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 $-t$. We emphasize in addition, possible signals
coming directly from such a new condition of matter, that may be
present in current experiments on inelastic processes.