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Table 2. Scattering parameter comparisons

Low-energy S-wave Positronium-Hydrogen collisions Denton Woods  , S. J. Ward  and P. Van Reeth †  University of North Texas, † University College London. ρ. Introduction

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Table 2. Scattering parameter comparisons

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  1. Low-energy S-wave Positronium-Hydrogen collisionsDenton Woods, S. J. Ward and P. Van Reeth†University of North Texas, † University College London ρ Introduction Positronium-Hydrogen (Ps-H) elastic scattering is of interest since it is a fundamental four-body Coulomb process. We have computed 1S and 3S phase shifts for low-energy elastic Ps-H scattering. We used the Kohn variational method and a number of variants on the method, namely, the inverse Kohn, generalized Kohn and the complex Kohn. We use atomic units throughout, unless stated otherwise. Kohn Variational Method The generalized Kohn functional is [9] , where τ is an adjustable parameter (0−). Special cases of τ are τ = 0 for the Kohn and τ = π/2 for the inverse Kohn. The stationary property of this functional yields the phase shifts. The complex Kohn functional for the T-matrix is . The agreement between the phase shifts for multiple values of τ is taken as a measure of the accuracy of the results and of the absence of linear dependence. Furthermore, we have implemented the procedure of Todd [7], which allows us to remove in a systematic manner specific short-range terms in the wavefunction which are responsible for linear dependence. Trial Wavefunction The short-range terms are of a Hylleraas type, where ,and ki, li, mi, ni, pi, and qiare non-negative integers. Table 2. Scattering parameter comparisons Conclusion Our phase shifts and resonance parameters compare well with previous Kohn calculations [2,3] and coupled-state (CS) approximations [4,5]. We have started to consider P-wave Ps-H scattering. Results r12 e− e+ Acknowledgements The authors acknowledge the UNT Computing and Information Technology Center's High Performance Computing Initiative for providing resources on the Talon HPC cluster. S.J.W. acknowledges support from NSF under grant no. PHYS-968638. r2 r23 r1 r13 Table 1. Phase shift comparisons as a function of κ e− p r3 References [1] Zong-Chao Yan and Y. K. Ho, Phys. Rev. A 59, 2697 (1999). [2] P. Van Reethand J. W. Humberston, J. Phys. B 36 (2003) 1923-1932. [3] P. Van Reeth and J. W. Humberston, Nucl. Instr. and Meth. in Phys. Res. B 221 (2004) 140-143. [4] Blackwood, McAlinden and Walters, Phys. Rev. A 65 032517 (2002). [5] H.R.J. Walters et al, Nucl. Instr. and Meth. in Phys. Res. B 221 (2003) 149-159. [6] A. Todd, Ph.D. thesis, The University of Nottingham, (2007), unpublished. [7] J. N. Cooper et al, J. Phys. A. 43 (2010) 175302. Figure 1. Coordinate System • Figure 2. Phase shifts for 1S and 3S Ps-H scattering (ω = 7)

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