  The ideas that extreme states of nuclear matter arise in events with total
dis- integration of nuclei (TDN) and as these states arise, the properties of
events qualitatively change with the number of protons emitted from the nucleus
Q,star- ting from its certain boundary numbe Q*,are used in this paper for the
experi- mentally search for extreme states of nuclear matter. For realization
of these ideas, the invariant inclusive spectra of protons and pi minus mesons
as a func- tion of their kinetic energies T in the lab. system for 4HeC and
12CC interacti- ons at the momentum 4.2 A GeV/c with different values of Q are
used. The spect- ra are fitted by the exponential expressions and the
Q-dependencies of the in- verses of slopes Ti are studied. It is found that
these spectra have two compo- nents and contain the regime change points .In
the TDN region the values of Ti for pi minus mesons begin to increase with
increasing the number of protons. We consider this increasing to be a signal
from the extreme states of nuclear mat- ter. The value of the "temperature" of
these states is about 0.140 GeV.
