Extracting the Phase of Scattering Amplitudes by Means of the Glauber Formula

We present a method for extracting information on the phases of $\pi p$ and $\pi n$ scattering amplitudes by comparing data on $\pi d$ scattering with the prediction of the Glauber formula. The essential feature of the analysis is our ability to write down the phase of the double-scattering term in terms of the phases, and their first derivatives, of the free $\pi$-nucleon amplitudes. The method is equally applicable to other beam particles ($K,p,\cdots$) scattering off deuterons. A correction to the standard interpretation of the Glauber formula as applied to total cross-section defects is also given.