Abstract In a previous paper [Z. Hao, Mod. Phys. Lett. B7 , 1439 (1993)] we have derived an energy dependent gap parameter, with the magnitude ¦Δ k ¦ being appreciable within only a few k B T c around the Fermi level. In this paper we use this energy dependent ¦Δ k ¦ to calculate the critical magnetic field H c , electronic specific heat C , and Josephson critical current density I c of an SIS junction, and compare the results with those obtained by using the cutoff approximation. The main significant difference is that the present result for I c is much smaller than that of the cutoff approximation, with the ratio between the former and the latter at T = 0 being only 0.35 for symmetric junctions and even less for asymmetric junctions. As to the temperature dependences of H c , C and I c , the differences between the present results and those of the cutoff approximation are much less significant; i.e., there exist only minor numerical modifications. A qualitative discussion is also given on the physical significance of the phase θ k of the gap parameter ( Δ k = ¦Δ k ¦e iθ k ).