# Model three-body problem in the molecular mass limit

## Abstract

The bound states of a three-body molecule composed of two identical heavy nuclei and a light ''electron'' interacting through short-range s-wave potentials are studied. The spectrum of three-body bound states grows as the mass ratio m between the heavy and light particles increases, and presents a remarkable vibration rotation structure that can be fitted with the usual empirical energy formulas of molecular spectroscopy. The results of the exact three-body calculation for the binding energy and bound-state wavefunction are compared with the predictions of the Born-Oppenheimer method for the same system. We find that for m>30, the Born-Oppenheimer approximation yields very good results for both the binding energies and wavefunctions. For smaller m (1

- Authors:

- Publication Date:

- Research Org.:
- Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742

- OSTI Identifier:
- 6088786

- Resource Type:
- Journal Article

- Journal Name:
- Ann. Phys. (N.Y.); (United States)

- Additional Journal Information:
- Journal Volume: 117:2

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; THREE-BODY PROBLEM; BORN-OPPENHEIMER APPROXIMATION; BOUND STATE; ANALYTICAL SOLUTION; BINDING ENERGY; INTERACTION RANGE; NUCLEAR MOLECULES; PARTIAL WAVES; ROTATIONAL STATES; S WAVES; VIBRATIONAL STATES; WAVE FUNCTIONS; DISTANCE; ENERGY; ENERGY LEVELS; EXCITED STATES; FUNCTIONS; MANY-BODY PROBLEM; 657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics; 645500 - High Energy Physics- Scattering Theory- (-1987); 653001 - Nuclear Theory- Nuclear Structure, Moments, Spin, & Models

### Citation Formats

```
Fonseca, A.C., and Shanley, P.E.
```*Model three-body problem in the molecular mass limit*. United States: N. p., 1979.
Web. doi:10.1016/0003-4916(79)90356-7.

```
Fonseca, A.C., & Shanley, P.E.
```*Model three-body problem in the molecular mass limit*. United States. doi:10.1016/0003-4916(79)90356-7.

```
Fonseca, A.C., and Shanley, P.E. Thu .
"Model three-body problem in the molecular mass limit". United States. doi:10.1016/0003-4916(79)90356-7.
```

```
@article{osti_6088786,
```

title = {Model three-body problem in the molecular mass limit},

author = {Fonseca, A.C. and Shanley, P.E.},

abstractNote = {The bound states of a three-body molecule composed of two identical heavy nuclei and a light ''electron'' interacting through short-range s-wave potentials are studied. The spectrum of three-body bound states grows as the mass ratio m between the heavy and light particles increases, and presents a remarkable vibration rotation structure that can be fitted with the usual empirical energy formulas of molecular spectroscopy. The results of the exact three-body calculation for the binding energy and bound-state wavefunction are compared with the predictions of the Born-Oppenheimer method for the same system. We find that for m>30, the Born-Oppenheimer approximation yields very good results for both the binding energies and wavefunctions. For smaller m (1},

doi = {10.1016/0003-4916(79)90356-7},

journal = {Ann. Phys. (N.Y.); (United States)},

number = ,

volume = 117:2,

place = {United States},

year = {1979},

month = {2}

}