# WATSON-SOMMERFELD TRANSFORMATION FOR MANY-PARTICLE SCATTERING AMPLITUDES

## Abstract

The continuation of many-particle partial-wave scattering amplitudes to complex values of the total anaular momentum is discussed in the framework of potential scattering. It is shown that if there is a continuation for which a Watson-Sommerfeld transformation of the full scattening amplitude can be made, then it is unique and determines the behavior of the amplitude for large values of any single scattering angle. The continuation of the partial-wave Schrodinger equation to complex values of the angular momentum is discussed, and tbe results are generalized to the case when exchange forces are present. As a simple application of the results, a crude nuclear model is discussed to illustrate how sequences of rotational levels can be described by Regge trajectories. (auth)

- Authors:

- Publication Date:

- Research Org.:
- California Inst. of Tech., Pasadena

- OSTI Identifier:
- 4006388

- NSA Number:
- NSA-18-021040

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

- Additional Journal Information:
- Journal Volume: Vol: 134; Other Information: Orig. Receipt Date: 31-DEC-64

- Country of Publication:
- Country unknown/Code not available

- Language:
- English

- Subject:
- PHYSICS; ANGULAR DISTRIBUTION; ANGULAR MOMENTUM; BEHAVIOR; ELEMENTARY PARTICLES; FIELD THEORY; LEVELS; MANY BODY PROBLEM; MATHEMATICS; MOMENTUM; NUCLEONS; QUANTUM MECHANICS; REGGE POLES; ROTATION; SCATTERING; SCATTERING AMPLITUDE; SCHROEDINGER EQUATION

### Citation Formats

```
Hartle, J B.
```*WATSON-SOMMERFELD TRANSFORMATION FOR MANY-PARTICLE SCATTERING AMPLITUDES*. Country unknown/Code not available: N. p., 1964.
Web. doi:10.1103/PhysRev.134.B612.

```
Hartle, J B.
```*WATSON-SOMMERFELD TRANSFORMATION FOR MANY-PARTICLE SCATTERING AMPLITUDES*. Country unknown/Code not available. doi:10.1103/PhysRev.134.B612.

```
Hartle, J B. Mon .
"WATSON-SOMMERFELD TRANSFORMATION FOR MANY-PARTICLE SCATTERING AMPLITUDES". Country unknown/Code not available. doi:10.1103/PhysRev.134.B612.
```

```
@article{osti_4006388,
```

title = {WATSON-SOMMERFELD TRANSFORMATION FOR MANY-PARTICLE SCATTERING AMPLITUDES},

author = {Hartle, J B},

abstractNote = {The continuation of many-particle partial-wave scattering amplitudes to complex values of the total anaular momentum is discussed in the framework of potential scattering. It is shown that if there is a continuation for which a Watson-Sommerfeld transformation of the full scattening amplitude can be made, then it is unique and determines the behavior of the amplitude for large values of any single scattering angle. The continuation of the partial-wave Schrodinger equation to complex values of the angular momentum is discussed, and tbe results are generalized to the case when exchange forces are present. As a simple application of the results, a crude nuclear model is discussed to illustrate how sequences of rotational levels can be described by Regge trajectories. (auth)},

doi = {10.1103/PhysRev.134.B612},

journal = {Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D},

number = ,

volume = Vol: 134,

place = {Country unknown/Code not available},

year = {1964},

month = {5}

}