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2012 | 122 | 1 | 42-48
Article title

Atomic Properties of the Two-Electron System using Variational Monte Carlo Technique

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EN
Abstracts
EN
Using variational Monte Carlo method we calculated the lowest order relativistic corrections for the ground state energies of the helium-like atoms, up to Z = 10, and also for some excited state energies of the helium atom. These relativistic corrections include: mass-velocity effect, orbit-orbit interaction, spin magnetic and dipole moments of the two electrons and the Darwin effect. Moreover, correction due to the nucleus motion has been also calculated. Our results were obtained by using two new types of compact and accurate trial wave functions for the helium ions. For excited states we used simple trial wave functions of good quality and accurate results. The obtained results are in good agreement with the most recent previous accurate values and also with the exact values.
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Contributors
author
  • Mathematics Department, Faculty of Science, Alexandria University, Alexandria, Egypt
author
  • Mathematics Department, Faculty of Science, Menofia University, Shebin El-Kom, Egypt
References
  • 1. S.A. Alexander, R.L. Coldwell, Int. J. Quantum Chem. 63, 1001 (1997)
  • 2. J.S. Sims, S.A. Hagstrom, Int. J. Quant. Chem. 90, 1600 (2002)
  • 3. K V. Rodriguez, G. Gasaneo, J. Phys. B, At. Mol. Opt. Phys. 38, 259 (2005)
  • 4. Y.X. Liu, X.H. Zhang, Y.S. Duan, Mod. Phys. Lett. A 23, 1853 (2008)
  • 5. H. Nakashima, H. Nakatsuji, J. Chem. Phys. 128, 154107 (2008)
  • 6. C. Amovilli, N.H. March, I.A. Howard, Á. Nagy, Phys. Lett. A 372, 4053 (2008)
  • 7. J.S. Sims, S.A. Hagstrom, Int. J. Quant. Chem. 90, 1600 (2002)
  • 8. V.A. Yerokhin, K. Pachucki, Phys. Rev. A 81, 022507 (2010)
  • 9. K. Pachucki, J. Phys. B 31, 3547 (1998)
  • 10. G.W.F. Drake, S.P. Goldman, Can. J. Phys. 77, 835 (1999)
  • 11. G.W.F. Drake, Can. J. Phys. 80, 1195 (2002)
  • 12. K. Pachucki, J. Komasa, Phys. Rev. A 68, 042507 (2003)
  • 13. M. Stanke, D. Kedziera, S. Bubin, L. Adamowicz, J. Chem. Phys. 127, 134107 (2007)
  • 14. M. Stanke, J. Komasa, D. Kedziera, S. Bubin, L. Adamowicz, Phys. Rev. A 78, 052507 (2008)
  • 15. C.L. Pekeris, Phys. Rev. 112, 1649 (1958)
  • 16. S.D. Kenny, G. Rajagopal, R.J. Needs, Phys. Rev. A 51, 1898 (1995)
  • 17. D. Yi-Shi, L. Yu-Xiao, Z. Li-Jie, Chin. Phys. Lett. 21, 1714 (2004)
  • 18. M. Stanke, D. Kędziera, S. Bubin, L. Adamowicz, J. Chem. Phys. 126, 194312 (2007)
  • 19. S.A. Alexander, S. Datta, R.L. Coldwell, Phys. Rev. A 81, 032519 (2010)
  • 20. V. Korobov, A. Yelkhovsky, Phys. Rev. Lett. 87, 193003 (2001)
  • 21. K. Pachucki, Phys. Rev. A 74, 022512 (2006)
  • 22. K. Pachucki, Phys. Rev. A 74, 062510 (2006)
  • 23. S.B. Doma, F.N. El-Gammal, Appl. Math. Inf. Sci. 5, 315S (2011)
  • 24. S. Pottorf, A. Puzer, M.Y. Chou, Eur. J. Phys. 20, 205 (1999)
  • 25. R.W. Hamming, Numerical Methods for Scientists and Engineers, 2nd ed., McGraw-Hill, New York 1973
  • 26. A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, New York 1965
  • 27. N. Metropolis, A.W. Rosenbluth, N.M. Rosenbluth, A.M. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953)
  • 28. I.I. Sobel'man, Introduction to the Theory of Atomic Spectra, Pergamon Press Ltd, New York 1972
  • 29. D. Kedziera, M. Stanke, S. Bubin, M. Barysz, L. Adamowicz, J. Chem. Phys. 125, 084303 (2006)
  • 30. M.B. Ruiz, Int. J. Quant. Chem. 101, 246 (2005)
  • 31. D. Bressanini, G. Morosi, J. Phys. B, At. Mol. Opt. Phys. 41, 145001 (2008)
  • 32. K.V. Rodriguez, G. Gasaneo, D.M. Mitnik, J. Phys. B, At. Mol. Opt. Phys. 40, 3923 (2007)
  • 33. L.C. Green, M.M. Mulder, P.C. Milner, Phys. Rev. 91, 35 (1953)
  • 34. S. Chandrasekhar, D. Elbert, G. Herzberg, Phys. Rev. 91, 1172 (1953)
  • 35. S. Chandrasekhar, G. Herzberg, Phys. Rev. 98, 1050 (1955)
  • 36. B.H. Bransden, C.J. Joachain, Physics of Atoms and Molecules, Longman Scientific and Technical, London 2003
  • 37. T.A. Galek, N.C. Handy, A.J. Cohen, G.K. Chan, Chem. Phys. Lett. 404, 156 (2005)
  • 38. J. Christophe Pain, M.Sc. Thesis, Ecole Normale Supérieure, Lyon, France, and Indian Institute of Technology, Bombay, India 1997
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YADDA identifier
bwmeta1.element.bwnjournal-article-appv122n1p10kz
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