Abstract
Nuclear shape transition has been actively studied in the past decade. In particular, the understanding of this phenomenon from a microscopic point of view is of great importance. Because of this reason, many works have been employed to investigate shape phase transition in nuclei within the relativistic and nonrelativistic mean field models by examining potential energy curves (PECs). In this paper, by using layered feed-forward neural networks (LFNNs), we have constructed consistent empirical physical formulas (EPFs) for the PECs of 38–66Ti calculated by the Hartree-Fock-Bogoliubov (HFB) method with SLy4 Skyrme forces. It has been seen that the PECs obtained by neural network method are compatible with those of HFB calculations.
Similar content being viewed by others
References
R. F. Casten and E. A. McCutchan, J. Phys. G: Nucl. Part. Phys. 34, R285–R320 (2007).
P. Cejnar, J. Jolie, and R. F. Casten, Rev. Mod. Phys. 82, 2155–2212 (2010).
F. Iachello, Phys. Rev. Lett. 85, 3580–3583 (2000).
F. Iachello, Phys. Rev. Lett. 87, 052502 (2001).
R. F. Casten and N. V. Zamfir, Phys. Rev. Lett. 85, 3584–3586 (2000).
R. F. Casten and N. V. Zamfir, Phys. Rev. Lett. 87, 052503 (2001).
H. Flocard et al., Nucl. Phys., Ser. A 203, 433–472 (1973).
P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, Berlin, 1980).
B. D. Serot and J. D. Walecka, Adv. Nucl. Phys. 16, 1–321 (1986).
P. Ring, Prog. Part. Nucl. Phys. 37, 193–263 (1996).
J. Meng et al., Prog. Part. Nucl. Phys. 57, 470–563 (2006).
J. Meng et al., Eur. Phys. J., Ser. A 25, 23–27 (2005).
R. Fossion, D. Bonatsos, and G. A. Lalazissis, Phys. Rev., Ser. C 73, 044310 (2006).
M. Yu et al., Int. J. Mod. Phys., Ser. E 15, 939 (2006).
R. Rodriguez-Guzmin and P. Sarriguren, Phys. Rev., Ser. C 76, 064303 (2007).
J.-Y. Guo, X. Z. Fang, and Z. Q. Sheng, Int. J. Mod. Phys., Ser. E 17, 539–548 (2008).
A. H. Yilmaz and T. Bayram, J. Korean Phys. Soc. 59, 3329–3336 (2011).
B.-M. Yao and J.-Y. Guo, Mod. Phys. Lett., Ser. A 25, 1177–1186 (2010).
T. Bayram, Mod. Phys. Lett., Ser. A 27, 1250162 (2012).
T. Bayram and A. H. Yilmaz, “A study on shape of Te isotopes in mean field formalism, arXiv: 1301.2684 [nucl-th].
T. Nikssic et al., Phys. Rev. Lett. 99, 092502 (2007).
M. Bender and P.-H. Heenen, Phys. Rev., Ser. C 78, 024309 (2008).
J. M. Yao et al., Phys. Rev., Ser. C 81, 044311 (2010).
T. R. Rodriguez and J. L. Egido, Phys. Rev., Ser. C 81, 064323 (2010).
A. Bholoa et al., Nucl. Instr. Meth., Ser. B 255, 1–7 (2007).
S. Athanassopoulos et al., Nucl. Phys., Ser. A 743, 222–235 (2004).
E. Mavrommatis, K. A. Gernoth, and J. W. Clark, “One and two proton separation energies from nuclear mass systematics using neural networks,” arXiv: nucl-th/0509075.
K. L. Peterson, Phys. Rev., Ser. A 44, 126–138 (1991).
R. M. Balabin and E. I. Lomakina, J. Chem. Phys. 131, 074104 (2009).
L. R. Marim, M. R. Lemes, and A. Dal Pino, Jr., Tho. Chem. 663, 159–165 (2003).
A. R. S. Latino Diogo et al., J. Electroanal. Chem. 624, 109–120 (2008).
N. Costris et al., “A global model of beta(-) decay halflives using neural networks,” arXiv: nucl-th/0701096v1.
C. David and J. Aichelin, Pisa, Italy, 1995, pp. 709–718.
M. V. Stoitsov et al., Comp. Phys. Commun. 167, 43–63 (2005).
S. Haykin, Neural Networks: A Comprehensive Foundation (Prentice-Hall Inc., USA, NJ, Englewood Cliffs, 1999).
K. Hornik, M. Stinchcombe, and H. White, Neural Networks 2, 359–366 (1989).
Neurosolutions, http://www.neurosolutions.com/.
K. Levenberg, Quart. Appl. Math. 2, 164–168 (1944).
D. Marquardt, SIAM J. Appl. Math. 11, 431–441 (1963).
N. Yildiz, Phys. Lett., Ser. A 345(1–3), 69 (2005).
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Akkoyun, S., Bayram, T., Kara, S.O. et al. Consistent empirical physical formulas for potential energy curves of 38–66Ti isotopes by using neural networks. Phys. Part. Nuclei Lett. 10, 528–534 (2013). https://doi.org/10.1134/S1547477113060022
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1547477113060022