No abstract

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 Schrodinger 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 (10 Mev) 2 -by introducing the nucleon-nucleon correlations combined with the Pauli principle.The correlations between nucleons will be considered by using the "polarized" nuclear wave functions defined by Vogt (reference 7, hereafter referred to as I) who considered the same problem. The present paper is a much more general and complete treatment of the problem considered in I. The properties of the "polarized" wave functions of I are discussed most simply in terms of the second moment of the strength function, and consequently many of the calculations of the present paper will involve the second moment.The extent to which the states with correlations solve the Schrodinger equation for the whole nucleus is discussed in Sec. II. The second moment of the strength function is shown to play an important role in the construction of an approximate solution of the Schrodinger equation. Section III gives an approximation method for evaluating the second moment in terms of the potential acting between nucleons. There are two principal approximations in this method, and both are shown to be physically reasonable. The first concerns the assumption that only two nucleons at a time are interacting strongly with each other and thus ignores those events which are caused by three or more nucleons in mutual proximity. As a consequence of this assumption, the interaction between a single nucleon and a residual nucleus can be calculated by treating in detail only the forces between the single nucleon and the nucleons of the residual nucleus, ignoring meanwhile the detailed interactions between the residual nucleons themselves. In this sense the present paper concerns the nucleon-nucleus interaction. The first of our two chief approximations, together with a suitable perturbation calculation for the nucleon-nucleon correlations, yields the second moment in terms of twonucleon matrix elements of the internucleon potential. The second consists of a simple method for extracting numerical answers from the multitude of two-nucleon integrals. This method is essentia...