VI. DETAILS OF THE NUMERICAL CALCULATIONS We used Saxon-Woods (SW) potential with spin-orbit term. For protons it was comple- mented by a Coulomb potential of uniformly charged sphere with diffuse edge. (To have this form is necessary for being able to calculate semi-classical results for comparison.) The parameters of the potentials were that of the so called universal potential given in Ref.[28]. The depth of the central potential for neutrons ( τ = ν ) t$_{3}$ = 1 / 2 or for protons ( τ = π ) t$_{3}$ = − 1 / 2 V$_{τ}$ ( Z, N ) = − V [ 1 − 2 κt$_{3}$ N − Z A ] , (35) V$_{so}$ = − λ$_{so}$V$_{τ}$ 4 ( ℏ 2 µc ) 2 , (36) where κ = 0 . 86, V = 49 . 6 MeV. The depth of the spin-orbit potential with the reduced mass µ of the nucleon and λ$_{so}$ = 35(36) for neutrons(protons). The diffuseness was a = a$_{so}$ = a$_{C}$ = 0 . 7 fm the same for all potential terms. The radius parameters were r$_{0}$ = 1 . 347 fm, r$_{0}$ = r$_{C}$ = 1 . 275 fm for neutrons and protons, respectively, while for the spin-orbit term r$_{so}$ = 1 . 31(1 . 32) fm for neutrons(protons). These potential parameters might not be optimal for the individual nuclei but give a good general N , Z dependence all over the nuclear chart at least for our purpose for testing our method. The single particle energies e$_{i}$ of the single particle Hamiltonian were calculated by diag- onalizing the matrix of the Hamiltonian in h.o. basis having twenty principal h.o. quanta and maximal orbital angular momentum nine. (An increase of the size of the basis did not change the results.) The same basis was used for diagonalizing the free Hamiltonian (with- out nuclear potential terms) to get the positive energies e (0) i needed to include the effect of the continuum in the Green’s function method described in Ref.[16] in detail. From the difference of the smoothed level densities of the spectra of the true and the free Hamiltonians the effect of the artificial nucleon gas cancels out and we get the same smoothed continuum level density as we could get by smoothing the continuum level density derived from the derivative of the scattering phase shifts [16]. In Fig. 5 we show the plateau curves for the $^{146}$Gd nucleus with the finite range smoothing and the result of the Wigner–Kirkwood calculation as a reference. The range of the p values used in the present work was taken to be the same as in Ref. [15] in order to make comparison with those results possible. Using the new method with the finite range smoothing we are 14