Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

Calculating the thermodynamic quantities of nucleus using the temperature dependence of level density parameter

Document Type : Research Paper

Authors

Kh. Benam 1
S.Z. Mousavi 2
V. Dehghani 2
S.A. Alavi 2

1 Department of Physics, Faculty of Basic Sciences, Shahrekord University, P.O. Box: 115, Shahrekord - Iran

2 Department of Physics, University of Sistan and Baluchestan, P.O. Box: 98155-987, Zahedan - Iran

https://doi.org/10.24200/nst.2022.1209.1785
Abstract
The nuclear level density parameter is an important quantity in nuclear physics. Nuclear level density parameter has been calculated using different methods. In this work at first, the single particle level density has been calculated by LDA method, then the nuclear level density parameter has been obtained as a function of temperature. Based on Lestone method and using Thomas-Fermi approximation, the level density parameter has been calculated to the order of next to Lestone results (corrected Lestone method). Using calculated nuclear level density parameter and taking into account the pairing energy, the nuclear level density, excitation energy, entropy and heat capacity have been calculated

Highlights

  1. J. Bardeen, L.N. Cooper, J.R. Schrieffer, Theory of superconductivity, Phys. Rev, 108(5), 1175 (1957).

 

  1. P. Arve, et al., Static path approximation for the nuclear partition function, Ann of Physics, 183(2), 309-319 (1988).

 

  1. B. Lauritzen, et al., Pairing phase transition in small particles, Ann of Physics, 223(2), 216 (1993).

 

  1. R. Rossignoli, et al., Thermal and quantal fluctuations for fixed particle number in finite superfluid systems, Phys. Rev. Lett, 80(9), 1853 (1998).

 

  1. V. Dehghani, Gh. Forozani, Kh. Benam, The effect of shell closure on the thermodynamic properties of 207Pb and 89Y, Int. J. Mod. Phys. E, 25(11), 1650098 (2016).

 

  1. V. Dehghani, Gh. Forozani, Kh. Benam, Thermal properties of 96,97Mo using Lipkin–Nogami model with an average value gap parameter, Int. J. Mod. Phys. E, 27(6), 1850045 (2018).

 

  1. A.J. Koning, et al., Global and local level density models, Nucl. Phys. A, 810(1-4), 13 (2008).

 

  1. P. Demetriou, S. Goriely, Microscopic nuclear level densities for practical applications, Nucl. Phys. A, 695(1-4), 95 (2001).

 

  1. H.T. Nyhus, et al., Level density and thermodynamic properties of dysprosium isotopes, Phys. Rev. C, 85(1), 014323 (2012).

 

  1. A.V. Ignatyuk, et al., Phenomenological description of energy dependence of the level density parameter, Sov. J. Nucl. Phys, 21(3), 485 (1975).

 

  1. T. Egidy, D. Bucurescu, Systematics of nuclear level density parameters, Phys. Rev. C, 72(4), 044311 (2005).

 

  1. D.J. Hinde, et al., Neutron emission as a probe of fusion-fission and quasi-fission dynamics, Phys. Rev. C, 45(3), 1229 (1992).

 

  1. J.P. Lestone, Determination of the time evolution of fission from particle emission, Phys. Rev. Lett, 70(15), 2245 (1993).

 

  1. Y. Alhassid, et al., Direct microscopic calculation of nuclear level densities in the shell model Monte Carlo approach, Phys. Rev. C, 92(2), 024307 (2015).

 

  1. R. Rahmatinejad, et al., Collective enhancements in the level densities of Dy and Mo isotopes, Phys. Rev. C, 101(5), 054315 (2020).

 

  1. S. Shlomo, J.B. Natowitz, Temperature and mass dependence of level density parameter, Phys. Rev. C, 44, 6 (1991).

 

  1. J.P. Lestone, Temperature dependenceof level density parameter, Phys. Rev. C, 52(2), 1118 (1995).

 

  1. B. Canbula, et al., A Laplace-like formula for the energy dependence of the nuclear level density parameter, Nucl. Phys. A, 929(54), 70 (2014).

 

  1. S. Hilaire, Energy dependence of the level density parameter, Phys. Lett. B, 583(3-4), 264 (2004).

 

  1. B. Canbula, H. Babacan, Calculation of the level density parameter using semi-classical approach, Nucl. Phys. A, 858(1), 32 (2011).

 

  1. V. Dehghani, S.A. Alavi, Nuclear level density of even-even nuclei with temperature dependent pairing energy, Eur. Phys. J. A, 52(306), 1-7 (2016).

 

  1. S. Alavi, V. Dehghani, Back shifted Fermi gas model with temperature dependent pairing energy: Thermal properties of 98Mo, Int. J. Mod. Phys. E, 25(9), 1650065 (2016).

 

  1. P. Ring, P. Schuck, The nuclear many-body Problem, Springer-Verlag, New-York (1980).

 

  1. S. Shlomo, Energy level density of nuclei, Nucl. Phys. A, 539(1), 17 (1992).

 

  1. J. Toke, W.J. Swiatecki, Surface-layer corrections to the level-density formula for a diffuse Fermi gas, Nucl. Phys. A, 372(1), 14 (1981).

 

  1. M. Prakash, J. Wambach, Z.Y. Ma, Effective mass in nuclei and the level density parameter, Phys. Lett. B, 128(3), 141 (1983).

