# s-wave scattering for deep potentials with attractive tails falling off faster than -1/r{sup 2}

## Abstract

For potentials with attractive tails, as occur in typical atomic interactions, we present a simple formula for the s-wave phase shift {delta}{sub 0}. It exposes a universal dependence of {delta}{sub 0}(E) on the potential tail and the influence of effects specific to a given potential, which enter via the scattering length a, or equivalently, the noninteger part {Delta}{sub th} of the threshold quantum number n{sub th}. The formula accurately reproduces {delta}{sub 0}(E) from threshold up to the semiclassical regime, far beyond the validity of the effective-range expansion. We derive the tail functions occurring in the formula for {delta}{sub 0}(E) and demonstrate the validity of the formula for attractive potential tails proportional to 1/r{sup 6} or to 1/r{sup 4}, and also for a mixed potential tail consisting of a 1/r{sup 4} term together with a non-negligible 1/r{sup 6} contribution.

- Authors:

- Physik Department, Technische Universitaet Muenchen, D-85747 Garching (Germany)

- Publication Date:

- OSTI Identifier:
- 22068703

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 3; Other Information: (c) 2011 American Institute of Physics; Country of input: Syrian Arab Republic; Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; INTERACTIONS; PHASE SHIFT; POTENTIALS; S WAVES; SCATTERING; SCATTERING LENGTHS; SEMICLASSICAL APPROXIMATION

### Citation Formats

```
Mueller, Tim-Oliver, Kaiser, Alexander, and Friedrich, Harald.
```*s-wave scattering for deep potentials with attractive tails falling off faster than -1/r{sup 2}*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.032701.

```
Mueller, Tim-Oliver, Kaiser, Alexander, & Friedrich, Harald.
```*s-wave scattering for deep potentials with attractive tails falling off faster than -1/r{sup 2}*. United States. doi:10.1103/PHYSREVA.84.032701.

```
Mueller, Tim-Oliver, Kaiser, Alexander, and Friedrich, Harald. Thu .
"s-wave scattering for deep potentials with attractive tails falling off faster than -1/r{sup 2}". United States. doi:10.1103/PHYSREVA.84.032701.
```

```
@article{osti_22068703,
```

title = {s-wave scattering for deep potentials with attractive tails falling off faster than -1/r{sup 2}},

author = {Mueller, Tim-Oliver and Kaiser, Alexander and Friedrich, Harald},

abstractNote = {For potentials with attractive tails, as occur in typical atomic interactions, we present a simple formula for the s-wave phase shift {delta}{sub 0}. It exposes a universal dependence of {delta}{sub 0}(E) on the potential tail and the influence of effects specific to a given potential, which enter via the scattering length a, or equivalently, the noninteger part {Delta}{sub th} of the threshold quantum number n{sub th}. The formula accurately reproduces {delta}{sub 0}(E) from threshold up to the semiclassical regime, far beyond the validity of the effective-range expansion. We derive the tail functions occurring in the formula for {delta}{sub 0}(E) and demonstrate the validity of the formula for attractive potential tails proportional to 1/r{sup 6} or to 1/r{sup 4}, and also for a mixed potential tail consisting of a 1/r{sup 4} term together with a non-negligible 1/r{sup 6} contribution.},

doi = {10.1103/PHYSREVA.84.032701},

journal = {Physical Review. A},

issn = {1050-2947},

number = 3,

volume = 84,

place = {United States},

year = {2011},

month = {9}

}