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.
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D. Vautherin and D. M. Brink, Phys. Rev. C 5, 626 (1972).
J. Dechargé and D. Gogny, Phys. Rev. C 21, 1568 (1980).
J. Boguta and A. R. Bodmer, Nucl. Phys.A 292, 413 (1977).
P. Ring, Prog. Part. Nucl. Phys. 37, 193 (1996).
G. A. Lalazissis, S. Raman, and P. Ring, At. Data Nucl. Data Tables 71, 1 (1999).
D. Vretenar, A. V. Afanasjev, G. A. Lalazissis, and P. Ring, Phys. Rep. 409, 101 (2005).
J. Meng, H. Toki, S. G. Zhou, S. Q. Zhang, W. H. Long, and L. S. Geng, Prog. Part. Nucl. Phys. 57, 470 (2006).
J. Piekarewicz, Phys. Rev. C 76, 064310 (2007).
A. H. Yilmaz and T. Bayram, J. Korean Phys. Soc. 59, 3329 (2011).
T. Bayram and A. H. Yilmaz, Mod. Phys. Lett. A 28, 1350068 (2013).
T. Bayram and S. Akkoyun, Phys. Scripta 87, 065201 (2013).
P. Ring, Y. K. Gambhir, and G. A. Lalazissis, Comput. Phys. Commun. 105, 77 (1997).
T. Nikšić, N. Paar, D. Vretenar, and P. Ring, Comput. Phys. Commun. 185, 1808 (2014).
G. A. Lalazissis, S. Karatzikos, R. Fossion, D. Pena Artega, A. V. Afanasjev, and P. Ring, Phys. Lett. B 671, 36 (2009).
M. E. Medhat, Ann. Nucl. Energy 45, 73 (2012).
S. Athanassopoulos, E. Mavrommatis, K. A. Gernoth, and J.W. Clark, Nucl. Phys. A 743, 222 (2004).
T. Bayram, S. Akkoyun, and S. O. Kara, Ann. Nucl. Energy 63, 172 (2014).
K. M. Graczyk and C. Juszczak, Phys. Rev. C 90, 054334 (2014).
R. Utama, J. Piekarewicz, and H. B. Prosper, Phys. Rev. C 93, 014311 (2016).
K.M. Graczyk, Phys. Rev. C 84, 034314 (2011).
C. David, M. Freslier, and J. Aichelin, Phys. Rev. C 51, 1453 (1995).
S. A. Bass, A. Bischoff, J. A. Maruhn, H. Stocker, and W. Greiner, Phys. Rev. C 53, 2358 (1996).
F. Haddad, K. Hagel, J. Li, N. Mdeiwayeh, J. B. Natowitz, R. Wada, B. Xiao, C. David, M. Freslier, and J. Aichelin, Phys. Rev. C 55, 1371 (1997).
N. Costiris, E. Mavrommatis, K. A. Gernoth, and J.W. Clark, nucl-th/0701096v1.
S. Akkoyun and T. Bayram, Int. J. Mod. Phys. E 23, 1450064 (2014).
S. Akkoyun, T. Bayram, S. O. Kara, and A. Sinan, J. Phys. G 40, 055106 (2013).
R. Utama, W.-C. Chen, and J. Piekarewicz, J. Phys. G 43, 114002 (2016).
K.M. Graczyk, Phys. Rev. C 88, 065205 (2013).
G. A. Lalazissis, J. König, and P. Ring, Phys. Rev. C 55, 540 (1997).
Y. K. Gambhir and A. Bhagwat, Phys. Part. Nucl. 37, 194 (2006).
S. Haykin, Neural Networks: a Comprehensive Foundation (Englewood Cliffs, Prentice-Hall, New Jersey, 1999).
G. Cybenko, Math. Control Signals Syst. 2, 303 (1989).
K. Levenberg, Quart. Appl.Math. 2, 164 (1944).
D.W. Marquardt, J. Soc. Indust. Appl.Math. 11, 431 (1963).
M. Wang, G. Audi, A. H. Wapstra, F. G. Kondev, M. MacCormick, X. Xu, and B. Pfeiffer, Chin. Phys. C 36, 1603 (2012).
T. Nikšić, D. Vretenar, and P. Ring, Phys. Rev. C 78, 034318 (2008).
G. A. Lalazissis, T. Nikšić, D. Vretenar, and P. Ring, Phys. Rev. C 71, 024312 (2005).
M. V. Stoitsov, J. Dobaczewski, W. Nazarewicz, S. Pittel, and D. J. Dean, Phys. Rev. C 68, 054312 (2003).
P. Moller, J. R. Nix, and K.-L. Kratz, At. Data Nucl. Data Tables 66, 131 (1997).
I. Angeli and K. P. Marinova, At. Data Nucl. Data Tables 99, 69 (2013).
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Bayram, T., Akkoyun, S. & Şentürk, Ş. Adjustment of Non-linear Interaction Parameters for Relativistic Mean Field Approach by Using Artificial Neural Networks. Phys. Atom. Nuclei 81, 288–295 (2018). https://doi.org/10.1134/S1063778818030043