# 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}

}