  We demonstrate the existence of an anomalous structure in the data on the
diffractive elastic scattering of hadrons at high energies and small momentum
transfer. We analyze five sets of experimental data on $p(\overline{p})-p $
scattering from five different experiments with colliding beams, ranging from
the first-- and second--generation experiments at $\sqrt{s} = 53 $ GeV to the
most recent experiments at 546 GeV and at 1800 GeV. All of the data sets
exhibit a localized anomalous structure in momentum transfer. We represent the
anomalous behavior by a phenomenological formula. This is based upon the idea
that a transient coherent condition of matter occurs in some of the
intermediate inelastic states which give rise, via unitarity, to diffractive
elastic scattering. The Fourier--Bessel transform into momentum--transfer space
of a spatial oscillatory behavior of matter in the impact--parameter plane
results in a small piece of the diffractive amplitude which exhibits a
localized anomalous behavior near a definite value of $-t $. In addition, we
emphasize possible signals coming directly from such a new condition of matter
that may be present in current experiments on inelastic processes.
