Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
Levan Chkhartishvili, Tamar Berberashvili
DOI: 10.4236/jemaa.2010.24029   PDF    HTML     4,158 Downloads   7,690 Views   Citations


Within the frames of semiclassical approach, intra-atomic electric field potentials are parameterized in form of radial step-like functions. Corresponding parameters for 80 chemical elements are tabulated by fitting of the semiclassical energy levels of atomic electrons to their first principle values. In substance binding energy and electronic structure calculations, superposition of the semiclassically parameterized constituent-atomic potentials can serve as a good initial approximation of its inner potential: the estimated errors of the determined structural and energy parameters make up a few percent.

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L. Chkhartishvili and T. Berberashvili, "Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation," Journal of Electromagnetic Analysis and Applications, Vol. 2 No. 4, 2010, pp. 205-243. doi: 10.4236/jemaa.2010.24029.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] L. S. Chkhartishvili, “Selection of Equilibrium Configu- rations for Crystalline and Molecular Structures Based on Quasi-Classical Inter-Atomic Potential,” Transactions of the Global Transaction Unit, Vol. 3(427), 1999, pp. 13-19.
[2] L. Chkhartishvili, D. Lezhava, O. Tsagareishvili and D. Gulua, “Ground State Parameters of B2, BC, BN and BO Diatomic Molecules,” Transactions of the AMIAG, Vol. 1, 2004, pp. 295-300.
[3] L. Chkhartishvili, D. Lezhava and O. Tsagareishvili, “Quasi-Classical Determination of Electronic Energies and Vibration Frequencies in Boron Compounds,” Journal of Solid State Chemistry, Vol. 154, 2000, pp. 148-152.
[4] L. Chkhartishvili and D. Lezhava, “Zero-Point Vibration Effect on Crystal Binding Energy: Quasi-Classical Calculation for Laminated Boron Nitride,” Transactions of the Global Transaction Unit, Vol. 6(439), 2001, pp. 87-90.
[5] L. Chkhartishvili, “Ground State Parameters of Wurtzite Boron Nitride: Quasi-Classical Estimations,” Proceedings of the 1st International Boron Symposium, 2002, pp. 139-143.
[6] L. Chkhartishvili, “Quasi-Classical Approach: Electronic Structure of Cubic Boron Nitride Crystals,” Journal of Solid State Chemistry, Vol. 177, 2004, pp. 395-399.
[7] L. S. Chkhartishvili, “Quasi-Classical Estimates of the Lattice Constant and Band Gap of a Crystal: Two-Dimensional Boron Nitride,” Physics of the Solid State, Vol. 46, 2004, pp. 2126-2133.
[8] L. Chkhartishvili, Quasi-Classical Analysis of Boron-Nitride Binding,” Proceedings of the 2nd International Boron Symposium, 2004, pp. 165-171.
[9] L. Chkhartishvili, “Quasi-Classical Analysis of Electron Bandwidths in Wurtzite-Like Boron Nitride,” Transactions of the IChTU, Vol. 1, 2005, pp. 296-314.
[10] L. S. Chkhartishvili, “Analytical Optimization of the Lattice Parameter Using the Binding Energy Calculated in the Quasi-Classical Approximation,” Physics of the Solid State, Vol. 48, 2006, pp. 846-853.
[11] L. Chkhartishvili, “Density of Electron States in Wurtzite-Like Boron Nitride: A Quasi-Classical Calculation,” Materials Science: An Indian Journal, Vol. 2, 2006, pp. 18-23.
[12] L. Chkhartishvili, “Zero-Point Vibration Energy within Quasi-Classical Approximation: Boron Nitrides,” Proceedings of the Javakhishvili TSU (Physics), Vol. 40, 2006, pp. 130-138.
[13] L. S. Chkhartishvili, “Equilibrium Geometry of the Boron Nitride Ultra-Small-Radius Nanotubes,” Material Science of Nanostructures, Vol. 1, 2009, pp. 33-44.
[14] L. Chkhartishvili, “Boron Nitride Nanosystems of Regular Geometry,” Journal of Physics: Conference Series, Vol. 176, 2009, p. 17.
[15] L. Chkhartishvili, “Equilibrium Geometries of the Boron Nitride Layered Systems,” Proceedings of the 4th International Boron Symposium, 2009, pp. 161-170.
