-called psuedo-double layers and have shown that they are potential jumps over the thickness of the order of Debye length and precede plasma expanding with velocity many times the ion-acoustic velocity. They do not represent metastable states of the plasma as suggested by earlier investigators.     

Periodic Driving Induced Anomalous End Modes in a Superconducting Wire with the Second-Neighbor Pairing Potential

The anomalous end modes are generated in a one-dimensional p-wave superconducting wire with second-neighbor couplings and a periodic driving in pairing potential. We show that the driving on the amplitude or the phase of the first-neighbor and second-neighbor pairing potential can both generate conventional end modes and anomalous end modes, with corresponding Floquet eigenvalues equal to ± 1 or appear in complex conjugate pairs. We have numerically studied the driving of the first-neighbor and second-neighbor pairing potential, and also analyzed the end modes, Floquet eigenvalues and the Fourier transform of these end modes.

     

Solutions of the Dirac Equation for the Davidson Potential

In the present paper we solve the Dirac equation with Davidson potential by Nikiforov-Uvarov method. The Dirac Hamiltonian contains a scalar S and a vector V Davidson potentials. With equal scalar and vector potential, analytical solutions for bound states of the corresponding Dirac equations are found.     

Cosmological Dynamics of the Tachyon with an Inverse Power-Law Potential

We investigate tachyon dynamics with an inverse power-law potential V () ^–. We find global attractors of the dynamics leading to a dust behavior for > 2 and to an accellerating universe for 0 < 2. We study linear cosmological perturbations and we show that metric fluctuations are constant on large scales in both cases. In the presence of an additional perfect fluid, the tachyon with this potential behaves as dust or dark energy.     

Lanczos Potential for the van Stockung Space-Time

The Lanczos Potential is a theoretical useful tool to find the conformal Weyl curvature tensor C _abcd of a given relativistic metric. In this paper we find the Lanczos potential L _abc for the van Stockung vacuum gravitational field. Also, we show how the wave equation can be combined with spinor methods in order to find this important three covariant index tensor.     

Potential energy of the K**-He quasimolecule

The potential curves of the nl(²Λ) electronically excited states of the K**-He quasimolecule (n, l, and Λ are the principal quantum number, angular momentum, and its projection on the molecular axis) are calculated. To describe the interaction of the weakly bound electron with the singly charged potassium ion and the ground-state helium atom (with taking into account their long-range electrostatic interactions), the formalism of two-center scattering theory and the finite-range pseudopotential method are used. A comparison with the results of calculations performed by the MRD CI method is carried out. The findings showed that, for small principal quantum numbers n, these methods complement each other, because the first is more reliable for large interatomic distances, R ≥ n, whereas second for small, R < n. The characteristic features of the behavior of the potential curves of the K**-He quasimolecule at large n and l are discussed.     

Analytical Solutions of the Kratzer-Fues Potential in an Arbitrary Number of Dimensions

No Heading Some aspects of the N dimensional Kratzer-Fues potential are discussed, which is an extension of the combined Coulomb-like potential with inverse quadratic potential in N dimensions. The analytical solutions obtained (eigenfunctions and eigenvalues) are dimensionally dependent, so also, the solutions depend on the value of the coefficient of the inverse quadratic term. The expectation values for < r^–2 >, < r^–1 > and the virial theorem for this potential are obtained and the values are also dimensions and parameter dependent.     

The Lanczos Potential for Weyl-Candidate Tensors Exists Only in Four Dimensions

We prove that a Lanczos potential L _abc for the Weyl candidate tensor W _abcd does not generally exist for dimensions higher than four. The technique is simply to assume the existence of such a potential in dimension n, and then check the integrability conditions for the assumed system of differential equations; if the integrability conditions yield another non-trivial differential system for L _abc and W _abcd, then this system's integrability conditions should be checked, and so on. When we find a non-trivial condition involving only W _abcd and its derivatives, then clearly Weyl candidate tensors failing to satisfy that condition cannot be written in terms of a Lanczos potential L _abc.     

