  Level density $\rho$ is derived for a finite system with strongly interacting
nucleons at a given energy E, neutron N and proton Z particle numbers,
projection of the angular momentum M, and other integrals of motion, within the
semiclassical periodic-orbit theory (POT) beyond the standard Fermi-gas
saddle-point method. For large particle numbers, one obtains an analytical
expression for the level density which is extended to low excitation energies U
in the statistical micro-macroscopic approach (MMA).The interparticle
interaction averaged over particle numbers is taken into account in terms of
the extended Thomas-Fermi component of the POT. The shell structure of
spherical and deformed nuclei is taken into account in the level density. The
MMA expressions for the level density $\rho$ reaches the well-known macroscopic
Fermi-gas asymptote for large excitation energies U and the finite combinatoric
power-expansion limit for low energies U. We compare our MMA results for the
averaged level density with the experimental data obtained from the known
excitation energy spectra by using the sample method under statistical and
plateau conditions. Fitting the MMA $\rho$ to these experimental data on the
averaged level density by using only one free physical parameter - inverse
level density parameter K - for several nuclei and their long isotope chain at
low excitation energies U, one obtains the results for K. These values of K
might be much larger than those deduced from neutron resonances. The shell,
isotopic asymmetry, and pairing effects are significant for low excitation
energies.
