# Influence of the Exchange and Correlation on the Electron-Phonon Interaction in Metals

## Abstract

Bearden and Pines investigated the role of electronelectron interactions in metals by extending the BohmPines collective description method. It was concluded that exchange and correlation effects on the dispersion relation m(q) and on the effective matrix element V/sub p/(q) for electron-phonon interaction is negligible for the small wave number vector q of a phonon. Further investigation leads to the conclusion that omega (q) and V/sub p/(q) must include the exchange and correlation terms even for small q. (A.C.) l6371 Results obtained by applying the A-S theory to elastic scattering of 156-Mev deuterons by carbon are reported. The effect of simultaneous scattering is shown and compared with results previously reported by Stapp. (A.C.) l6372 A study was made to determine whether the framework of a Hilbert space is compatible with the quantum theory of fields. An inquiry is made as to the characteristic features of field theory and how these features can be described in this framework. For this purpose the character of additive field theories, which are used in ace of field operators, and the relation between a system extending over the whole space and one restricted within a finite volume are examined. After these considerations the conclusion wss mademore »

- Authors:

- Publication Date:

- Research Org.:
- Hokkaido Univ., Sapporo

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 4243818

- NSA Number:
- NSA-13-016370

- Resource Type:
- Journal Article

- Journal Name:
- Progress of Theoretical Physics (Kyoto)

- Additional Journal Information:
- Journal Volume: 20; Journal Issue: 6; Other Information: Orig. Receipt Date: 31-DEC-59; Journal ID: ISSN 0033-068X

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

- Language:
- English

- Subject:
- PHYSICS AND MATHEMATICS; DISPERSION RELATIONS; ELECTRONS; ELEMENTARY PARTICLES; FIELD THEORY; INTERACTIONS; MATRICES; METALS; OSCILLATIONS; PHONONS; PINES-BOHM THEORY; PLASMA; SOUND; VECTORS; VIBRATIONS

### Citation Formats

```
Toya, Tomiyuki.
```*Influence of the Exchange and Correlation on the Electron-Phonon Interaction in Metals*. Country unknown/Code not available: N. p., 1958.
Web. doi:10.1143/PTP.20.971.

```
Toya, Tomiyuki.
```*Influence of the Exchange and Correlation on the Electron-Phonon Interaction in Metals*. Country unknown/Code not available. doi:10.1143/PTP.20.971.

```
Toya, Tomiyuki. Mon .
"Influence of the Exchange and Correlation on the Electron-Phonon Interaction in Metals". Country unknown/Code not available. doi:10.1143/PTP.20.971.
```

```
@article{osti_4243818,
```

title = {Influence of the Exchange and Correlation on the Electron-Phonon Interaction in Metals},

author = {Toya, Tomiyuki},

abstractNote = {Bearden and Pines investigated the role of electronelectron interactions in metals by extending the BohmPines collective description method. It was concluded that exchange and correlation effects on the dispersion relation m(q) and on the effective matrix element V/sub p/(q) for electron-phonon interaction is negligible for the small wave number vector q of a phonon. Further investigation leads to the conclusion that omega (q) and V/sub p/(q) must include the exchange and correlation terms even for small q. (A.C.) l6371 Results obtained by applying the A-S theory to elastic scattering of 156-Mev deuterons by carbon are reported. The effect of simultaneous scattering is shown and compared with results previously reported by Stapp. (A.C.) l6372 A study was made to determine whether the framework of a Hilbert space is compatible with the quantum theory of fields. An inquiry is made as to the characteristic features of field theory and how these features can be described in this framework. For this purpose the character of additive field theories, which are used in ace of field operators, and the relation between a system extending over the whole space and one restricted within a finite volume are examined. After these considerations the conclusion wss made that there is sufficient reason to treat the quantum theory of fields within the framework of a Hilbert space. (A.C.)},

doi = {10.1143/PTP.20.971},

journal = {Progress of Theoretical Physics (Kyoto)},

issn = {0033-068X},

number = 6,

volume = 20,

place = {Country unknown/Code not available},

year = {1958},

month = {12}

}