Statistical Multifragmentation Model within the Extended Morphological Thermodynamics Approach

Authors

  • V.S. Kucherenko Igor Sikorsky Kyiv Polytechnic Institute, Institute of Physics and Technology
  • K.A. Bugaev Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine, Department of Physics, Taras Shevchenko National University of Kyiv
  • V. Sagun CFisUC, Department of Physics, University of Coimbra
  • O. Ivanytskyi Institute of Theoretical Physics, University of Wroclaw

DOI:

https://doi.org/10.15407/ujpe67.9.639

Keywords:

morphological thermodynamics, induced surface and curvature tensions, equation of state, nuclear liquid-gas phase transition, statistical multifragmentation

Abstract

On the basis of the morphological thermodynamics, we develop an exactly solvable version of the statistical multifragmentation model for the nuclear liquid-gas phase transition. It is shown that the hard-core repulsion between spherical nuclei generates only the bulk (volume), surface, and curvature parts of the free energy of the nucleus, while the Gaussian curvature one does not appear in the derivation. The phase diagram of the nuclear liquid-gas phase transition is studied for a truncated version of the developed model.

References

P.-M. K¨onig, R. Roth, K.R. Mecke. Morphological thermodynamics of fluids: Shape dependence of free energies. Phys. Rev. Lett. 93, 160601 (2004).

https://doi.org/10.1103/PhysRevLett.93.160601

H. Hadwiger. Vorlesungen Uber Inhalt, Oberfl¨ache und ¨ Isoperimetrie (Springer, 1957).

https://doi.org/10.1007/978-3-642-94702-5

K.R. Mecke. Integral geometry in statistical physics. Int. J. Mod. Phys. B 12, 861 (1998).

https://doi.org/10.1142/S0217979298000491

N.S. Yakovenko, K.A. Bugaev, L.V. Bravina, E.E. Zabrodin. The concept of induced surface and curvature tensions for EoS of hard discs and hard spheres. Eur. Phys. J. Special Topics 229, 3445 (2020).

https://doi.org/10.1140/epjst/e2020-000036-3

K.A. Bugaev. Self-consistent analysis of quantum gases of hard spheres beyond the Van der Waals approximation. Eur. Phys. J. A 55, (2019) 215.

https://doi.org/10.1140/epja/i2019-12920-2

K.A. Bugaev. Alternative formulation of the induced surface and curvature tensions approach. J. Phys. G 48, No. 5, 055105 (2021).

https://doi.org/10.1088/1361-6471/abce92

K.A. Bugaev, O.V. Vitiuk, B.E. Grinyuk, P.P. Panasiuk, N.S. Yakovenko E.S. Zherebtsova, V.V. Sagun, O.I. Ivanytskyi, L.V. Bravina, D.B. Blaschke, S. Kabana, S.V. Kuleshov, A.V. Taranenko, E.E. Zabrodin, G.M. Zinovjev. Induced surface and curvature tension equation of state for hadron resonance gas in finite volumes and its relation to morphological thermodynamics. [arXiv:2104.05351 [hep-ph]].

K.A. Bugaev, N.S. Yakovenko, P.V. Oliinyk, E.G. Nikonov, D.B. Blaschke, L.V. Bravina, E.E. Zabrodin. Induced surface and curvature tensions equation of state of hadrons with relativistic excluded volumes and its relation to morphological thermodynamics. [arXiv:2104.06528 [nucl-th]].

K.A. Bugaev, M.I. Gorenstein, I.N. Mishustin, W. Greiner. Exactly soluble model for nuclear liquid-gas phase transition. Phys. Rev. C 62, 044320-1 (2000).

https://doi.org/10.1103/PhysRevC.62.044320

V.V. Sagun, A.I. Ivanytskyi, K.A. Bugaev, I.N. Mishustin. The statistical multifragmentation model for liquid-gas phase transition with a compressible nuclear liquid. Nucl. Phys. A 924, 24 (2014).

https://doi.org/10.1016/j.nuclphysa.2013.12.012

M.E. Fisher. The theory of condensation and the critical point. Physics 3, 255 (1967).

https://doi.org/10.1103/PhysicsPhysiqueFizika.3.255

K.A. Bugaev, L. Phair, J.B. Elliott. Surface partition of large clusters. Phys. Rev. E 72, 047106 (2005).

https://doi.org/10.1103/PhysRevE.72.047106

M. Brack, C. Guet, H.B. H'okansson. Selfconsis-tent semiclassical description of average nuclear properties - a link between microscopic and macroscopic models. Phys. Rep. 123, 276 (1984).

https://doi.org/10.1016/0370-1573(86)90078-5

K. Pomorski, J. Dudek. Nuclear liquid-drop model and surface-curvature effects. Phys. Rev. C 67, 044316-1 (2003).

https://doi.org/10.1103/PhysRevC.67.044316

V.V. Sagun, K.A. Bugaev, A.I. Ivanytskyi. On relation between bulk, surface and curvature parts of nuclear binding energy within the model of hexagonal clusters. Phys. Part. Nucl. Lett. 16, No. 6, 671 (2019).

https://doi.org/10.1134/S1547477119060517

L.G. Moretto, K.A. Bugaev, J.B. Elliott, R. Ghetti, J. Helgesson, L. Phair. The complement: A solution to liquid drop finite size effects in phase transitions. Phys. Rev. Lett. 94, 202701 (2005).

https://doi.org/10.1103/PhysRevLett.94.202701

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Published

2022-12-21

How to Cite

Kucherenko, V., Bugaev, K., Sagun, V., & Ivanytskyi, O. (2022). Statistical Multifragmentation Model within the Extended Morphological Thermodynamics Approach. Ukrainian Journal of Physics, 67(9), 639. https://doi.org/10.15407/ujpe67.9.639

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Section

Fields and elementary particles