The collective nuclear model of A. Bohr is applied to the interpretation of inelastic scattering of neutrons, as was briefly described in our previous report6l. The present paper deals with the detailed theory of the inelastic scattering of neutrons by a direct excitation of the nuclear surface rctation, as well as by the resonance scattering via compound nuclei. The cross section for the former process is proportional to the square of the intrinsic quadrupole moment and depends strongly upon the amplitudes of neutron waves at the nuclear surface. This strong dependence makes it difficult to compare our theory with experiments. Conversely the strong dependence may be employed to know the optical potential which distorts neutron waves. It is pointed out that the contributior.s from the direct and compound nucleus forming processes can be distinguished by observing the angular distribution. The inelastic scattering of neutrons has thus far been analyzed mostly in terms of the statistical theory of nuclear reactions. However, for the reaction in which only a few energy levels are excited in a residual nucleus, the statistical assumption is no longer valid for the final nucleus, so that the properties of the f.nd levels make a significant influence on the scattering cross section. This fact is taken into account by Hauser and Feshbach1' who gave the cross sections for given initial and final nuclear spins and parities. In their theory an impinging neutron is assumed always to form a compound nucleus whose level density is high enough to permit the application of the statistical assumption for the intermediate nucleus. The assumptions are justified, provided that the interaction of a neutron with a nucleus is so strong that the neutron is always absorbed once it hits the nuclear surface, and provided that the level distance of a compound nucleus is small compared with the level width and with the energy spread in the neutron beam. The latter is not satisfied in a recent experiment by Kiehn and Goodman2' who were able to observe the resonances which are thought to show the contributions from the indivi­ dual levels of compound nuclei. The strong absorption may not strictly hold if one takes into account the rather weak interaction shown by Feshbach, Porter and W eisskopfl' through the analysis of elastic scattering of neutrons. As the resonance reaction may be accounted for in ordinary terms of the resonance theory, we are mainly concerned with the reaction in the case of the weak interaction between a neutron and a nucleus. What is important in this case, is the cause of transition between initial and final