انرژی تقارنی و انرژی آزاد تقارنی ماده هسته ای نامتقارن در تقریب توماس-فرمی

نوع مقاله: مقاله پژوهشی کامل

نویسندگان

1 استادیار فیزیک هسته ای در دانشگاه کاشان

2 دانشگاه کاشان

چکیده

در چارچوب تقریب نیمه -کلاسیکی توماس-فرمی که مبتنی بر یک رهیافت آماری است، ضریب اشغال نوکلئونی در فضای فاز برای ماده هسته ای، با به کارگیری نظریه مایعات کوانتومی لاندائو به دست می آید. با بهره گیری از برهمکنش های نوکلئون-نوکلئون مایرز و شواتکی، موسوم به TF(96) و TF(90)، در ابتدا معادله حالت ماده هسته ای نامنقارن بدست می آید. سپس، توجه ویژه ای به بررسی رفتار کمیتهای انرژی تقارنی و انرژی آزاد تقارنی که در معادله حالت تاثیر زیادی دارند، می شود. از این رو، سخت تر شدن معادله حالت در برهمکنش TF(90) نسبت به TF(96) به تاثیر کلیدی این کمیتها برمی گردد. قابلیت تعمیم پذیری مدل کنونی با تعیین چگالی اشباع و ضریب تراکم ناپذیری اشباع ماده هسته ای به ازای دماها و پارامترهای مختلف عدم تقارن، به خوبی نشان داده شده است. همچنین، علاوه بر مقایسه ضرائب مربوط به انرژی آزاد تقارنی، چگالی اشباع و ضریب تراکم ناپذیری اشباع برای ماده هسته ای سرد با نتایج حاصل از مدلهای دیگر، تاثیر دما بر روی این کمیتها نیز بررسی می شود.

کلیدواژه‌ها


عنوان مقاله [English]

Symmetry energy and symmetry free energy of asymmetric nuclear matter in the Thomas-Fermi Approximation

نویسندگان [English]

  • Mehdi Ghazanfari Mojarrad 1
  • Maryam Sadat Fatemi 2
1 Assistant professor of Nuclear Physics in Kashan university
2 Department of Physics, University of Kashan
چکیده [English]

Within the semi-classical approximation of Thomas-Fermi, which is based on a statistical approach, the phase-space occupation equation number of nuclear matter is obtained by employing the Landau Fermi-Liquid theory. At the first, using the NN-interactions of Myers and Swiatecki, known as TF(96) and TF(90), the equation of state of nuclear matter (EOS) is derived. Then, a special attention is devoted to studying the behavior of symmetry energy and symmetry free energy quantities which have a substantial effect on the equation of state. Hence, the stiffer behavior of the EOS in the TF(90) interaction compared to the TF(96) interaction, refers to the important effects of these quantities. The extensibility feature of the present model is shown by determining the saturation density and the saturation incompressibility coefficient. In addition to the comparison of symmetry energy, symmetry free energy and incompressibility coefficient with the results of other models, the temperature effects on these quantities are also studied.

کلیدواژه‌ها [English]

  • Thomas-Fermi approximation
  • Nuclear matter
  • Equation of state
  • Symmetry energy and symmetry free energy
  • Incompressibility

 

[1] M.F. Rivet et al., Correlations between signals of the liquid-gas phase transition in nuclei, Nuclear Physics A 749 (2005) 73.

 

[2] O.N. Ghodsi, H.R. Moshfegh, R. Gharaei, Role of the saturation properties of hot nuclear matter in the proximity formalism, Physical ReviewC 88 (2013) 034601.

 

[3] H.A. Bethe, supernova mechanism, Reviews of Modern Physics62 (1990) 801.

[4] N.K. Glendenning, Compact Stars, New York: Springer (1997).

 

[5] K. Strobel, C. Schaab, M.K. Weigel, Properties of non-rotating and rapidly rotating protoneutron stars, Astron. Astrophys. 350 (1999) 497.

 

[6] P. Haensel, A.Y. Potekhin, D.G. Yakovlev, Neutron Stars 1: Equation of State and Structure, Springer Science and Business Media 326 (2007).

 

[7] M. Camenzind, Compact Objects in Astro-physics, Springer-Verlag, Berlin, Heidelberg (2007).

 

[8] H.R. Moshfegh, M. Ghazanfari Mojarrad, Strange baryonic matter in the Thomas-Fermi theory, The European Physical JournalA 49 (2013) 1.

 

[9] M. Ghazanfari Mojarrad, R. Arabsaeidi, Hyperon-rich matter in a two-solar-mass neutron star within the Thomas-Fermi approximation, International Journal of Modern Physics. E 25 (2016) 1650102.

 

[10] B. Friedman, V.R. Pandharipande, Hot and cold, nuclear and neutron matter, Nuclear Physics A 361 (1981) 502.

 

[11] R.B. Wiringa, V. Ficks, A. Fabrocini, Equation of state for dense nucleon matter, Physical ReviewC 38 (1988) 1010.