Formation and Dynamics of Very Deep Negative Potential Well in the Small Tokamak Device CSTN-IV

We achieved a potential well more than fifty times deeper than the plasma electron temperature, down to -0.3 kV with the electrode biasing, by the cross-field radial arcing current of up to 150 A which flows between the small electron-emitting electrode (LaB₆) inserted to the plasma center and the stainless-steel wall of vacuum chamber. The empirical scaling of the radial resistance of plasma R _r on the radial arcing current I _b and the toroidal magnetic field B _T is found to be R _r I _b ^-1.2 B _T ^1.0. Structural dynamics of negative potential well formation is observed: the potential dip propagates from the plasma core to the periphery. The ion saturation current also increases, starting from the inner region. The fluctuation frequency in I _sat changes abruptly from 200 kHz to 30 kHz in a time of around 0.25 ms after negative biasing.     

Quantum Mayer Graphs for Coulomb Systems and the Analog of the Debye Potential

Within the Feynman–Kac path integral representation, the equilibrium quantities of a quantum plasma can be represented by Mayer graphs. The well known Coulomb divergencies that appear in these series are eliminated by partial resummations. In this paper, we propose a resummation scheme based on the introduction of a single effective potential that is the quantum analog of the Debye potential. A low density analysis of shows that it reduces, at short distances, to the bare Coulomb interaction between the charges (which is able to lead to bound states). At scale of the order of the Debye screening length ^–1 _D, approaches the classical Debye potential and, at large distances, it decays as a dipolar potential (this large distance behaviour is due to the quantum nature of the particles). The prototype graphs that result from the resummation obey the same diagrammatical rules as the classical graphs of the Abe–Meeron series. We give several applications that show the usefulness of to account for Coulombic effects at all distances in a coherent way.     

Solution of the Fokker-Planck Equation with a Logarithmic Potential

We investigate the diffusion of particles in an attractive one-dimensional potential that grows logarithmically for large |x| using the Fokker-Planck equation. An eigenfunction expansion shows that the Boltzmann equilibrium density does not fully describe the long-time limit of this problem. Instead this limit is characterized by an infinite covariant density. This non-normalizable density yields the mean square displacement of the particles, which for a certain range of parameters exhibits anomalous diffusion. In a symmetric potential with an asymmetric initial condition, the average position decays anomalously slowly. This problem also has applications outside the thermal context, as in the diffusion of the momenta of atoms in optical molasses.     

Potential theory of strong electrolyte solutions using the Bogoliubov-Born-Green-Yvon integral equations

A potential analysis of strong electrolyte solutions is undertaken using the BBGY hierarchy of integral equations. An estimate for the fluctuation potential is found which implies damped oscillatory solutions of the Debye-Hückel potential for κa ? 1·720 (κ = Debye-Hückel constant, a = ionic diameter). The relation to the work of Martynov is also given.     

Letter: Gravitational Potential in the Palatini Formulation of Modified Gravity

General Relativity has so far passed almost all the ground-based and solar-system experiments. Any reasonable extended gravity models should consistently reduce to it at least in the weak field approximation. In this work we derive the gravitational potential for the Palatini formulation of the modified gravity of the L(R) type which admits a de Sitter vacuum solution. We argue that the Newtonian limit is always obtained in those class of models and the deviations from General Relativity are very small for a slowly moving source.     

Schrödinger-Like Relativistic Wave Equation of Motion for the Lorentz-Scalar Potential

A Schrödinger-like relativistic wave equation of motion for the Lorentz-scalar potential is formulated based on a Lagrangian formalism of relativistic mechanics with a scaled time as the evolution parameter. Applications of this Schrödinger-like formalism for the Lorentz-scalar potential are given: For the square-step potential, the predictions of this formalism are free from the Klein paradox, and for the Coulomb potential, this formalism yields the exact bound-state eigenenergies and eigenfunctions.