  The energy dependence is investigated for a wide set of space-time
characteristics derived from Bose - Einstein correlations of secondary pion
pairs produced in proton-proton and nucleus-nucleus interactions. Analytic
functions suggested for smooth approximations of the energy dependence of
emission region parameters demonstrate reasonable agreement with all available
experimental results for proton-proton collisions while the approximations
correspond to most of experimental data for nucleus-nucleus collisions at
energies above 5 GeV. Estimations for a wide set of space-time quantities are
obtained for energies for the Future Circular Collider (FCC) project based on
the smooth approximations. The space particle densities at freeze-out are
derived also from estimations for the volume of the emission region and for
total multiplicity at FCC energies. Estimations for charged particle density
and its critical value allow the possibility of lasing behavior for secondary
pions in nucleus-nucleus collisions at FCC energy. The mathematical formalism
is presented for study of the peak shape of correlation function for general
case of central-symmetrical Levy - Feldheim distribution.
