  Here we develop a model equation of state which successfully parameterizes
the thermodynamic functions of hadron resonance gas model at chemical
freeze-out and which allows us to naturally explain the adiabatic chemical
freeze-out criterion. The present model enables us to clearly demonstrate that
at chemical freeze-out the resulting hadronic mass spectrum used in the hadron
resonance gas model is not an exponential-like, but a power-like. We argue that
such a property of hadronic mass spectrum at chemical freeze-out can be
explained by the two new effects found here for wide resonances existing in a
thermal environment: the near threshold thermal resonance enhancement and the
near threshold resonance sharpening. The effect of resonance sharpening is
studied for a sigma meson and our analysis shows that for the temperatures well
below 92 MeV the effective width of sigma meson is about 50 to 70 MeV. Thus,
the effect of resonance sharpening justifies the usage of the sigma-like
field-theoretical models for the strongly interacting matter equation of state
at such temperatures. Also we argue that the most optimistic hope to find the
quark gluon bags experimentally may be related to their sharpening and
enhancement in a thermal medium. In this case the wide quark gluon bags may
appear directly or in decays as narrow resonances that are absent in the tables
of elementary particles and that have the width about 50-150 MeV and the mass
about or above 2.5 GeV.
