# New approach to folding with the Coulomb wave function

## Abstract

Due to the long-range character of the Coulomb interaction theoretical description of low-energy nuclear reactions with charged particles still remains a formidable task. One way of dealing with the problem in an integral-equation approach is to employ a screened Coulomb potential. A general approach without screening requires folding of kernels of the integral equations with the Coulomb wave. A new method of folding a function with the Coulomb partial waves is presented. The partial-wave Coulomb function both in the configuration and momentum representations is written in the form of separable series. Each term of the series is represented as a product of a factor depending only on the Coulomb parameter and a function depending on the spatial variable in the configuration space and the momentum variable if the momentum representation is used. Using a trial function, the method is demonstrated to be efficient and reliable.

- Authors:

- Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)
- Department of Physics, Astronomy and Medical Radiation Sciences, Curtin University, GPO Box U1987, Perth 6845 (Australia)
- Cyclotron Institute, Texas A and M University, College Station, Texas 77843 (United States)

- Publication Date:

- OSTI Identifier:
- 22403140

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics

- Additional Journal Information:
- Journal Volume: 56; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHARGED PARTICLES; COULOMB FIELD; INTEGRAL EQUATIONS; KERNELS; NUCLEAR REACTIONS; PARTIAL WAVES; WAVE FUNCTIONS

### Citation Formats

```
Blokhintsev, L. D., Savin, D. A., Kadyrov, A. S., and Mukhamedzhanov, A. M.
```*New approach to folding with the Coulomb wave function*. United States: N. p., 2015.
Web. doi:10.1063/1.4919674.

```
Blokhintsev, L. D., Savin, D. A., Kadyrov, A. S., & Mukhamedzhanov, A. M.
```*New approach to folding with the Coulomb wave function*. United States. doi:10.1063/1.4919674.

```
Blokhintsev, L. D., Savin, D. A., Kadyrov, A. S., and Mukhamedzhanov, A. M. Fri .
"New approach to folding with the Coulomb wave function". United States. doi:10.1063/1.4919674.
```

```
@article{osti_22403140,
```

title = {New approach to folding with the Coulomb wave function},

author = {Blokhintsev, L. D. and Savin, D. A. and Kadyrov, A. S. and Mukhamedzhanov, A. M.},

abstractNote = {Due to the long-range character of the Coulomb interaction theoretical description of low-energy nuclear reactions with charged particles still remains a formidable task. One way of dealing with the problem in an integral-equation approach is to employ a screened Coulomb potential. A general approach without screening requires folding of kernels of the integral equations with the Coulomb wave. A new method of folding a function with the Coulomb partial waves is presented. The partial-wave Coulomb function both in the configuration and momentum representations is written in the form of separable series. Each term of the series is represented as a product of a factor depending only on the Coulomb parameter and a function depending on the spatial variable in the configuration space and the momentum variable if the momentum representation is used. Using a trial function, the method is demonstrated to be efficient and reliable.},

doi = {10.1063/1.4919674},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 5,

volume = 56,

place = {United States},

year = {2015},

month = {5}

}