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

By K. Wildermuth, Y.C. Tang

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14), become now only approximately valid and one must be more careful in discussing equivalences between wave functions in different cluster representations. 41 4. 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.

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.

This means that, in calculating the expectation value of the microscopic nuclear Hamiltonian with this wave function, the only flexibility is contained in the variation of the common width parameter a. In fact, even this variation has to be severely limited. 32 fm- 2 [EL 61]. Therefore, with this added restriction, the wave function has rather limited flexibility and, in general, cannot correctly account for the correlation behaviour of the nucleons. To remedy the above situation, one could, of course, use a large number of oscillator cluster functions in calculating the energy expectation values.

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