In this paper we apply Boltzmann-Fokker-Planck (BFP) theory to analyze the (isotropic) photoelectron flux in the Earth's ionosphere at energies in the vicinity of photoionization peaks where the electron impact cross sections are slowly varying functions of energy. We give a Green's function solution for the photoelectron flux which shows that the energy derivative terms in the BFP method dominate the solution in spectral regions of high slope. Analytical results for the photoelectron flux and the forward and backward half widths in the vicinity of isolated photoionization peaks are given which explain the observed asymmetry and shift of the photoionization peaks with increasing altitude. At low altitudes these results indicate that the theoretical width of an isolated photoionization peak is less than the experimental resolution of recent AE-E data. A comparison between the theoretical photoelectron flux averaged using the experimental resolution and the experimental photoelectron flux from 15 to 35 eV at 182 km shows reasonable relative agreement.