# A Unified Theory of the Nucleus by K. Wildermuth, Y.C. Tang

By K. Wildermuth, Y.C. Tang

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1. General Remarks We apply now the basis wave functions discussed in Chapter 3, in particular the generalized cluster wave functions, to the time-dependent and time-independent Schrodinger equations, written in the form of projection equations (see eqs. 3)), to formulate a unified microscopic nuclear structure and reaction theory. As has been mentioned already in Chapter 2, the most important feature of this theory is that all open and closed channels will be treated on an equal footing and, consequently, the asymptotic boundary conditions in all the channels can be fulfilled in a very natural manner.

By lifting up one nucleon from the 1 p shell to the 2s1d shell, the orbital angular momenta of the nucleons can couple to yield only total angular-momentum values J = 3,2, and 1. Further, one sees that for J = 3 and for J = 2, just one coupling possibility exists. Therefore, 16 0 has one r and one 2- state which are one-particle-excitation states to the next higher oscillator shell and in which simultaneously no ex cluster is broken up. For the J = 1 case, there are two coupling possibilities. But one of these couplings must describe a pure center-of-mass excitation of the 16 0 nucleus in the space-fixed oscillator potential, which is irrelevant for us.

But because the presence of the other cluster (in 6Li the a-cluster) confines the two uncorrelated nucleons within the nuclear volume. the uncertainty principle does not permit a correspondingly large decrease in their kinetic energies ttt as in the case of the free deuteron. Therefore, we conclude that it is energetically unfavourable to destroy the deuteron-cluster correlation and a deuteron cluster could be considered as a relatively stable substructure inside a larger nucleus. Based on the qualitative argument given above, we can presume that T = 0 6Li states with excitation energies less than about 5 MeV can be described, in a first approximation, by a + d cluster wave functions with unexcited clusters.