Two-Centre Close-Coupling method in charge transfer

Bagheri, Reza; Shojaei, Farideh

doi:10.18869/acadpub.ijpr.17.3.345

Two-Centre Close-Coupling method in charge transfer

Authors

Reza Bagheri

Farideh Shojaei

https://doi.org/10.18869/acadpub.ijpr.17.3.345

Abstract

In the present work, the transition matrix elements as well as differential and total scattering cross-sections for positronium formation in Positron-Hydrogen atom collision and hydrogen formation in Positronium-Hydrogen ion collision, through the charge transfer channel by Two-Centre Close-Coupling method up to a first order approximation have been calculated. The charge transfer collision is assumed to be a three-body reaction, while the projectile is a plane wave. Additionally, the hydrogen and positronium atoms are assumed, initially, to be in their ground states. For the case of charge transfer in the scattering of positron by hydrogen atoms, the differential cross sections are plotted for the energy range of 50eV to 10keV, where the Thomas peak is clearly observable. Finally, the total scattering cross-section for the charge transfer in the collision of Positron-Hydrogen and Positronium-Hydrogen ion are plotted as a function of projectile energies and compared with other methods in the literature.

Keywords

Two-Centre Close-Coupling

electron Capture

Thomas Peaks

transition matrix

Scattering Cross-Sections

[1] J. Chadwick, “The existence of a neutron”, Proc. Roy. soc. A 136, (1932) 692.
[2] C. J. Joachain, “Quantum collision theory”, North-Holland Publishing Company Amsterdam, (1975).
[3] L. H. Thomas: Proc. Soc. A 114, (1927), 561.
[4] N. R. Hewitt, C. J. Noble and B. H. Bransden, J. Phys. B 23, (1990), 4185.
[5] H. R. J. Walters, A. A. Kernoghan, M. T. McAlinden, and C. P. Campbell,“in Photon and Electron Collisions with Atoms and Molecules”, edited by P. G. Burke and C. J. Joachain (Plenum Press, New York, 1997), pp. 313–345.
[6] K. Higgins and P. G. Burke, J. Phys. B 24, (1991), L343.
[7] A. S. Kadyrov and I. Bray, “Two-center convergent close-coupling approach to positron-hydrogen collisions”, Phys. Rev. A 66, (2002) 012710.
[8] I. Bray, “Convergent close-coupling method for the calculation of electron scattering on hydrogenlike targets”, Phys. Rev. A 49, (1994c) 1066.
[9] I. Bray and A. T. Selbovics, “Calculation of electron scattering on hydrogenic targets”, Advances in At. Mol. Opt. Phys. VOL . 35 (1995).
[10] I. Bray and A. T. Stelbovics,” The convergent close-coupling method for a Coulomb three-body problem”, Computer Physics Communications 85 (1995), 1.
[11] K. Ratnavelu, J. Mitroy and A. T. Stelbovics,” Positron–hydrogen and positronium–proton scattering at intermediate and high energies”, J. Phys. B: At. Mol. Opt. Phys. 29 (1996) 2775.
[12] W. Sperber, “PhD Thesis”, University Bielefeld, Germany (1993).
[13] W. Sperber, D. Becke, K. G. Lynn, W. Raith, A. Schweb, A. Sinapius, G.Spicher and M. Weber, “Measurement of positronium formation in positron collisions with hydrogen atoms”, Phys. Rev. Lett. 68 (1992) 3690.
[14] S. J. Ward and J. H. Macek, “Positronium formation by electronic capture from hydrogenic ions”, Hyperfine Interactions. 89, (1994) 477.
[15] F. Shojaei, “PhD Thesis” Shahid Bahonar University, Kerman (2008).
[16] J. H. McGuier, N. C. Sil and N. C. Deb, “Capture of atomic electrons by high-velocity positrons”, Phys. Rev. A 34, (1986) 685.
[17] A. Igarashi and N. Toshima, “Second-order Born cross sections for positronium formation in positron-hydrogen collisions”, Phys. Rev. A 47 (1993) 2386.