Positron Annihilation in Perfect and Defective TiO2 Rutile Crystal with Single Particle Wave Function: Slater Type Orbital and Modified Jastrow Functions
Affiliation(s)
Faculty of Physics and Engineering Physics, University of Science, Ho Chi Minh City, Vietnam. Swinburne University of Technology, Melbourne, Australia.
Faculty of Physics and Engineering Physics, University of Science, Ho Chi Minh City, Vietnam. Swinburne University of Technology, Melbourne, Australia.
ABSTRACT
Positron annihilation in TiO2 rutile crystal is studied by an assumption that a positron binds with valance electrons of a titanium dioxide to form a pseudo TiO2-positron molecule before it annihilates with these electrons. The orbital modification consisting of explicit electron-positron and electron-electron correlation in each electronic orbital is used for the electrons and positron wave functions. By these wave functions, the calculation results of the positron lifetimes in unmitigated and defective TiO2 crystals are about 170 ps, 266 ps and 243 ps, respectively. These results are in good agreement with experimental data of the positron lifetimes in vacancies of TiO2 from 180 ps to 300 ps.
Cite this paper
T. Lang, C. Tao, K. Dung and L. Chien, "Positron Annihilation in Perfect and Defective TiO2 Rutile Crystal with Single Particle Wave Function: Slater Type Orbital and Modified Jastrow Functions," World Journal of Nuclear Science and Technology, Vol. 4 No. 1, 2014, pp. 33-39. doi: 10.4236/wjnst.2014.41006.
T. Lang, C. Tao, K. Dung and L. Chien, "Positron Annihilation in Perfect and Defective TiO2 Rutile Crystal with Single Particle Wave Function: Slater Type Orbital and Modified Jastrow Functions," World Journal of Nuclear Science and Technology, Vol. 4 No. 1, 2014, pp. 33-39. doi: 10.4236/wjnst.2014.41006.
References
[1] F. Jensen, “Introduction to Computational Chemistry,” John Wiley and Sons Ltd, Chichester, 2007. [2] E. Boronski and R. M. Nieminen, “Electron-Positron Density-Functional Theory,” Physical Review B, Vol. 34, No. 6, 1985, pp. 3820-3831.
http://dx.doi.org/10.1103/PhysRevB.34.3820 [3] H. Yukawa, “On the Interaction of Elementary Particles,” Progress of Theoretical Physics Supplement, Vol. 1, 1955, pp. 24-45. http://dx.doi.org/10.1143/PTPS.1.24 [4] W. Kohn and L. J. Sham, “Self-Consistent Equations Including Exchange and Correlation Effects,” Physical Review Journal, Vol. 140, No. 4A, 1965, pp. A1133-A1138.
http://link.aps.org/doi/10.1103/PhysRev.140.A1133 [5] S. Daiuk, M. Sob and A. Rubaszek, “Theoretical calculations of positron annihilation with rare gas core electrons in simple and transition metals,” Journal of Physics F: Metal Physics B, Vol. 43, No. 4, 1991, pp. 2580-2593.
http://link.aps.org/doi/10.1103/PhysRevB.43.2580 [6] M. J. Puska and R. M. Nieminen, “Defect Spectroscopy with Positron: A General Calculation Method,” Journal of Physics F: Metal Physics, 1983, pp. 333-346.
http://dx.doi.org/10.1088/0305-4608/13/2/009 [7] A. Gil, J. Segura and N. Temme, “Numerical Methods for Special Functions,” Society for Industrial Mathematics, 3600 University Science Center, Philadelphia., 2007. [8] N. W. Ashcroft and N. D. Mermin, “Solid State Physics,” Thomson Learning, Inc., 1976. [9] V. Magnasco, “Methods of Molecular Quantum Mechanics,” John Wiley and Sons Ltd, Hoboken, 2009.
http://dx.doi.org/10.1002/9780470684559 [10] G. F. Gribakin and C. M. R. Lee, “Application of the zero-range potential model to positron annihilation on molecules,” Nuclear Instruments and Methods in Physics Research B, Vol. 247, No. 1, 2006, pp. 31-37.
http://dx.doi.org/10.1016/j.nimb.2006.01.035m [11] E. M. Hassan, B. A. A. Balboul and M. A. Abdel-Rahman, “Probing the Phase Transition in Nanocrystalline TiO2 Powders by Positron Lifetime (PAL) Technique,” Defect and Diffusion Forum, Vol. 319-320, 2011, pp 151-159.
[1] F. Jensen, “Introduction to Computational Chemistry,” John Wiley and Sons Ltd, Chichester, 2007. [2] E. Boronski and R. M. Nieminen, “Electron-Positron Density-Functional Theory,” Physical Review B, Vol. 34, No. 6, 1985, pp. 3820-3831.
http://dx.doi.org/10.1103/PhysRevB.34.3820 [3] H. Yukawa, “On the Interaction of Elementary Particles,” Progress of Theoretical Physics Supplement, Vol. 1, 1955, pp. 24-45. http://dx.doi.org/10.1143/PTPS.1.24 [4] W. Kohn and L. J. Sham, “Self-Consistent Equations Including Exchange and Correlation Effects,” Physical Review Journal, Vol. 140, No. 4A, 1965, pp. A1133-A1138.
http://link.aps.org/doi/10.1103/PhysRev.140.A1133 [5] S. Daiuk, M. Sob and A. Rubaszek, “Theoretical calculations of positron annihilation with rare gas core electrons in simple and transition metals,” Journal of Physics F: Metal Physics B, Vol. 43, No. 4, 1991, pp. 2580-2593.
http://link.aps.org/doi/10.1103/PhysRevB.43.2580 [6] M. J. Puska and R. M. Nieminen, “Defect Spectroscopy with Positron: A General Calculation Method,” Journal of Physics F: Metal Physics, 1983, pp. 333-346.
http://dx.doi.org/10.1088/0305-4608/13/2/009 [7] A. Gil, J. Segura and N. Temme, “Numerical Methods for Special Functions,” Society for Industrial Mathematics, 3600 University Science Center, Philadelphia., 2007. [8] N. W. Ashcroft and N. D. Mermin, “Solid State Physics,” Thomson Learning, Inc., 1976. [9] V. Magnasco, “Methods of Molecular Quantum Mechanics,” John Wiley and Sons Ltd, Hoboken, 2009.
http://dx.doi.org/10.1002/9780470684559 [10] G. F. Gribakin and C. M. R. Lee, “Application of the zero-range potential model to positron annihilation on molecules,” Nuclear Instruments and Methods in Physics Research B, Vol. 247, No. 1, 2006, pp. 31-37.
http://dx.doi.org/10.1016/j.nimb.2006.01.035m [11] E. M. Hassan, B. A. A. Balboul and M. A. Abdel-Rahman, “Probing the Phase Transition in Nanocrystalline TiO2 Powders by Positron Lifetime (PAL) Technique,” Defect and Diffusion Forum, Vol. 319-320, 2011, pp 151-159.