Equation of State for Electron-Electron Interaction Energy by Padé Approximation

Abstract:

Describing the electron-electron interaction contribution to the Helmholtz free energy, we obtained a new fitting formula by revising the electronic exchange contribution to the Helmholtz free energy of the previous fitting formula. Using Fortran program, we calculated the curves with some sensitive parameters like the electron-electron interaction contribution to the free energy and the Coulomb coupling parameter , temperature , the mean distance between the electrons making a comparison between the revised fitting formula and the formers. It is concluded that the theoretical value of the revised fitting formula basically has agreement with the previous theoretical value at , when , the revised value completely has a consistent with the previous results. It is illustrated that the curve of the revised fitting formula is more smooth, perfect, and we obtained a very good agreement between the theoretical result of the revised Helmholtz free energy and the theoretical result of the former Padé formulas, which illustrates us to get a more accurate fitting formula and result. Therefore, the revised fitting formula is a more complete and accurate description of the thermodynamic properties of the electron-electron interaction contribution to the Helmholtz free energy.

• Periodical: Applied Mechanics and Materials (Volume 320)
• Pages: 701-706
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.320.701
• Online since: May 2013
• Authors: Xing Rong Zheng, Chun Ling Tian, Jiao Yang, Yun Fu
• Keywords: Electron-Electron Interaction Contribution to Helmholtz Free Energy, Hydrogen Plasma, Padé Formula, Revising

References

[1] E. Wigner and H. B. Huntington, J. Chem. Phys. 3, 764 (1935).

[2] E. Wigner, Phys. Rev. 40, 749 (1932); J. G. Kirkwood, Phys. Rev. 44, 31(1933).

[3] Elisa Liberatore, Carlo Pierleoni, and D. M. Ceperley , J. Chem. Phys. 134, 184505 (2011)

[4] J. M. McMahon and D.M. Ceperley, Phys. Rev. Lett. 106, 165302 (2011).

[5] F. Perrot，M. W. C. Dharma-wardana，Phys. Rev. E 52, 5352–5367 (1995)

[6] Stolzmann W and Blöcker T , Astron.Astrophys, 314, 1024-1040(1996)

[7] Ichimaru.S, Iyetomi.H, Tanaka.S,Phys.Rep, 149, 91-205 (1987)

[8] G.Chabrier and A.Y. Potekhin,Phys.Rev.E, 62, 8554-8563(2000)

[9] Saumon D and Chabrier G ,Phys Rev A, 1991 44 5122.

[10] Saumon D and Chabrier G , Phys Rev A,1992 46 2084.

[11] Ebeling W, Forster A, Fortov V E and Grynaznov V K, Thermophysical properties of hot dense plasmas, ed. B. G. Teuber VerlagsgesellSCHhaft Stuttgart Leipzig 1991 p.7

[12] D. G. Yakovlev and D. A. Shalybkov, Astrophys. Space Phys. Rev. 7, 311 (1989)

[13] Stolzmann W and Blöcker T , Physics Letters A, 221 (1996) 99-103

[14] Stolzmann W and Ebeling W , Physics Letters A, 248 (1998) 242-246

[15] W.Ebeling,Contrib.Plasmas Phys.30 (1990) 553.

[16] W.Ebeling and W. Richert Phys.stat. sol.(b),128 (1990) 467.

[17] G.Chabrier and J., Phys.(Pairs) 51 (1990) 1607

[18] G.Chabrier and A.Y. Potekhin, Phys.Rev.E 58 (1998) 4941-4949

[19] Ichimaru.S,.Rev. Mod.Phys. 54(1982) 1017