[16] L. Chkhartishvili, “Boron Nitride Nanosystems,” In L. Chkhartishvili (Ed.), Boron Based Solids, Research Signpost, Trivandrum, 2010, in Press.
[17] L. Chkhartishvili, On Quasi-Classical Estimations of Boron Nanotubes Ground-State Parameters,” Journal of Physics: Conference Series, Vol. 176, 2009, p. 9.
[18] L. Chkhartishvili, “Molar Binding Energy of the Boron Nanosystems,” Proceedings of the 4th International Boron Symposium, 2009, pp. 153-160.
[19] L. Chkhartishvili, Nanotubular Boron: Ground-State Estimates,” Georgian International Journal of Science and Technology, 2010, in Press.
[20] L. S. Chkhartishvili, D. L. Gabunia and O. A. Tsagareishvili, “Estimation of the Isotopic Effect on the Melting Parameters of Boron,” Inorganic Materials, Vol. 43, 2007, pp. 594-596.
[21] L. S. Chkhartishvili, D. L. Gabunia and O. A. Tsagareishvili, “Effect of the Isotopic Composition on the Lattice Parameter of Boron,” Powder Metallurgy & Metal Ceramics, Vol. 47, 2008, 616-621.
[22] D. Gabunia, O. Tsagareishvili, L. Chkhartishvili and L. Gabunia, “Isotopic Composition Dependences of Lattice Constant and Thermal Expansion of  Rhombohedral Boron,” Journal of Physics: Conference Series, Vol. 176, 2009.
[23] L. Chkhartishvili, “Isotopic Effects of Boron,” Trends in Inorganic Chemistry, 2010, in Press.
[24] N. Bohr, “On the Constitution of Atoms and Molecules,” Philosophical Magazine, Vol. 26, 1913, pp. 1-25.
[25] K. G. Kay, “Exact Wave Functions for Coulomb Problem from Classical Orbits,” Physical Review Letters, Vol. 83, 1999, pp. 5190-5193.
[26] S. I. Nikitin and V. N. Ostrovskij “Problem of the Vibration-Rotation States in Two-Electron Atom,” In V. N. Ostrovskij (Ed.), Perturbation Theory in Atomic Calculations, Nauka, Moscow, 1985, pp. 146-165.
[27] B. Baghchi and P. Holody, “An Interesting Application of Bohr Theory,” American Journal of Physics, Vol. 56, 1988, pp. 746-747.
[28] T. Yamamoto and K. Kaneko, “Exploring a Classical Model of the Helium Atom,” Progress in Theoretical Physics, Vol. 100, 1998, pp. 1089-1100.
[29] G. Tanner, K. Richter and J.-M. Rost, “The Theory of Two-Electron Atoms: Between Ground State and Complete Fragmentation,” Reviews of Modern Physics, Vol. 72, 2000, pp. 497-544.
[30] K. M. Magomedov and P. M. Omarova, “Quasi-Classical Calculation of Electronic Systems,” Dagestan Academy of Sciences Press, Makhachkala, 1989.
[31] M. Casas, A. Plastino and A. Puente, “Alternative Approach to the Semiclassical Description of N Fermions Systems,” Physical Review A, Vol. 49, 1994, pp. 2312- 2317.
[32] D. Vrinceanu and M. R. Flannery, “Classical Atomic form Factor,” Physical Review Letters, Vol. 82, 1999, pp. 3412-3415.
[33] A. Jaroń, J. Z. Kamiński and F. Ehlotzky, “Bohr’s Correspondence Principle and X Ray Generation by Laser- Stimulated Electron–Ion Recombination,” Physical Review A, Vol. 63, 2001, p. 4.
[34] M. I. Petrashen, “On Semiclassical Method of Solving of the Wave Equation,” Proceedings of the Leningrad State University (Series of Physical Sciences), Vol. 7, 1949, pp. 59-78.
[35] R. Gaspar, I. I. Glembotskij, I. Y. Petkyavichyus and A. P. Yutsis, “Quantum Numbers and Universal Potential,” In A. P. Yutsis (Ed.), Theory of Atoms and Atomic Spectra, I., Latvian State University, Riga, 1974, pp. 54-58.
[36] B. Rohwedder and B.-G. Englert, “Semiclassical Quantization in Momentum Space,” Physical Review A, Vol. 49, 1994, pp. 2340-2346.
[37] M. G. Veselov and L. N. Labzovskij, “Atomic Theory, Electron Shell Structure,” Nauka, Moscow, 1986.
