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

Journal Article · Tue Mar 01 04:00:00 EST 1983 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.525728· OSTI ID:6364519

Romo, W J

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.

• Research Organization: Department of Physics, Carleton University, Ottawa, Canada, K1S 5B6
• OSTI ID: 6364519
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 24:3; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMPLITUDES
BORN APPROXIMATION
COUPLING CONSTANTS
CROSS SECTIONS
DIFFERENTIAL EQUATIONS
ENERGY DEPENDENCE
EQUATIONS
FUNCTIONS
PARTIAL DIFFERENTIAL EQUATIONS
PARTIAL WAVES
RECURSION RELATIONS
S WAVES
SCATTERING
SCATTERING AMPLITUDES
SCHROEDINGER EQUATION
SERIES EXPANSION
VAN DER WAALS FORCES
WAVE EQUATIONS
WAVE FUNCTIONS