# ONE-PARTICLE MOTIONS IN MANY-PARTICLE SYSTEMS AND THE OPTICAL MODEL IN NUCLEAR REACTIONS

## Abstract

A possible scheme of the systematic one-particle motion in a many- particle system is presented as a time-dependent formalism. The theory is formulated for the optical model in nuclear reactions, although it can be utilized to study various problems in solid state physics. First the oneparticle amplitude is so defined as to describe the processes of elastic scattering. Then it is shown that the systematic part of the amplitude, corresponding to the coarse-grained molion of the system. obeys the oneparticle Schroedinger equation with the optical potential, and that the fluctuating part of the amplitude is governed by the Langevin-in-like equation with the same optical potential and by the fluctuation-dissipation theorem. Tbe optical potential can be calculated from its definition given as tbe Fourier transform of the so-called "self-energy" part appearing in the equation of the one-particle Green function in the medium of the target nucleus. From the definition it is easily seen that the optical potential is, in general, noniocal and slightly energy-dependent. The optical potential is decomposed into two parts, one being the static (or energy-independent) part to be observed in the target nucleus in the fixed ground state and the other representing reactions of nuclear excitations. The facemore »

- Authors:

- Publication Date:

- Research Org.:
- Waseda Univ., Tokyo

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 4169641

- NSA Number:
- NSA-14-020855

- Resource Type:
- Journal Article

- Journal Name:
- Progr. Theoret. Phys. (Kyoto)

- Additional Journal Information:
- Journal Volume: Vol: 23; Other Information: Orig. Receipt Date: 31-DEC-60

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

- Language:
- English

- Subject:
- PHYSICS; DIFFERENTIAL EQUATIONS; ENERGY; EXCITATION; GREEN FUNCTION; INTERACTIONS; MANY BODY PROBLEM; MOTION; NUCLEAR MODELS; NUCLEAR REACTIONS; NUCLEAR THEORY; OPTICAL MODEL; QUANTUM MECHANICS; SCATTERING; SOLIDS

### Citation Formats

```
Namiki, M.
```*ONE-PARTICLE MOTIONS IN MANY-PARTICLE SYSTEMS AND THE OPTICAL MODEL IN NUCLEAR REACTIONS*. Country unknown/Code not available: N. p., 1960.
Web. doi:10.1143/PTP.23.629.

```
Namiki, M.
```*ONE-PARTICLE MOTIONS IN MANY-PARTICLE SYSTEMS AND THE OPTICAL MODEL IN NUCLEAR REACTIONS*. Country unknown/Code not available. doi:10.1143/PTP.23.629.

```
Namiki, M. Fri .
"ONE-PARTICLE MOTIONS IN MANY-PARTICLE SYSTEMS AND THE OPTICAL MODEL IN NUCLEAR REACTIONS". Country unknown/Code not available. doi:10.1143/PTP.23.629.
```

```
@article{osti_4169641,
```

title = {ONE-PARTICLE MOTIONS IN MANY-PARTICLE SYSTEMS AND THE OPTICAL MODEL IN NUCLEAR REACTIONS},

author = {Namiki, M.},

abstractNote = {A possible scheme of the systematic one-particle motion in a many- particle system is presented as a time-dependent formalism. The theory is formulated for the optical model in nuclear reactions, although it can be utilized to study various problems in solid state physics. First the oneparticle amplitude is so defined as to describe the processes of elastic scattering. Then it is shown that the systematic part of the amplitude, corresponding to the coarse-grained molion of the system. obeys the oneparticle Schroedinger equation with the optical potential, and that the fluctuating part of the amplitude is governed by the Langevin-in-like equation with the same optical potential and by the fluctuation-dissipation theorem. Tbe optical potential can be calculated from its definition given as tbe Fourier transform of the so-called "self-energy" part appearing in the equation of the one-particle Green function in the medium of the target nucleus. From the definition it is easily seen that the optical potential is, in general, noniocal and slightly energy-dependent. The optical potential is decomposed into two parts, one being the static (or energy-independent) part to be observed in the target nucleus in the fixed ground state and the other representing reactions of nuclear excitations. The face of the optical potential may be of the same type irrespective of the question whether the incident beam is a simple short wave- packet or a mixed beam, so far as the coarsegrained motlons are concerned. Flnally it is proved that the fluctuation-dissipatlon theorem holds for the correlation function of the fluctuating source or amplitude if the system is excited in quasi-equilibrium. (auth)},

doi = {10.1143/PTP.23.629},

journal = {Progr. Theoret. Phys. (Kyoto)},

number = ,

volume = Vol: 23,

place = {Country unknown/Code not available},

year = {1960},

month = {4}

}