Two- and Three-Body Coulomb Solution Method in a Momentum Space

We present a method to calculate two- and three-body amplitudes including the Coulomb potential in a momentum space. Our aim is to obtain the exact two-body Coulomb amplitudes used in three-body calculations, which reproduce the analytic phase shifts. For the purpose, our theory is based on the modified Coulomb potential (MCP) whose Fourier transformation is equivalent to the pure Coulomb potential in a configuration space, and the two-potential theory with an auxiliary potential. Moreover, one can analytically determine a decisive range R _dec in the MCP. By using the MCP, we obtain the two-body Coulomb modified nuclear amplitude as well as the pure Coulomb amplitude. The calculated phase shift are very good fitting with the experimental data.     

Approximate eigensolutions of Dirac equation for the superposition Hellmann potential under spin and pseudospin symmetries

The Hellmann potential is simply a superposition of an attractive Coulomb potential ?a/r plus a Yukawa potential be^{?δ r} /r. The generalized parametric Nikiforov–Uvarov (NU) method is used to examine the approximate analytical energy eigenvalues and two-component wave function of the Dirac equation with the Hellmann potential for arbitrary spin-orbit quantum number κ in the presence of exact spin and pseudospin (p-spin) symmetries. As a particular case, we obtain the energy eigenvalues of the pure Coulomb potential in the non-relativistic limit.     

Influence of the coulomb blockade effect on heat transfer in a one-dimensional system of spinless electrons

An analysis is made of some characteristics of the low-temperature thermal conductivity of a ballistic quantum dot, attributed to the influence of long-range Coulomb interaction in the geometric capacitance approximation. It is shown that at fairly low temperatures the thermal conductivity K exhibits Coulomb oscillations as a function of the electrostatic potential of the quantum dot. At the maximum of the Coulomb peak we find K ∝ T whereas at the minimum K ∝ T ³. The dependence K(T) is essentially nonmonotonic at temperatures corresponding to the characteristic spacing between the size-quantization levels in the quantum dot.     

Mapping of Shape Invariant Potentials by the Point Canonical Transformation

In this paper by using the method of point canonical transformation we find that the Coulomb and Kratzer potentials can be mapped to the Morse potential. Then we show that the Pöschl-Teller potential type I belongs to the same subclass of shape invariant potentials as Hulthén potential. Also we show that the shape-invariant algebra for Coulomb, Kratzer, and Morse potentials is SU(1,1), while the shape-invariant algebra for Pöschl-Teller type I and Hulthén is SU(2).     

Equilibria of point charges on convex curves

We study the equilibrium positions of three points on a convex curve under influence of the Coulomb potential. We identify these positions as orthotripods, three points on the curve having concurrent normals. This relates the equilibrium positions to the caustic (evolute) of the curve. The concurrent normals can only meet in the core of the caustic, which is contained in the interior of the caustic. Moreover, we give a geometric condition for three points in equilibrium with positive charges only. For the ellipse we show that the space of orthotripods is homeomorphic to a 2-dimensional bounded cylinder.     

The short distance behaviour of the anomalous magnetic moment of the electron

The effective anomalous magnetic moment of the electron vanishes at short distances because the electrodynamic form factor F₂(q²) vanishes for |q²| → ∞. The effective potential due to the interaction between the anomalous magnetic moment and the Coulomb field of a nucleus only diverges logarithmically at short distances, and not, as might naively be expected, quadratically. There are no other bound states of an electron in a Coulomb field than the well-known atomic states. In particular, there is no room for high mass resonances emulating the ψ as suggested by Barut and Kraus.     

Investigation of scattering processes in quantum few-body systems involving long-range interaction by the complex-rotation method

The complex-rotation method adapted to solving the multichannel scattering problem in the two-body system where the interaction potential contains the long-range Coulomb components is described. The scattering problem is reformulated as the problem of solving a nonhomogeneous Schrödinger equation in which the nonhomogeneous term involves a Coulomb potential cut off at large distances. The incident wave appearing in the nonhomogeneous term is a solution of the Schrödinger equation with longrange Coulomb interaction. This formulation is free from approximations associated with a direct cutoff of Coulomb interaction at large distances. The efficiency of this formalism is demonstrated by considering the example of solving scattering problems in the α-α and p-p systems.     

Coulomb correction due to the true nonlocality of the optical-model potential

We show that the value currently used for the Coulomb correction is approximately 30 percent too small, mainly because it includes a spurious contribution from the dynamical energy dependence of the optical potential. This observation brings in good agreement the empirical values of the symmetry potential U₁ (≈ 16 MeV) determined respectively from neutron and from proton scattering data.     

A Proton in the Quark-Meson Coupling Model

We investigate the structure of a proton in free space by using the quark-meson coupling model. In the model, a proton in free space is regarded as a MIT bag with σ, ω and ρ meson fields and the Coulomb potential. With the boundary condition at bag surface, the wave functions of u and d quarks and potentials are calculated self-consistently.     

Gaussian approximations for the nuclear Coulomb interaction

The kernel 1/¦r-r′¦=1/y in the direct term of the average Coulomb potential of the nuclear Hartree-Fock model is approximated by a sum of gaussians iny. For 0.5≦y≦30 Fm, a sixteen term expression is found such the direct Coulomb energy is obtained to one part in 10³. The exchange Coulomb potential is estimated in the statistical model. Applications of these accurate and practical approximations to fission calculations are discussed.     

Effective Field Theory of 3He

We examine the effects of the long range Coulomb force on the three-body contact interaction in a pionless effective theory of ³He. The corresponding interaction in ³H exhibits limit-cycle behavior and we show that this is not altered by the 1/r singularity of the potential.