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A new ab initio method of calculating \(\mathsf{Z_{eff}}\) and positron annihilation rates using coupled-channel T-matrix amplitudes

  • P. K. BiswasEmail author
Article

Abstract.

We present a new ab initio theoretical formulation to calculate \(Z_{\it eff}\) and hence the positron annihilation rates directly from the onshell and offshell (half) scattering amplitudes. The method does not require any explicit use of the scattering wave function and is formally exact within the framework of the well established Lippmann-Schwinger equation. It could serve as an effective tool as all the T-, K-, and S-matrix formulations, yield directly the scattering amplitudes; not the wave function. Numerical test of the method is presented considering sample static calculations in positron-hydrogen and positron-helium systems.

Keywords

Wave Function Static Calculation Numerical Test Theoretical Formulation Positron Annihilation 
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References

  1. 1.
    Proceedings of the Low Energy Positron and Positronium Physics, 2001, Santa Fé, USA, Nucl. Inst. Meth. B 192 (2002); see in particular, J.P. Sullivan et al. , ibid., 3; P.G. Coleman et al. , ibid., 83; A.P. Mills Jr, ibid. 107Google Scholar
  2. 2.
    D.W. Gidley, W.E. Fireze, T.L. Dull, J. Sun, A.F. Yee, C.V. Nguyen, D.Y. Yoon, Appl. Phys. Lett. 77, 1282 (2000)CrossRefGoogle Scholar
  3. 3.
    M.P. Petkov, M.H. Weber, K.G. Lynn, K.P. Rodbell, Appl. Phys. Lett. 77, 2470 (2000)CrossRefGoogle Scholar
  4. 4.
    J.W. Humberston, J.B.G. Wallace, J. Phys. B 5, 1138 (1972)CrossRefGoogle Scholar
  5. 5.
    E.P. da Silva, J.S.E. Germano, M.A.P. Lima, Phys. Rev. A 49, R1527 (1994)Google Scholar
  6. 6.
    E.P. da Silva, J.S.E. Germano, M.A.P. Lima, Phys. Rev. Lett. 77, 1028 (1996)CrossRefGoogle Scholar
  7. 7.
    G.G. Ryzhikh, J. Mitroy, J. Phys. B: 33, 2229 (2000)CrossRefGoogle Scholar
  8. 8.
    G.F. Gribakin, Phys. Rev. A 61, 022720 (2000)CrossRefGoogle Scholar
  9. 9.
    A.S. Ghosh, N.C. Sil, P. Mandal, Phys. Rep. 87, 313 (1982)CrossRefGoogle Scholar
  10. 10.
    W. Glockle, The Quantum Mechanical Few-Body Problem (Springer-Verlag, Berlin, Heidelberg, 1983), p. 93Google Scholar
  11. 11.
    A.S. Ghosh, D. Basu, Ind. J. Phys. 47, 765 (1973)Google Scholar
  12. 12.
    Corrected results on reference [5] has kindly been communicated by M. Varella, M.A.P. Lima (private communication)Google Scholar
  13. 13.
    E. Clementi, C. Roetti, At. Data. Nucl. Data Tables 14, 177 (1974)Google Scholar
  14. 14.
    J. Chaudhuri, A.S. Ghosh, N.C. Sil, Phys. Rev. A 10, 2257 (1974)CrossRefGoogle Scholar
  15. 15.
    A.A. Kernoghan, M.T. McAlinden, H.R.J. Walters, J. Phys. B 27, L543 (1994)Google Scholar
  16. 16.
    This form can be obtained by recasting the three-body (electron-positron-proton) Fadeev equations into Lippmann-Schwinger form and eliminating the unphysical positron-proton bound channel (see p. 93 and p. 97 of Ref. [10])Google Scholar
  17. 17.
    References [46-75] of the article “Overview of the Present Theoretical Status of Positron-Atom Collisions”, edited by H.R.J. Walters et al. , in the AIP Conference Proceedings 360 on the XIX International Conference on The Physics of Electronic and Atomic Collisions, 1995Google Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Departamento de FísicaInstituto Tecnológico de AeronáuticaCTA São José dos CamposSP, Brasil
  2. 2.Divisão de Engenharia Biomédica, Instituto de Pesquisa e DesenvolvimentoUniversidade do Vale do ParaibaSão José dos CamposSP, Brasil

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