[38] R. Sakenshaft and L. Spruch, “Semiclassical Evaluation of Sums of Squares of Hydrogenic Bound-State Wave Functions,” Journal of Physics B, Vol. 18, 1985, pp. 1919-1925.
[39] J. Tao and G. Li, “Approximate Bound to the Average Electron Momentum Density for Atomic Systems,” Physica Scripta, Vol. 58, 1998, pp. 193-195.
[40] K. M. Magomedov, “On Quasi-Classical Self-Consistent Atomic Field,” Proceedings of the USSR Academy of Sciences, Vol. 285, 1985, pp. 1110-1115.
[41] A.-N. Popa, “Accurate Bohr-Type Semiclassical Model for Atomic and Molecular Systems,” Reports of the Institute of Atomic Physics, Vol. E12, 1991, pp. 1-90.
[42] J. N. L. Connor, “Semiclassical Theory of Elastic Scattering,” In M. S. Child (Ed.), Semiclassical Methods in Molecular Scattering and Spectroscopy, Reidel Publishing, Dordrecht–Boston–London, 1979, pp. 45-107.
[43] R. J. le Roy, “Applications of Bohr Quantization in Diatomic Molecular Spectroscopy,” In M. S. Child (Ed.), Semiclassical Methods in Molecular Scattering and Spectroscopy, Reidel Publishing, Dordrecht–Boston– London, 1979, pp. 109-126.
[44] H. Kuratsuji, “Semiclassical Asymptotics for Fermions Systems Based on the Coherent-State Path Integral,” Physics Letters A, Vol. 108, 1985, pp. 139-143.
[45] J.-T. Kim, “Semiclassical Wentzel-Kramers-Brillouin (WKB) Method for Generating the Potential Energy Curve and the Therm Energies of Diatomic K2 Molecule,” The Journal of the Korean Physical Society, Vol. 35, 1999, pp. 168-170.
[46] A. G. Magner, S. N. Fedotkin, F. A. Ivanyuk, P. Meier and M. Brack, “Shells and Periodic Orbits in Fermions Systems,” Czechoslovak Journal of Physics, Vol. 48, 1998, pp. 845-852.
[47] J. Marañon, “Path Integral’s Semiclassical Quantification,” Quantum Chemistry, Vol. 52, 1994, pp. 609-616.
[48] K. Sohlberg, R. E. Tuzun, B. G. Sumpter and D. W. Noid, Full Three-Body Primitive Semiclassical Treatment of H2 + ,” Physical Review A, Vol. 57, 1998, pp. 906-913.
[49] F. Remacle and R. D. Levine, “On the Classic Limit for Electronic Structure and Dynamics in the Orbital Approximation,” Journal of Chemical Physics, Vol. 113, 2000, pp. 4515-4523.
[50] W. A. Fedak and J. J. Prentis, “Quantum Jumps and Classical Harmonics,” American Journal of Physics, Vol. 70, 2002, pp. 332-344.
[51] A. G. Chirkov and I. V. Kazanets, “Classical Physics and Electron Spin,” Technical Physics, Vol. 45, 2000, pp. 1110-1114.
[52] M. Madhusoodanan and K. G. Kay, “Globally Uniform Semiclassical Wave-Function for Multidimensional Systems,” Journal of Chemical Physics, Vol. 109, 1998, pp. 2644-2655.
[53] G. V. Shpatakovskaya, “Quasi-Classical Description of Electronic Super-Shells in Simple Metal Clusters,” JETP Letters, Vol. 70, 1999, pp. 334-339.
[54] G. V. Shpatakovskaya, “Quasi-Classical Analysis of the Spectra of Two Groups of Central Potentials,” JETP Letters, Vol. 73, 2001, pp. 268-270.
[55] M. Brack, “The Physics of Simple Metal Clusters: Self- Consistent Jellium Model and Semiclassical Approach- es,” Reviews of Modern Physics, Vol. 65-I, 1993, pp. 677-732.
[56] V. P. Maslov, “Perturbation Theory and Asymptotic Methods,” Moscow University Press, Moscow, 1965.
[57] L. Chkhartishvili, “Quasi-Classical Theory of Substance Ground State,” Technical University Press, Tbilisi, 2004.
[58] C. Froese–Fischer, “The Hartree–Fock Method for Atoms, A numerical approach,” Wiley, New York, 1977.

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