The formalism of the coupled-channel analysis of the scattering of nuclear projectiles by nuclei is presented in detail. Since the necessity for coupled-channel calculations increases with the degree of collectivity exhibited by the target nucleus, the presentation is particularly suited to collective nuclei, with the target states described by phenomenological collective coordinates. Within this restriction the formalism given here is quite general so that the following cases can be considered: The target can be any (collective) nucleus, even-$A$ or odd-$A$, vibrational or rotational; the projectile can be either charged or uncharged, and can have any spin; either or both the projectile and the target can be polarized; finally, the energy of the projectile can be very low since the contribution of the compound-state formation to the cross section can be included. Using a computer program which was written following the above formalism (which can be used to do any of the calculations enumerated above) scattering cross sections for several typical cases were obtained and are presented to show their contrasting behavior when different targets (and different coupling schemes) and different projectiles are chosen. Realistic calculations were also made in order to fit a large number of existing experimental data. Good fits were obtained in most cases which indicates that the coupled-channel calculation is a very powerful tool in explaining various complicated scattering data, and further in extracting useful spectroscopic informations about the target nucleus. Possible future developments of the present analyses are discussed.

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