Formation of clusters in the nuclear surface

An operator formalism is constructed which allows one to calculate a movie of nuclear density plots showing the linear oscillation of two chosen fragments (clusters) in a given ground state or virtual state of a nucleus. The main ingredients of the formalism are the projection of a nuclear wave function onto a chosen antisymmetrized cluster decomposition, and the knowledge that a quantum mechanicalL=0 motion is a linear motion averaged over angles. The formalism is tested and results are discussed in the well-known cases of a shell-model description and a resonating-group-model description of8Be. It is seen that two α-clusters appear even in the surface of the compact harmonic-oscillator shell model ground-state. They are formed with higher probability in the resonating-group-model description of the more realistic8Be virtual state at 92 keV.