Multichannel Effective Range Theory Analysis of Zeros in the Positronium formation Scattering Amplitude for Positron-Hydrogen Collisions

Recently, using the Kohn and inverse Kohn variational methods we found two zeros in the Ps-formation scattering amplitude for positron-hydrogen scattering in the Ore gap and we determined their positions accurately [1]. Two separate circular rings of zeros are present in the corresponding differential cross section due to azithumal symmetry. We are currently analyzing the zeros in the Ps-formation scattering amplitude using a multichannel effective range theory (MERT) that includes the polarization potential in the second channel [2], which in our case is the Ps-p channel. This MERT has previously been applied to positron-hydrogen collisions [3] for partial waves $L \le 2$ and shown to provide for the Ore gap reasonable results for the partial wave cross sections for Ps-formation and for Ps-p scattering. [1] A.~W.~Alrowaily, S.~J.~Ward, P.~Van Reeth, {\it submitted}. [2] S.~Watanabe and C.~H.~Greene, Phys.~Rev.~A {\bf 22}, 158 (1980). [3] S.~J.~Ward and J.~H.~Macek, Phys.~Rev. A {\bf 62}, 052715 (2000).