A systematic analysis using the cloudy crystal ball model of Feshbach, Porter and Weisskopf is carried out for the total cross sections and the non-elastic cross sections of neutron scattering by nuclei. The energy range considered extends from 3.5 to 14.0 Mev. Almost all the regions of mass number of the target nuclei are covered except for very light ones. The optical potentials asumed are of square well shape. The energy dependence of the potential strength, V + iW, and the mass number dependence of the range of potential, R, are carefully studied. It is found that the mass number dependence of the total cross sections at each of the fixed energies is well reproduced by the calculation with the suitable choice of the potential parameters. On the other hand, the calculation fails to give the correct magnitude of the non-elastic cross sections. The calculated values are considerably smaller than the experimental ones especially for lower incident energies. The parameters which have been found to give the best fit to the experimental data are as follows: R = (0.5 + 1.35 A1/3) ×10-13cm, V = 40 Mev for all the neutron energies studied and W varies from 2 to 7 Mev as the incident energy increases from 3.5 to 14.0 Mev.