A Search on Two-Electron Atoms

ABSTRACT

Using the basic ingredient of two-body problem, we propose accurate algebraic solutions in a closed form for the ground state of helium and helium-like atoms. These simple but explicit expressions involve exact screening parameters for each system considered and provide an insight into their physical structure. The energy eigenvalues have been exactly calculated for atoms with nuclear charge*Z* in the range 1 ≤ *Z* ≤ 12, clarifying the relation between the screening parameteter and *Z*.

Using the basic ingredient of two-body problem, we propose accurate algebraic solutions in a closed form for the ground state of helium and helium-like atoms. These simple but explicit expressions involve exact screening parameters for each system considered and provide an insight into their physical structure. The energy eigenvalues have been exactly calculated for atoms with nuclear charge

Cite this paper

nullM. Çapak and B. Gönül, "A Search on Two-Electron Atoms,"*Journal of Modern Physics*, Vol. 2 No. 9, 2011, pp. 1051-1055. doi: 10.4236/jmp.2011.29127.

nullM. Çapak and B. Gönül, "A Search on Two-Electron Atoms,"

References

[1] L. D. A. Siebbeles and C. Le Sech, “ A Simple Method to Calculate Potential Curves of Two-Electron Molecules at Intermediate Nuclear Distance,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 27, No. 19, 1994, pp. 4443-4452. doi:10.1088/0953-4075/27/19/007

[2] D. N. Tripathy, B. Padhy and D. K. Rai, “ Two-Parameter Wavefunction for the Ground State of the Helium Isoe-lectronic Sequence,” Journal of Physics B: Atomic, Mo-lecular and Optical Physics, Vol. 28, No. 3, 1995, pp. L41-L46. doi:10.1088/0953-4075/28/3/001

[3] S. Bhattacharyya, A. Bhattacharyya, B. Talukdar and N. C. Deb, “Analytical Approach to the Helium-Atom Ground State Using Correlated Wavefunctions,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 29, No. 5, 1996, pp. L147-L150. doi:10.1088/0953-4075/29/5/003

[4] C. Le Sech, “Accurate Analytic Wavefunctions for Two-Electron Atoms,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 30, No. 2, 1997, pp. L47-L50. doi:10.1088/0953-4075/30/2/003

[5] S. H. Patil, “Electron Correlation in He and Isoelectronic Ions,” European Journal of Physics, Vol. 25, No. 1, 2004, pp. 91-100. doi:10.1088/0143-0807/25/1/012

[6] V. A. Yerokhin and K. Pachucki, “Theoretical Energies of Low-Lying States of Light Helium-Like Ions,” Physical Review A, Vol. 81, No. 2, 2010, Article ID: 022507.

[7] F. Cooper, A. Khare and U. Sukhatme, “Supersymmetric Quantum Mechanics,” Physics Reports, Vol. 251. No. 5, 1995, pp. 267-385. doi:10.1016/0370-1573(94)00080-M

[8] D. E. Freund, B. D. Huxtabler and J. D. Morgan, “Varia-tional Calculations on the Helium Isoelectronic Sequence,” Physical Review A, Vol. 29, No. 2, 1984, pp. 980-982. doi:10.1103/PhysRevA.29.980

[9] J. Thakkar and V. H. Jr. Smith, “Compact and Accurate Integral-Transform Wavefunctions,” Physical Review A, Vol. 15, No. 1, 1977, pp. 1-15. doi:10.1103/PhysRevA.15.1

[10] A. Moumeni, O. Dulieu and C. Le Sech, “Correlated Wavefunctions for Two-Electron Systems Using New Screened Hydrogen-Like Orbitals,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 23, No. 22, 1990, pp. L739-L745. doi:10.1088/0953-4075/23/22/002

[11] K. V. Rodriguez and G. Gasaneo, “Accurate Hylleraas- like Functions for the He Atom for the Correct Cusp Conditions,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 38, No. 16, 2005, pp. L259- L267. doi:10.1088/0953-4075/38/16/L01

[1] L. D. A. Siebbeles and C. Le Sech, “ A Simple Method to Calculate Potential Curves of Two-Electron Molecules at Intermediate Nuclear Distance,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 27, No. 19, 1994, pp. 4443-4452. doi:10.1088/0953-4075/27/19/007

[2] D. N. Tripathy, B. Padhy and D. K. Rai, “ Two-Parameter Wavefunction for the Ground State of the Helium Isoe-lectronic Sequence,” Journal of Physics B: Atomic, Mo-lecular and Optical Physics, Vol. 28, No. 3, 1995, pp. L41-L46. doi:10.1088/0953-4075/28/3/001

[3] S. Bhattacharyya, A. Bhattacharyya, B. Talukdar and N. C. Deb, “Analytical Approach to the Helium-Atom Ground State Using Correlated Wavefunctions,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 29, No. 5, 1996, pp. L147-L150. doi:10.1088/0953-4075/29/5/003

[4] C. Le Sech, “Accurate Analytic Wavefunctions for Two-Electron Atoms,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 30, No. 2, 1997, pp. L47-L50. doi:10.1088/0953-4075/30/2/003

[5] S. H. Patil, “Electron Correlation in He and Isoelectronic Ions,” European Journal of Physics, Vol. 25, No. 1, 2004, pp. 91-100. doi:10.1088/0143-0807/25/1/012

[6] V. A. Yerokhin and K. Pachucki, “Theoretical Energies of Low-Lying States of Light Helium-Like Ions,” Physical Review A, Vol. 81, No. 2, 2010, Article ID: 022507.

[7] F. Cooper, A. Khare and U. Sukhatme, “Supersymmetric Quantum Mechanics,” Physics Reports, Vol. 251. No. 5, 1995, pp. 267-385. doi:10.1016/0370-1573(94)00080-M

[8] D. E. Freund, B. D. Huxtabler and J. D. Morgan, “Varia-tional Calculations on the Helium Isoelectronic Sequence,” Physical Review A, Vol. 29, No. 2, 1984, pp. 980-982. doi:10.1103/PhysRevA.29.980

[9] J. Thakkar and V. H. Jr. Smith, “Compact and Accurate Integral-Transform Wavefunctions,” Physical Review A, Vol. 15, No. 1, 1977, pp. 1-15. doi:10.1103/PhysRevA.15.1

[10] A. Moumeni, O. Dulieu and C. Le Sech, “Correlated Wavefunctions for Two-Electron Systems Using New Screened Hydrogen-Like Orbitals,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 23, No. 22, 1990, pp. L739-L745. doi:10.1088/0953-4075/23/22/002

[11] K. V. Rodriguez and G. Gasaneo, “Accurate Hylleraas- like Functions for the He Atom for the Correct Cusp Conditions,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 38, No. 16, 2005, pp. L259- L267. doi:10.1088/0953-4075/38/16/L01