Abstract
The geometry of configurations of identical particles in a shell is extended from two to four particles. Results are derived for a general ℓ shell and particular attention is paid to the p shell (ℓ=1), which is of relevance for the nucleus 8He. 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 p 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.
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