# Asymptotic Normalization Coefficients in a Potential Model Involving Forbidden States

## Abstract

It is shown that values obtained for asymptotic normalization coefficients by means of a potential fitted to experimental data on elastic scattering depend substantially on the presence and the number n of possible forbidden states in the fitted potential. The present analysis was performed within exactly solvable potential models for various nuclear systems and various potentials without and with allowance for Coulomb interaction. Various methods for changing the number n that are based on the use of various versions of the change in the parameters of the potential model were studied. A compact analytic expression for the asymptotic normalization coefficients was derived for the case of the Hulthén potential. Specifically, the d + α and α + {sup 12}C systems, which are of importance for astrophysics, were examined. It was concluded that an incorrect choice of n could lead to a substantial errors in determining the asymptotic normalization coefficients. From the results of our calculations, it also follows that, for systems with a low binding energy and, as a consequence, with a large value of the Coulomb parameter, the inclusion of the Coulomb interaction may radically change the asymptotic normalization coefficients, increasing them sharply.

- Authors:

- Moscow State University, Skobeltsyn Institute of Nuclear Physics (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22761749

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Atomic Nuclei

- Additional Journal Information:
- Journal Volume: 81; Journal Issue: 2; Other Information: Copyright (c) 2018 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7788

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; ASTROPHYSICS; ASYMPTOTIC SOLUTIONS; BINDING ENERGY; CARBON 12; COULOMB SCATTERING; ERRORS; EXACT SOLUTIONS

### Citation Formats

```
Blokhintsev, L. D., E-mail: blokh@srd.sinp.msu.ru, and Savin, D. A., E-mail: rhdp@mail.ru.
```*Asymptotic Normalization Coefficients in a Potential Model Involving Forbidden States*. United States: N. p., 2018.
Web. doi:10.1134/S1063778818020047.

```
Blokhintsev, L. D., E-mail: blokh@srd.sinp.msu.ru, & Savin, D. A., E-mail: rhdp@mail.ru.
```*Asymptotic Normalization Coefficients in a Potential Model Involving Forbidden States*. United States. doi:10.1134/S1063778818020047.

```
Blokhintsev, L. D., E-mail: blokh@srd.sinp.msu.ru, and Savin, D. A., E-mail: rhdp@mail.ru. Thu .
"Asymptotic Normalization Coefficients in a Potential Model Involving Forbidden States". United States. doi:10.1134/S1063778818020047.
```

```
@article{osti_22761749,
```

title = {Asymptotic Normalization Coefficients in a Potential Model Involving Forbidden States},

author = {Blokhintsev, L. D., E-mail: blokh@srd.sinp.msu.ru and Savin, D. A., E-mail: rhdp@mail.ru},

abstractNote = {It is shown that values obtained for asymptotic normalization coefficients by means of a potential fitted to experimental data on elastic scattering depend substantially on the presence and the number n of possible forbidden states in the fitted potential. The present analysis was performed within exactly solvable potential models for various nuclear systems and various potentials without and with allowance for Coulomb interaction. Various methods for changing the number n that are based on the use of various versions of the change in the parameters of the potential model were studied. A compact analytic expression for the asymptotic normalization coefficients was derived for the case of the Hulthén potential. Specifically, the d + α and α + {sup 12}C systems, which are of importance for astrophysics, were examined. It was concluded that an incorrect choice of n could lead to a substantial errors in determining the asymptotic normalization coefficients. From the results of our calculations, it also follows that, for systems with a low binding energy and, as a consequence, with a large value of the Coulomb parameter, the inclusion of the Coulomb interaction may radically change the asymptotic normalization coefficients, increasing them sharply.},

doi = {10.1134/S1063778818020047},

journal = {Physics of Atomic Nuclei},

issn = {1063-7788},

number = 2,

volume = 81,

place = {United States},

year = {2018},

month = {3}

}