 

[12] A. Akmal, V.R. Pandharipande, D.G. Ravenhall, Equation of state of nucleon matter and neutron star structure, Physical ReviewC 58 (1998)1804.

 

[13] G.H. Bordbar, Calculation of the saturation properties of symmetrical nuclear matter with inclusion of Δ isobar, Iranian Journal of Physics Research 3 (2001) 1.

 

]13[غ.بردبار،محاسبة خصوصیات اشباع مادة هسته‌ای متقارن با در نظر گرفتن ایزوبار Δ، مجلةپژوهشفیزیکایران 3 (1380) 1.

[14] M. Baldo, A. Fiasconaro, H.Q. Song, G. Giansiracusa, U. Lombardo, High density symmetric nuclear matter in the Bethe-Brueckner-Goldstone approach, Physical ReviewC 65 (2001) 017303.

 

[15] W. Zuo, Z.H. Li, A. Li, and U. Lombardo, Effect of three-body interaction on phase transition of hot asymmetric nuclear matter, Nuclear Physics A 745 (2004) 34.

 

[16] H.R. Moshfegh, M. Modarres, Thermal properties of asymmetrical nuclear matter with the new charge-dependent Reid potential, Nuclear Physics A 792 (2007) 201.

 

[17] G. Bordbar, B. Khosropour, Calculation of the effect of neutrinos on the protoneutron star structure, Iranian Journal of Physics Research 8 (2008) 129.

 

]17[غ. بردبار، ب. خسروپور، محاسبة اثر نوترینو در محاسبة ساختار ستارة نوترونی تازه متولد شده، مجلة پژوهش فیزیک ایران 8 (1387) 129.

 

[18] A. Rios, A. Polls, A. Ramos, H. Müther, Liquid-gas phase transition in nuclear matter from realistic many-body approaches, Physical ReviewC 78 (2008) 044314.

 

[19] A. Rios, A. Polls, I. Vidana, Hot neutron matter from a self-consistent Green's-functions approach, Physical ReviewC 79 (2009) 025802.

 

[20] S. Zaryouni, H.R. Moshfegh, A relativistic approach to the equation of state of asymmetric nuclear matter, The European Physical JournalA 45 (2010) 69.

 

[21] M. Modarres, A. Tafrihi, The LOCV nucleonic matter correlation and distribution functions versus the FHNC/SOC and the Monte Carlo calculations, Nuclear Physics A 941 (2015) 212.

 

[22] A. Fedoseew, H. Lenske, Thermal properties of asymmetric nuclear matter, Physical ReviewC 91 (2015) 034307.

 

[23] H.R. Moshfegh, S. Goudarzi, Temperature Dependence of Nuclear Symmetry Free Energy, Acta Physica Polonica B 46 (2015).

 

 [24] S. Zaryouni, Incompressibility of Nuclear Matter, Journal of research on Manybody systems 4 (2015) 21.

 

]24[س. زریونی، تراکم ناپذیری ماده هسته‌ای، مجله پژوهش سیستم‌های بس‌ذره‌ای 4 (1393) 21.

 

[25] S. Goudarzi, H.R. Moshfegh, Erratum: Proto-neutron star structure within an extended lowest-order constrained variational method at finite temperature [Physical ReviewC 92, 035806 (2015)], Physical ReviewC 97 (2018) 049904.

 

[26] S. Goudarzi, H.R. Moshfegh, P. Haensel, The role of three-body forces in nuclear symmetry energy and symmetry free energy, Nuclear Physics A 969 (2018) 206.

 

[27] W.D. Myers, W.J. Swiatecki, A Thomas-Fermi model of nuclei. Part I. Formulation and first results, Annals of Physics 204 (1990) 401.

 

[28] W.D. Myers, W.J. Swiatecki, Nuclear properties according to the Thomas-Fermi model, Nuclear Physics A 601 (1996) 141.

 

[29] D. Serot, J.D. Walecka, The relativistic nuclear many body problem, Adv. Nuclear Physics 16 (1986) 1.

 

[30] H. Müller, B.D. Serot, Relativistic mean-field theory and the high-density nuclear equation of state, Nuclear Physics A 606 (1996) 508.

 

[31] H. Müller, B.D. Serot, Phase transitions in warm, asymmetric nuclear matter, Physical ReviewC 52 (1995) 2072.

 

[32] E. Chabanat, P. Bonche, P. Haensel, J. Mayer, and R. Schaeffer, A Skyrme parametrization from subnuclear to neutron star densities Part II. Nuclei far from stabilities, Nuclear Physics A 635 (1998) 231.

 

[33] J. Randrup, E. Lima Medeiros, Model for statistical properties of nuclear systems at finite temperature, Nuclear Physics A 526 (1991) 115.

 

[34] K. Strobel, F. Weber, M.K. Weigel, Symmetrie and Asymmetrie Nuclear Matter in the Thomas-Fermi Model at Finite Temperatures, Z. Naturforschr A 54 (1999) 83.

