Application of a modified determinantal method to Yukawa potential scattering

1966 ◽  
Vol 43 (4) ◽  
pp. 834-839
Author(s):  
J. Smith
Keyword(s):  
Yukawa Potential ◽  
Potential Scattering

On higher Born approximations in potential scattering

1951 ◽  
Vol 206 (1087) ◽  
pp. 509-520 ◽  
Keyword(s):  
Cross Section ◽  
Coulomb Potential ◽  
Yukawa Potential ◽  
Complete Solution ◽  
Potential Scattering ◽  
Matrix Formalism ◽  
Relativistic Case ◽  
Born Series ◽  
Dirac Electron ◽  
The Cross

Many discussions of higher Born approximations have followed the work of Distel (1932) and Sauter (1933 b ), which contains an error in its development, causing many conclusions presented in the literature to be incorrect. In this paper, the second Born approximation for scattering of a Dirac electron by a Yukawa potential is calculated by a correct method. For the limiting case of the Coulomb potential, the cross-section thus obtained is just the expression obtained by McKinley & Feshbach (1948) by expansion of Mott’s complete solution. A corresponding calculation is sketched for the meson, using β-matrix formalism, and its physical interpretation considered. For the non-relativistic case, the behaviour of the Born series (up to third order) is discussed for the transition from Yukawa to Coulomb potential, disproving the conclusions of Distel (1932), M∅ller (1930) and Urban (1943) that contributions to the cross-section from higher Born approximations become infinite in this limit.

Threshold Zeros and theNDMethod in Yukawa-Potential Scattering

1971 ◽  
Vol 3 (12) ◽  
pp. 3108-3113 ◽  
Author(s):  
E. B. Nemanic ◽  
P. R. Auvil
Keyword(s):  
Yukawa Potential ◽  
Potential Scattering

scholarly journals A Covariant and Unitary Equation for Single Quantum Exchange

1983 ◽  
Vol 36 (5) ◽  
pp. 601 ◽  
Author(s):  
H Pierre Noyes ◽  
James V Lindesay
Keyword(s):  
Yukawa Potential ◽  
Bound State ◽  
Potential Scattering ◽  
Kinematic Region ◽  
Nuclear Potential ◽  
Particle Scattering ◽  
Single Quantum ◽  
Definition Of

By requiring the 'bound state' of particle and quantum to have the mass of the particle and be physically indistinguishable from the particle we derive fully covariant and unitary equations for particle-particle scattering; these reduce to the Lippmann-Schwinger equation for Yukawa potential scattering in the nonrelativistic kinematic region and provide a new definition of the 'nuclear potential'.

The Yukawa Potential Function and Reciprocal Univalent Function

2013 ◽  
Vol 3 (2) ◽  
pp. 197-202
Author(s):  
Amir Pishkoo ◽  
Maslina Darus
Keyword(s):  
Mathematical Model ◽  
Unit Disk ◽  
Potential Function ◽  
Univalent Function ◽  
Open Problem ◽  
Yukawa Potential ◽  
Reciprocal Theorem ◽  
Problem Statement ◽  
Fundamental Forces

This paper presents a mathematical model that provides analytic connection between four fundamental forces (interactions), by using modified reciprocal theorem,derived in the paper, as a convenient template. The essential premise of this work is to demonstrate that if we obtain with a form of the Yukawa potential function [as a meromorphic univalent function], we may eventually obtain the Coloumb Potential as a univalent function outside of the unit disk. Finally, we introduce the new problem statement about assigning Meijer's G-functions to Yukawa and Coloumb potentials as an open problem.

Single Subdynamics for potential scattering

2002 ◽  
Vol 13 (1) ◽  
pp. 9-34
Author(s):  
Michel De Haan ◽  
Claude D. George
Keyword(s):  
Potential Scattering

Electron-atom potential scattering assisted by a bichromatic elliptically polarized laser field

2017 ◽  
Vol 71 (10) ◽  
Author(s):  
Arman Korajac ◽  
Dino Habibović ◽  
Aner Čerkić ◽  
Mustafa Busuladžić ◽  
Dejan B. Milošević
Keyword(s):  
Laser Field ◽  
Potential Scattering ◽  
Electron Atom ◽  
Elliptically Polarized ◽  
Atom Potential

scholarly journals Nonequilibrium Transport and Phase Transitions in Driven Diffusion of Interacting Particles

2020 ◽  
Vol 75 (5) ◽  
pp. 449-463
Author(s):  
Dominik Lips ◽  
Artem Ryabov ◽  
Philipp Maass
Keyword(s):  
Current Density ◽  
Lattice Gas ◽  
Yukawa Potential ◽  
Exclusion Process ◽  
Quantum Spin ◽  
Nonequilibrium Steady States ◽  
Interacting Particles ◽  
Driven Diffusive Systems ◽  
Periodic Potentials ◽  
Symmetry Effect

AbstractDriven diffusive systems constitute paradigmatic models of nonequilibrium physics. Among them, a driven lattice gas known as the asymmetric simple exclusion process (ASEP) is the most prominent example for which many intriguing exact results have been obtained. After summarising key findings, including the mapping of the ASEP to quantum spin chains, we discuss the recently introduced Brownian ASEP (BASEP) as a related class of driven diffusive system with continuous space dynamics. In the BASEP, driven Brownian motion of hardcore-interacting particles through one-dimensional periodic potentials is considered. We study whether current–density relations of the BASEP can be considered as generic for arbitrary periodic potentials and whether repulsive particle interactions other than hardcore lead to similar results. Our findings suggest that shapes of current–density relations are generic for single-well periodic potentials and can always be attributed to the interplay of a barrier reduction, blocking, and exchange symmetry effect. This implies that in general up to five different phases of nonequilibrium steady states are possible for such potentials. The phases can occur in systems coupled to particle reservoirs, where the bulk density is the order parameter. For multiple-well periodic potentials, more complex current–density relations are possible, and more phases can appear. Taking a repulsive Yukawa potential as an example, we show that the effects of barrier reduction and blocking on the current are also present. The exchange symmetry effect requires hardcore interactions, and we demonstrate that it can still be identified when hardcore interactions are combined with weak Yukawa interactions. The robustness of the collective dynamics in the BASEP with respect to variations of model details can be a key feature for a successful observation of the predicted current–density relations in actual physical systems.

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