Interaction of a Nucleon with the Nucleus

The importance of nucleon-nucleon correlations and the Pauli principle in the excited states of nuclei is studied. It is shown that the polarized wave functions defined in an earlier paper by Vogt describe: (a) the correlated motion appropriate to a pair of nucleons whenever the pair is in close proximity, and (b) the motion of a single nucleon, when averaged over the positions of the nucleons to which it is correlated, as that given by the shell model. By use of the second moment of the strength function the polarized states are shown to solve the Schrödinger equation approximately. Previous calculations on the second moment are extended to show that when the correlations are neglected the second moment is not only large but also strongly dependent on the form of the internucleon potential—particularly when this potential contains strong repulsion at small distances. The large result obtained for the second moment in each case is reduced to a reasonably small value—less than ${\mathrm{}\left(10\mathrm{M}\mathrm{e}\mathrm{v}\right)\mathrm{}}^2$—by introducing the nucleon-nucleon correlations combined with the Pauli principle.