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

We present a new ab initio theoretical formulation to calculate 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.Received: 15 January 2004, Published online: 15 April 2004PACS: 03.65.Nk Scattering theory - 34.85. + x Positron scattering - 71.60. + z Positron states - 78.70.Bj Positron annihilation