Skyrme-Hartree-Fock on Deformed Nucleus for the Island of Inversion Case
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Abstract
The Island of Inversion is a state where the energy levels are not in a standard order. As a result, it will affect the calculation of several other physical quantities. One of those affected is the calculation of the radius of the nuclear charge. For this reason, this paper will present the analysis of the radius of the nucleus charge using the Skrme Hartree Fock method on a deformed nucleus. Through deformation effects, especially the quadruple effect, it is expected that the radius of the nuclear charge will increase. In this paper, we will present the calculation of the nucleus radius using the SHF deformed nucleus method and compare it with the SHF for the ground state nucleus. The calculation results show that this method can adequately handle the island of the inversion effect.
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kurniadi, rizal. (2022). Skyrme-Hartree-Fock on Deformed Nucleus for the Island of Inversion Case. Indonesian Journal of Physics, 33(2), 13-17. https://doi.org/10.5614/itb.ijp.2022.33.2.3
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References
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(32) M. Zhafran, Final Project. , ITB, 2021.
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(3) S. Nummela, et. al, Intruder features in the island of inversion: The case of 33Mg, Phys. Rev. C 64, 054313, 2001
(4) E.G. Nadjakov, K.P. Marinova, Y.P. Gangrsky, Systematics of Nuclear Charge Radii, Atomic Data and Nuclear Data Tables 56, Issue 1, 133-157, 1994
(5) I. Angeli, K.P. Marinova, Table of experimental nuclear ground state charge radii: An update, Atomic Data and Nuclear Data Tables 99, 1, 69-95, 2013.
(6) K. Kreim, Nuclear charge radii of potassium isotopes beyond N=28, Physics Letters B 731, 97-102, 2014.
(7) Tao Li, Yani Luo, Ning Wang, Compilation of recent nuclear ground state charge radius measurements and tests for models, Atomic Data and Nuclear Data Tables 140, 101440, 2021.
(8) Yunfei Ma, Chen Su, Jian Liu, Zhongzhou Ren, Chang Xu, and Yonghao Gao, Predictions of nuclear charge radii and physical interpretations based on the naive Bayesian probability classifier, Phys. Rev. C 101, 014304, 2020
(9) Xiao-Xu Dong, Rong An, Jun-Xu Lu, and Li-Sheng Geng, Novel Bayesian neural network based approach for nuclear charge radii, Phys. Rev. C 105, 014308, 2022
(10) V.A. Macaulay, B. Buck, The determination of nuclear charge distributions using a Bayesian maximum entropy method, Nuclear Physics A, 591, 1, 85-103, 1995.
(11) Yifan Liu, Chen Su, Jian Liu, Pawel Danielewicz, Chang Xu, and Zhongzhou Ren, Improved naive Bayesian probability classifier in predictions of nuclear mass, Phys. Rev. C 104, 014315, 2021.
(12) W. A. Richter and B. A. Brown, Nuclear charge densities with the Skyrme Hartree-Fock method, Phys. Rev. C 67, 034317, 2003
(13) Sheng, Z., Fan, G., Qian, J. et al. An effective formula for nuclear charge radii. Eur. Phys. J. A 51, 40 (2015).
(14) Ning Wang and Tao Li, Shell and isospin effects in nuclear charge radii, Phys. Rev. C 88, 011301(R), 2013.
(15) C. Piller, et. al, Nuclear charge radii of the tin isotopes from muonic atoms, Phys. Rev. C 42, 182, 1990
(16) Z. Boger and H. Guterman, Knowledge extraction from artificial neural network models, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation 4, 3030-3035, 1997.
(17) Geoffrey G. Towell, Jude W. Shavlik, Knowledge-based artificial neural networks, Artificial Intelligence 70, Issues 1–2, 119-165, 1994.
(18) N. Muralidhar, M. R. Islam, M. Marwah, A. Karpatne and N. Ramakrishnan, Incorporating Prior Domain Knowledge into Deep Neural Networks, 2018 IEEE International Conference on Big Data (Big Data), 2018, pp. 36-45.
(19) G. Bebis and M. Georgiopoulos, "Feed-forward neural networks," in IEEE Potentials, vol. 13, no. 4, pp. 27-31, Oct.-Nov. 1994,
(20) Daniel Svozil, Vladimír Kvasnicka, Jir̂í Pospichal, Introduction to multi-layer feed-forward neural networks, Chemometrics and Intelligent Laboratory Systems 39, Issue 1, 43-62, 1997.
(21) Yılmaz Koçak, Gülesen Üstündağ Şiray, New activation functions for single layer feedforward neural network,Expert Systems with Applications, 164, 2021, 113977.
(22) K. Sumiyoshi, D. Hirata, H. Toki, H. Sagawa, Comparison of the relativistic mean-field theory and the Skyrme Hartree-Fock theory for properties of nuclei and nuclear matter, Nuclear Physics A 552, Issue 4, 437-450, 1993.
(23) J. M. Pearson and M. Farine, Relativistic mean-field theory and a density-dependent spin-orbit Skyrme force, Phys. Rev. C 50, 185 1994
(24) W. Pannert, P. Ring, and J. Boguta, Relativistic Mean-Field Theory and Nuclear Deformation, Phys. Rev. Lett. 59, 2420 1987
(25) Mitsuru Tohyama, Properties of Skyrme force as a residual interaction in beyond-mean-field theories, Progress of Theoretical and Experimental Physics, Volume 2021, Issue 8, August 2021, 083D01,
(26) R E Peierls, J Yoccoz, The Collective Model of Nuclear Motion, Proceedings of the Physical Society. Section A 70, 5, 1957.
(27) F Villars - The collective model of nuclei, Annual Review of Nuclear Science, 1957
(28) D. Vautherin, D.M. Brink, Hartree-Fock calculations with Skyrme's interaction, Physics Letters B, 32, 3, 149-153, 1970.
(29) Reinhard, P. G.,The Skyrme-Hartree-Fock Model of the Nuclear Ground State, in Computational Nuclear Physics I, 28-50, Springer-Verlag, 1991
(30) Ring, P., dan Schuck, P. (1980): The Nuclear Many-Body Problem, Springer-Verlag, New York, 175.
(31) Friedrich, J., dan Reinhard, P,Skyrme-force parametrization: Least-squares fit to nuclear ground-state properties, Physical Review C, 33(1), 1986.
(32) M. Zhafran, Final Project. , ITB, 2021.