The level density parameter and the back shift energy El. are determined for nuclei with A-values across the whole periodic table from fits to complete level schemes at low excitation energy near the neutron binding energies. We find that the energy back shift E, shows complicated behavior and depends, on the type of the nucleus, even-even, odd mass, and odd-odd. The spin cut-off factor has also been investigated for nuclei mentioned above. The results are compared with the previous results and different experimental data on level densities.