Spatial particle correlations in light nuclei. II four-particle systems

The geometry of configurations of identical particles in a shell is extended from two to four particles. Results are derived for a general ℓℓ shell and particular attention is paid to the pp shell (ℓ=1ℓ=1), which is of relevance for the nucleus 88He. Expressions are given for the angular probability density in terms of the six angles between pairs of position vectors of the particles. The analysis of the pp shell reveals the existence of two classes of favored four-particle configurations, with three members each. The transition from one class to the other is governed by the nuclear dynamics and depends on the conflicting tendencies of the short-range nuclear interaction versus the spin–orbit splitting.

► We study analytically the geometry of four-particle systems in a shell.
► General expressions are found for an arbitrary l shell.
► Angular correlation is generalized from two to four-particle systems.
► For 88He, the analysis of the p shell reveals two classes of configurations.
► The transition from one class to the other governed by nuclear dynamics is found.