# Reduced equations of motion and reduced S matrix for scattering processes

## Abstract

Reduced equations of motion (REM) are derived for the reduced density matrix of some of the degrees of freedom taking part in a scattering process. The derivation is made making use of the Zwanzig--Mori projection operator technique and utilizing a partial time ordering prescription (POP) which results in simple REM which contain no convolution in time. The present formulation is convenient for the direct calculation of reduced information on scattering events since it avoids the necessity of calculating the complete S matrix. The entire dynamical information relevant for the present description is expressed in terms of a hierarchy of correlation functions which in turn depend on the potential surface only in the region of interest. We further develop an exponential approximation for the reduced tetradic scattering S matrix in Liouville space, which forms a convenient framework for systematic approximations.

- Authors:

- Publication Date:

- Research Org.:
- Chemical Physics Department, Weizmann Institute of Science, Rehovot, Israel

- OSTI Identifier:
- 6439973

- Resource Type:
- Journal Article

- Journal Name:
- J. Chem. Phys.; (United States)

- Additional Journal Information:
- Journal Volume: 75:1

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; SCATTERING; EQUATIONS OF MOTION; CORRELATION FUNCTIONS; POTENTIAL ENERGY; S MATRIX; DIFFERENTIAL EQUATIONS; ENERGY; EQUATIONS; FUNCTIONS; MATRICES; PARTIAL DIFFERENTIAL EQUATIONS; 645500* - High Energy Physics- Scattering Theory- (-1987)

### Citation Formats

```
Mukamel, S.
```*Reduced equations of motion and reduced S matrix for scattering processes*. United States: N. p., 1981.
Web. doi:10.1063/1.441817.

```
Mukamel, S.
```*Reduced equations of motion and reduced S matrix for scattering processes*. United States. https://doi.org/10.1063/1.441817

```
Mukamel, S. Wed .
"Reduced equations of motion and reduced S matrix for scattering processes". United States. https://doi.org/10.1063/1.441817.
```

```
@article{osti_6439973,
```

title = {Reduced equations of motion and reduced S matrix for scattering processes},

author = {Mukamel, S},

abstractNote = {Reduced equations of motion (REM) are derived for the reduced density matrix of some of the degrees of freedom taking part in a scattering process. The derivation is made making use of the Zwanzig--Mori projection operator technique and utilizing a partial time ordering prescription (POP) which results in simple REM which contain no convolution in time. The present formulation is convenient for the direct calculation of reduced information on scattering events since it avoids the necessity of calculating the complete S matrix. The entire dynamical information relevant for the present description is expressed in terms of a hierarchy of correlation functions which in turn depend on the potential surface only in the region of interest. We further develop an exponential approximation for the reduced tetradic scattering S matrix in Liouville space, which forms a convenient framework for systematic approximations.},

doi = {10.1063/1.441817},

url = {https://www.osti.gov/biblio/6439973},
journal = {J. Chem. Phys.; (United States)},

number = ,

volume = 75:1,

place = {United States},

year = {1981},

month = {7}

}