Quantification of the clustering properties of nuclear states

The amount of a particular type of clustering in a nuclear state is defined in this paper as the norm square of the projection of the wave function onto the particular cluster-model subspace. It is pointed out that, although the clusters cannot be localized in space by measurement, the amount of clustering characterizes the cluster formation in close analogy with a quantum mechanical probability. The cluster-model component of the wave function is proved to have a variational property. This facilitates the computation of the amount of clustering. The model dependence of the amounts of various clusterings and their relationship to the corresponding spectroscopic factors are studied via numerical examples for the nucleus 6Li. It is pointed out that, in a relative sense, the spectroscopic factor, which is more directly related to experiment, is also characteristic of the clustering contents of different states of the same nucleus, but it cannot be used for comparisons between different nuclei or clusterings. An analysis by means of the amount of clustering shows that even apparently minute changes on the cluster-model space modify the ground-state wave function of 6Li appreciably. But the extensions of the model space considered do not invalidate the α+d picture since the amount of α+d clustering in terms of consistently modified cluster internal wave functions remains close to unity. Copyright 1987 Academic Press, Inc