 

[35] H.R. Moshfegh, Equation of state of hot nuclear and neutron matter: A statistical approach, International Journal of Modern Physics. E 15 (2006) 1127.

 

[36] H.R. Moshfegh, M. Ghazanfari Mojarrad, Thermal properties of baryonic matter, Journal of Physics G: Nuclear and Particle Physics 15 (2011) 085102.

 

[37] M. Ghazanfari Mojarrad,S.K. Mousavi Khoreshtami,A. Mostajeran Gurtani,   Thomas-Fermi calculations for determination of critical properties of symmetric nuclear matter on the basis of extended effective mass approach,  Iranian Journal of Physics Research 16 (2016) 207.

 

]37[م .غضنفری مجرد، س .ک. موسوی خرشتمیو ا. مستأجران گورتانی، محاسبات توماس- فرمی برای تعیین خواص بحرانی ماده هسته‌ای متقارن براساس رهیافت جرم مؤثر تعمیم‌یافته، مجله پژوهش فیزیک ایران 16 (1395) 207.

[38] M. Ghazanfari Mojarrad, S.K. Mousavi Khoroshtomi, Thomas–Fermi approximation for the equation of state of nuclear matter: A semi-classical approach from the Landau Fermi-Liquid theory, International Journal of Modern Physics. E 26 (2017) 1750038.

 

[39] M. Ghazanfari Mojarrad, N.S. Razavi, S. Vaezzade, Thomas–Fermi approximation for β-stable nuclear matter in the Landau Fermi-liquid theory, Nuclear Physics A 980 (2018) 51.

 

[40] D.N. Basu, Nuclear incompressibility using the density-dependent M3Y effective interaction, Journal of Physics G: Nuclear and Particle Physics. 30 (2004) B7.

 

[41] J. Xu, L.W. Chen, B. A. Li, H.R. Ma, Temperature effects on the nuclear symmetry energy and symmetry free energy with an isospin and momentum dependent interaction, Physical ReviewC 75 (2007) 014607.

 

[42] C.C. Moustakidis, Thermal effects on nuclear symmetry energy with a momentum-dependent effective interaction, Physical ReviewC 76 (2007) 025805.

 

[43] C.C. Moustakidis, Temperature and momentum dependence of single-particle properties in hot asymmetric nuclear matter, Physical ReviewC 78 (2008) 054323.

 

[44] J. Xu, L.W. Chen, B.A. Li, H.R. Ma, Effects of isospin and momentum dependent interactions on thermal properties of asymmetric nuclear matter, Physical ReviewC 77 (2008) 014302.

 

[45] L.W. Chen et al., Higher-order effects on the incompressibility of isospin asymmetric nuclear matter, Physical ReviewC80 (2009) 014322.

 

[46] J. Piekarewicz, M. Centelles, Incompressibility of neutron-rich matter, Physical ReviewC 79 (2009) 054311.

 

[47] D.N. Basu, P.R. Chowdhury, C .Samanta, Isobaric incompressibility of isospin asymmetric nuclear matter, Physical ReviewC 80 (2009) 057304.

 

[48] A. Rios, Effective interaction dependence of the liquid–gas phase transition in symmetric nuclear matter, Nuclear Physics A 845 (2010) 58.

 

[49] G. Baym, C.J. Pethick, Landau Fermi-Liquid Theory. Concepts and Applications, Wiley, New York, (1991).

 

[50] R.K. Pathria, Statistical Mechanics, Oxford: Butterworth-Heinemann (1996).

 

[51] M. Brack, R.K. Bhaduri, Semi-classical Physics,Addison-Wesley, (1997).

 

[52] C.F. von Weizsacker, On the theory of nuclear masses, Zeitschrift für Physik 96 (1935) 431.

 

[53] H.A. Bethe, R.F. Bacher, Nuclear physics A. Stationary states of nuclei, Reviews of Modern Physics8 (1936) 82.

 

[54] H.T. Janka, K. Langanke, A. Marek, G Martínez-Pinedo, B Müller, Theory of core-collapse supernovae, Physics Reports 442 (2007)

 

[55] L. Roberts, G. Shen, V. Cirigliano, J. Pons, S. Reddy, S. Woosley, Protoneutron star cooling with convection: The effect of the symmetry energy, Physical Review Letters 108 (2012) 061103.

 

[56] L.W. Chen, C.M. Ko, B.A. Li, Nuclear matter symmetry energy and the neutron skin thickness of heavy nuclei, Physical Review C 72 (2005) 064309

 

[57] M.M. Sharma and et al., Giant monopole resonance in Sn and Sm nuclei and the compressibility of nuclear matter, Physical ReviewC 38 (1988) 2562.

 

[58] J.R. Stone, N.J. Stone, S.A. Moszkowski, Incompressibility in finite nuclei and nuclear matter, Physical ReviewC 89 (2014) 044316.

[59] T. Li et al., Isotopic Dependence of the Giant Monopole Resonance in the Even-A Sn 112–124 Isotopes and the Asymmetry Term in Nuclear Incompressibility, Physical Review Letters 99 (2007) 162503.