Level density within a micro-macroscopic approach

Statistical level density $\rho(E,A)$ is derived for nucleonic system with a given energy $E$, particle number $A$ and other integrals of motion in the micro-macroscopic approximation beyond standard saddle-point method Fermi gas model. This reaches two limits; well-known grand-canonical ensemble limit large entropy $S$ related to excitation energies, finite micro-canonical small combinatorical at low energies. The inverse parameter $K$ as function semiclassical periodic orbit theory, taking into account extended Thomas-Fermi Strutinsky shell corrections, calculated compared experimental data.