# Adjustment of Non-linear Interaction Parameters for Relativistic Mean Field Approach by Using Artificial Neural Networks

## Abstract

The relativistic mean field (RMF) model with a small number of adjusted parameters has been used successfully in the last thirty years for predictions of various ground-state nuclear properties of nuclei. In this model, Dirac and Klein–Gordon like equations obtained from application of variation principle on phenomenological Lagrangian density are solved iteratively for calculations of nuclear properties of nuclei. For this purpose, parameters such as masses of considered mesons, nucleon–meson coupling constants, and self-couplings of mesons are needed and they are fitted from experimental data. Some parameter sets for RMF model introduced to correct predictions of nuclear properties of nuclei cover nuclidic chart. Besides Artificial Neural Network (ANN) method is used successfully in many field of science as in nuclear physics. ANN is known as a very powerful tool that are used when standard techniques fail to estimate the correlation between the variables. In the present study, ANN method has been employed to check its understanding capability of relations between RMF model parameters and their predictions on the ground-state binding energies of some spherical nuclei. Understanding capability of ANN method for these relations of considered nuclei has been found well. Based on this success, new non-linear parameter set for RMFmore »

- Authors:

- Karadeniz Technical University, Department of Physics (Turkey)
- Cumhuriyet University, Department of Physics (Turkey)

- Publication Date:

- OSTI Identifier:
- 22761734

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Atomic Nuclei

- Additional Journal Information:
- Journal Volume: 81; Journal Issue: 3; 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; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BINDING ENERGY; COUPLING CONSTANTS; DIRAC EQUATION; GROUND STATES; ITERATIVE METHODS; KLEIN-GORDON EQUATION; LAGRANGIAN FUNCTION; MEAN-FIELD THEORY; MESON-NUCLEON INTERACTIONS; MESONS; NEURAL NETWORKS; NONLINEAR PROBLEMS; NUCLEAR PHYSICS; NUCLEAR PROPERTIES; NUCLEI; RELATIVISTIC RANGE; SPHERICAL CONFIGURATION

### Citation Formats

```
Bayram, T., E-mail: t.bayram@ymail.com, Akkoyun, S., and Şentürk, Ş.
```*Adjustment of Non-linear Interaction Parameters for Relativistic Mean Field Approach by Using Artificial Neural Networks*. United States: N. p., 2018.
Web. doi:10.1134/S1063778818030043.

```
Bayram, T., E-mail: t.bayram@ymail.com, Akkoyun, S., & Şentürk, Ş.
```*Adjustment of Non-linear Interaction Parameters for Relativistic Mean Field Approach by Using Artificial Neural Networks*. United States. doi:10.1134/S1063778818030043.

```
Bayram, T., E-mail: t.bayram@ymail.com, Akkoyun, S., and Şentürk, Ş. Tue .
"Adjustment of Non-linear Interaction Parameters for Relativistic Mean Field Approach by Using Artificial Neural Networks". United States. doi:10.1134/S1063778818030043.
```

```
@article{osti_22761734,
```

title = {Adjustment of Non-linear Interaction Parameters for Relativistic Mean Field Approach by Using Artificial Neural Networks},

author = {Bayram, T., E-mail: t.bayram@ymail.com and Akkoyun, S. and Şentürk, Ş.},

abstractNote = {The relativistic mean field (RMF) model with a small number of adjusted parameters has been used successfully in the last thirty years for predictions of various ground-state nuclear properties of nuclei. In this model, Dirac and Klein–Gordon like equations obtained from application of variation principle on phenomenological Lagrangian density are solved iteratively for calculations of nuclear properties of nuclei. For this purpose, parameters such as masses of considered mesons, nucleon–meson coupling constants, and self-couplings of mesons are needed and they are fitted from experimental data. Some parameter sets for RMF model introduced to correct predictions of nuclear properties of nuclei cover nuclidic chart. Besides Artificial Neural Network (ANN) method is used successfully in many field of science as in nuclear physics. ANN is known as a very powerful tool that are used when standard techniques fail to estimate the correlation between the variables. In the present study, ANN method has been employed to check its understanding capability of relations between RMF model parameters and their predictions on the ground-state binding energies of some spherical nuclei. Understanding capability of ANN method for these relations of considered nuclei has been found well. Based on this success, new non-linear parameter set for RMF model called DEFNE by us have been produced by using ANN method. Furthermore, predictions of RMF model with DEFNE parameter set for ground-state binding energies and charge radii of nuclei cover nuclidic chart have been found as in agreement with the available experimental data.},

doi = {10.1134/S1063778818030043},

journal = {Physics of Atomic Nuclei},

issn = {1063-7788},

number = 3,

volume = 81,

place = {United States},

year = {2018},

month = {5}

}