# Phenomenological local nucleon-nucleon potentials obtained from the inverse scattering problem at a fixed energy

## Abstract

An approximate method of determining the central, the spin-orbit, and the tensor parts of a local nucleon-nucleon interaction from the dependence of the eigenphase shifts and the mixing parameter on the total angular momentum J is studied. With the assumption that the tensor force is zero at the origin, the wave equation is transformed into a differential equation which can accurately be approximated by a matrix difference equation. The finite difference analog of the scrR matrix obtained from the solution of this matrix difference equation has a unique continued fraction expansion which enables one to obtain the central, the spin-orbit, and the tensor potentials provided that the exchange characters of all of the forces are specified. Model calculations are presented to show the utility and the accuracy of the method and a brief discussion is given about the possibility of extension of the inverse problem to include certain nonstatic potentials.

- Authors:

- Publication Date:

- Research Org.:
- Theoretical Physics Institute, Department of Physics, University of Alberta, Edmonton, Alberta, Canada, T6G2J1

- OSTI Identifier:
- 5169344

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev. C; (United States)

- Additional Journal Information:
- Journal Volume: 29:1

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; NUCLEON-NUCLEON POTENTIAL; INVERSE SCATTERING PROBLEM; ANGULAR MOMENTUM; ISOSPIN; L-S COUPLING; PHASE SHIFT; PIONS; S MATRIX; SCATTERING AMPLITUDES; SPIN; AMPLITUDES; BOSONS; COUPLING; ELEMENTARY PARTICLES; HADRONS; INTERMEDIATE COUPLING; MATRICES; MESONS; PARTICLE PROPERTIES; POTENTIALS; PSEUDOSCALAR MESONS; 653003* - Nuclear Theory- Nuclear Reactions & Scattering; 645207 - High Energy Physics- Particle Interactions & Properties-Theoretical- Strong Interactions, Baryon No. Greater than 1- (-1987)

### Citation Formats

```
Hooshyar, M A, and Razavy, M.
```*Phenomenological local nucleon-nucleon potentials obtained from the inverse scattering problem at a fixed energy*. United States: N. p., 1984.
Web. doi:10.1103/PhysRevC.29.20.

```
Hooshyar, M A, & Razavy, M.
```*Phenomenological local nucleon-nucleon potentials obtained from the inverse scattering problem at a fixed energy*. United States. https://doi.org/10.1103/PhysRevC.29.20

```
Hooshyar, M A, and Razavy, M. Sun .
"Phenomenological local nucleon-nucleon potentials obtained from the inverse scattering problem at a fixed energy". United States. https://doi.org/10.1103/PhysRevC.29.20.
```

```
@article{osti_5169344,
```

title = {Phenomenological local nucleon-nucleon potentials obtained from the inverse scattering problem at a fixed energy},

author = {Hooshyar, M A and Razavy, M},

abstractNote = {An approximate method of determining the central, the spin-orbit, and the tensor parts of a local nucleon-nucleon interaction from the dependence of the eigenphase shifts and the mixing parameter on the total angular momentum J is studied. With the assumption that the tensor force is zero at the origin, the wave equation is transformed into a differential equation which can accurately be approximated by a matrix difference equation. The finite difference analog of the scrR matrix obtained from the solution of this matrix difference equation has a unique continued fraction expansion which enables one to obtain the central, the spin-orbit, and the tensor potentials provided that the exchange characters of all of the forces are specified. Model calculations are presented to show the utility and the accuracy of the method and a brief discussion is given about the possibility of extension of the inverse problem to include certain nonstatic potentials.},

doi = {10.1103/PhysRevC.29.20},

url = {https://www.osti.gov/biblio/5169344},
journal = {Phys. Rev. C; (United States)},

number = ,

volume = 29:1,

place = {United States},

year = {1984},

month = {1}

}