  The idea of a thermalized non-equilibrated state of matter offers a
conceptually new understanding of the strong angular asymmetry. In this compact
review we present some clarifications, corrections and further developments of
the approach, and provide a brief account of results previously discussed but
not reported in the literature. The cross symmetry compound nucleus $S$-matrix
correlations are obtained (i) starting from the unitary $S$-matrix
representation, (ii) by explicitly taking into account a process of energy
equilibration, and (iii) without taking the thermodynamic limit of an infinite
number of particles in the thermalized system. It is conjectured that the long
phase memory is due to the exponentially small total spin off-diagonal
resonance intensity correlations. This manifestly implies that the strong
angular asymmetry intimately relates to extremely small deviations of the
eigenfunction distribution from Gaussian law. The spin diagonal resonance
intensity correlations determine a new time/energy scale for a validity of
random matrix theory. Its definition does not involve overlaps of the many-body
interacting configurations with shell model non-interacting states and thus is
conceptually different from the physical meaning (inverse energy relaxation
time) of the spreading widths introduced by Wigner. Exact Gaussian distribution
of the resonance wave functions corresponds to the instantaneous phase
relaxation. We invite the nuclear reaction community for the competition to
describe, as the first challenge, the strong forward peaking in the typically
evaporation part of the proton spectra. This is necessary to initiate revealing
long-term misconduct in the heavily cross-disciplinary field, also important
for nuclear industry applications.
