  A long-standing problem with the solution of the Schr\"odinger equation has
been its inability to account for the electron-positron annihilation in
positron hydrogen scattering above the positronium formation threshold. This
letter shows that this problem has been resolved by the use of the modified
Faddeev equations. A number of $e^- e^+$ annihilation cross sections in the
energy gap between $Ps(1s)$ and $H(n=2)$ thresholds are reported for both the
positron plus hydrogen incoming channel as well as the proton plus positronium
incoming channel. However the indirect annihilation cross sections after
formation of the positronium themselves are well known, they will not be
included in this report.
