Irregular solutions of the s-wave radial Schroedinger equation for van der Waals potentials
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), Vol. 24:3
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
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