 

  1. H.A. Bethe, Nuclear Physics B. Nuclear Dynamics, Theoretical, Rev. Mod. Phys, 9(2), 69 (1937).

 

  1. T. Ericson, The statistical model and nuclear level densities, Adv. Phys, 9(36), 425 (1960).

 

  1. A. Bohr, B.R. Mottelson, Nuclear Structure,Vol. I, 155 (1969).

 

  1. A. Bohr, B.R. Mottelson, Nuclear Structure I, World Scientific, Singapore (1998).

 

  1. V. Dehghani, Gh. Forozani, Kh. Benam, Calculating the thermal properties of 93,94,95Mo using the BCS model with an average value gap parameter, Nucl. Sci. Tech, 128(28), 1-6 (2017)

Keywords

Single particle level density
Level density
Level density parameter
Pairing energy
Excitation energy
  1. J. Bardeen, L.N. Cooper, J.R. Schrieffer, Theory of superconductivity, Phys. Rev, 108(5), 1175 (1957).

 

  1. P. Arve, et al., Static path approximation for the nuclear partition function, Ann of Physics, 183(2), 309-319 (1988).

 

  1. B. Lauritzen, et al., Pairing phase transition in small particles, Ann of Physics, 223(2), 216 (1993).

 

  1. R. Rossignoli, et al., Thermal and quantal fluctuations for fixed particle number in finite superfluid systems, Phys. Rev. Lett, 80(9), 1853 (1998).

 

  1. V. Dehghani, Gh. Forozani, Kh. Benam, The effect of shell closure on the thermodynamic properties of 207Pb and 89Y, Int. J. Mod. Phys. E, 25(11), 1650098 (2016).

 

  1. V. Dehghani, Gh. Forozani, Kh. Benam, Thermal properties of 96,97Mo using Lipkin–Nogami model with an average value gap parameter, Int. J. Mod. Phys. E, 27(6), 1850045 (2018).

 

  1. A.J. Koning, et al., Global and local level density models, Nucl. Phys. A, 810(1-4), 13 (2008).

 

  1. P. Demetriou, S. Goriely, Microscopic nuclear level densities for practical applications, Nucl. Phys. A, 695(1-4), 95 (2001).

 

  1. H.T. Nyhus, et al., Level density and thermodynamic properties of dysprosium isotopes, Phys. Rev. C, 85(1), 014323 (2012).

 

  1. A.V. Ignatyuk, et al., Phenomenological description of energy dependence of the level density parameter, Sov. J. Nucl. Phys, 21(3), 485 (1975).

 

  1. T. Egidy, D. Bucurescu, Systematics of nuclear level density parameters, Phys. Rev. C, 72(4), 044311 (2005).

 

  1. D.J. Hinde, et al., Neutron emission as a probe of fusion-fission and quasi-fission dynamics, Phys. Rev. C, 45(3), 1229 (1992).

 

  1. J.P. Lestone, Determination of the time evolution of fission from particle emission, Phys. Rev. Lett, 70(15), 2245 (1993).

 

  1. Y. Alhassid, et al., Direct microscopic calculation of nuclear level densities in the shell model Monte Carlo approach, Phys. Rev. C, 92(2), 024307 (2015).

 

  1. R. Rahmatinejad, et al., Collective enhancements in the level densities of Dy and Mo isotopes, Phys. Rev. C, 101(5), 054315 (2020).

 

  1. S. Shlomo, J.B. Natowitz, Temperature and mass dependence of level density parameter, Phys. Rev. C, 44, 6 (1991).

 

  1. J.P. Lestone, Temperature dependenceof level density parameter, Phys. Rev. C, 52(2), 1118 (1995).

 

  1. B. Canbula, et al., A Laplace-like formula for the energy dependence of the nuclear level density parameter, Nucl. Phys. A, 929(54), 70 (2014).

 

  1. S. Hilaire, Energy dependence of the level density parameter, Phys. Lett. B, 583(3-4), 264 (2004).

 

  1. B. Canbula, H. Babacan, Calculation of the level density parameter using semi-classical approach, Nucl. Phys. A, 858(1), 32 (2011).

 

  1. V. Dehghani, S.A. Alavi, Nuclear level density of even-even nuclei with temperature dependent pairing energy, Eur. Phys. J. A, 52(306), 1-7 (2016).

 

  1. S. Alavi, V. Dehghani, Back shifted Fermi gas model with temperature dependent pairing energy: Thermal properties of 98Mo, Int. J. Mod. Phys. E, 25(9), 1650065 (2016).

 

  1. P. Ring, P. Schuck, The nuclear many-body Problem, Springer-Verlag, New-York (1980).

 

  1. S. Shlomo, Energy level density of nuclei, Nucl. Phys. A, 539(1), 17 (1992).

 

  1. J. Toke, W.J. Swiatecki, Surface-layer corrections to the level-density formula for a diffuse Fermi gas, Nucl. Phys. A, 372(1), 14 (1981).

 

  1. M. Prakash, J. Wambach, Z.Y. Ma, Effective mass in nuclei and the level density parameter, Phys. Lett. B, 128(3), 141 (1983).

 

  1. H.A. Bethe, Nuclear Physics B. Nuclear Dynamics, Theoretical, Rev. Mod. Phys, 9(2), 69 (1937).

 

  1. T. Ericson, The statistical model and nuclear level densities, Adv. Phys, 9(36), 425 (1960).

 

  1. A. Bohr, B.R. Mottelson, Nuclear Structure,Vol. I, 155 (1969).

 

  1. A. Bohr, B.R. Mottelson, Nuclear Structure I, World Scientific, Singapore (1998).

 

  1. V. Dehghani, Gh. Forozani, Kh. Benam, Calculating the thermal properties of 93,94,95Mo using the BCS model with an average value gap parameter, Nucl. Sci. Tech, 128(28), 1-6 (2017)

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