Differential cross sections for <(p)over bar p> elastic scattering have been measured for very small momentum transfers at six different incident antiproton momenta in the range 3.7 to 6.2 GeV/c by the detection of recoil protons at scattering angles close to 90 degrees. Forward scattering parameters sigma(T), b, and rho have been determined. For the rho-parameter, up to an order of magnitude higher level of precision has been achieved compared to that in earlier experiments. It is found that existing dispersion theory predictions are in disagreement with our results for the rho-parameter.
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