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Title: Irregular solutions of the s-wave radial Schroedinger equation for van der Waals potentials

Abstract

Simple ideas based on quantum chromodynamics suggest that the strong nuclear force might possess a long-range van der Waals component. Such a component, if it exists, would be most apparent in low-energy interactions between pairs of hadrons, at least one of which is neutral. In this article, as the initial part of a program to set limits on the magnitude of the strength of such a van der Waals interaction, we construct low-energy series expansions of the two irregular solutions f/sub 0/( +- k,r) to the s-wave Schroedinger equation that describes the interaction of a pair of particles interacting through a potential with a van der Waals tail of the form V(r)approx.-lambdahcr/sup N/-1/sub 0/ /r/sup N/, for arbitrary values of the potential parameters, lambda, r/sub 0/, and N. Accurate approximation schemes based on the series expansions are developed, and the results are used to obtain an expression for the low-energy elastic cross section. The effects of the van der Waals component of this interaction are clearly evident in the energy dependence of the cross section.

Authors:
Publication Date:
Research Org.:
Department of Physics, Carleton University, Ottawa, Canada, K1S 5B6
OSTI Identifier:
6364519
Resource Type:
Journal Article
Journal Name:
J. Math. Phys. (N.Y.); (United States)
Additional Journal Information:
Journal Volume: 24:3
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; SCHROEDINGER EQUATION; SERIES EXPANSION; VAN DER WAALS FORCES; S WAVES; BORN APPROXIMATION; COUPLING CONSTANTS; CROSS SECTIONS; ENERGY DEPENDENCE; RECURSION RELATIONS; SCATTERING; SCATTERING AMPLITUDES; WAVE FUNCTIONS; AMPLITUDES; DIFFERENTIAL EQUATIONS; EQUATIONS; FUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS; PARTIAL WAVES; WAVE EQUATIONS; 657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics

Citation Formats

Romo, W J. Irregular solutions of the s-wave radial Schroedinger equation for van der Waals potentials. United States: N. p., 1983. Web. doi:10.1063/1.525728.
Romo, W J. Irregular solutions of the s-wave radial Schroedinger equation for van der Waals potentials. United States. https://doi.org/10.1063/1.525728
Romo, W J. Tue . "Irregular solutions of the s-wave radial Schroedinger equation for van der Waals potentials". United States. https://doi.org/10.1063/1.525728.
@article{osti_6364519,
title = {Irregular solutions of the s-wave radial Schroedinger equation for van der Waals potentials},
author = {Romo, W J},
abstractNote = {Simple ideas based on quantum chromodynamics suggest that the strong nuclear force might possess a long-range van der Waals component. Such a component, if it exists, would be most apparent in low-energy interactions between pairs of hadrons, at least one of which is neutral. In this article, as the initial part of a program to set limits on the magnitude of the strength of such a van der Waals interaction, we construct low-energy series expansions of the two irregular solutions f/sub 0/( +- k,r) to the s-wave Schroedinger equation that describes the interaction of a pair of particles interacting through a potential with a van der Waals tail of the form V(r)approx.-lambdahcr/sup N/-1/sub 0/ /r/sup N/, for arbitrary values of the potential parameters, lambda, r/sub 0/, and N. Accurate approximation schemes based on the series expansions are developed, and the results are used to obtain an expression for the low-energy elastic cross section. The effects of the van der Waals component of this interaction are clearly evident in the energy dependence of the cross section.},
doi = {10.1063/1.525728},
url = {https://www.osti.gov/biblio/6364519}, journal = {J. Math. Phys. (N.Y.); (United States)},
number = ,
volume = 24:3,
place = {United States},
year = {1983},
month = {3}
}