Alternative Method for Determining the Pion-Nucleon Forward Scattering Amplitude

Since existing experiments fail to confirm the Goldberger form of the pion-nucleon dispersion relations, and no satisfactory theoretical or experimental explanation has been found, it is clearly desirable to increase the precision of this conclusion. It is shown that by extending the measurements of the ${\pi }^{\pm }+p$ differential elastic cross sections down to about 15° c.m., the real parts of the forward scattering amplitudes can be measured directly with precision comparable to that obtained for the cross sections. This method depends on the assumption of charge independence only through explicitly given $\frac{e^2}{\hslash v}$ corrections, and above 100 Mev is less sensitive to these corrections than the method of Puppi and Stanghellini. Comparison between the results obtained by the two methods would give a useful test for the presence of systematic error.