Quantum-mechanical analysis of single particle level density

A quantum-mechanical calculation of the single-particle level (s.p.l.) density g(ε) is carried out by using the connection with the single-particle Green's function. The relation between the imaginary part of Green's function and single-particle wave functions is used separately for the discrete and continuous states. Within the bound-states region the imaginary part of Green's function is calculated by using the Wronskian theorem. The Green's function corresponding to the continuum is written by using the regular and Jost solutions of the radial Schroedinger equation. The smooth part of the rapidly fluctuating s.p.l. density is calculated by means of the Strutinsky procedure. The continuum component of the s.p.l. density has rather close values within either exact quantum-mechanical calculations with the Woods-Saxon (WS) potential of Thomas-Fermi approximation with WS or finite-square potential wells, provided that the free gas contributions is subtracted. A similar trend is obtained by means of the simple FGM formula for the s.p.l. density if the continuum effect is taken into account. (author)