## Angular momentum reduction for physical amplitudes in the three-body problem

## Abstract

We give here an approach to the angular momentum reduction that is tailed to be appropriate for the multichannel structure of the three-body problem. Wherever possible we work directly with the physical scattering amplitudes. We obtain concrete partial-wave expansions of elastic, rearrangement, and breakup amplitudes. For these amplitudes we obtain a coupled two-variable integral equation. The effects of parity, time reversal, and rotational invariance are fully discussed. Finally, we provide expressions for the multichannel partial-wave cross sections, asymptotic coordinate-space wave functions, off-shell unitarity, and the partial-wave version of the optical theorem as well as phase-shift parametrizations of the amplitudes.

- Authors:

- Stanford Univ., CA (United States)

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1442899

- Report Number(s):
- SLAC-PUB-1289

Journal ID: ISSN 0556-2813; PRVCAN

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review. C, Nuclear Physics

- Additional Journal Information:
- Journal Volume: 9; Journal Issue: 2; Journal ID: ISSN 0556-2813

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Bollé, D., and Osborn, T. A. Angular momentum reduction for physical amplitudes in the three-body problem. United States: N. p., 1974.
Web. doi:10.1103/PhysRevC.9.441.
```

```
Bollé, D., & Osborn, T. A. Angular momentum reduction for physical amplitudes in the three-body problem. United States. doi:10.1103/PhysRevC.9.441.
```

```
Bollé, D., and Osborn, T. A. Fri .
"Angular momentum reduction for physical amplitudes in the three-body problem". United States. doi:10.1103/PhysRevC.9.441. https://www.osti.gov/servlets/purl/1442899.
```

```
@article{osti_1442899,
```

title = {Angular momentum reduction for physical amplitudes in the three-body problem},

author = {Bollé, D. and Osborn, T. A.},

abstractNote = {We give here an approach to the angular momentum reduction that is tailed to be appropriate for the multichannel structure of the three-body problem. Wherever possible we work directly with the physical scattering amplitudes. We obtain concrete partial-wave expansions of elastic, rearrangement, and breakup amplitudes. For these amplitudes we obtain a coupled two-variable integral equation. The effects of parity, time reversal, and rotational invariance are fully discussed. Finally, we provide expressions for the multichannel partial-wave cross sections, asymptotic coordinate-space wave functions, off-shell unitarity, and the partial-wave version of the optical theorem as well as phase-shift parametrizations of the amplitudes.},

doi = {10.1103/PhysRevC.9.441},

journal = {Physical Review. C, Nuclear Physics},

number = 2,

volume = 9,

place = {United States},

year = {1974},

month = {2}

}

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