Pair counting, pion-exchange forces and the structure of light nuclei

A simple but useful guide for understanding the structure of light nuclei is presented. It is based on counting the number of interacting pairs in different spin-isospin (S,T) states for a given spatial symmetry and estimating the overall binding according to the sum of σ_i·σ_jτ_i·τ_j expectation values, as suggested by one-pion exchange. Applied to s- and p-shell nuclei, this simple picture accounts for the relative stability of nuclei as A increases and as T changes across isobars, the saturation of nuclear binding in the p shell, and the tendency to form d,t, or α subclusters there. With allowance for pairwise tensor and spin-orbit forces, which are also generated or boosted by pion exchange, the model explains why mixing of different spatial symmetries in ground states increases as T increases across isobars and why, for states of the same spatial symmetry, the ones with greater S are lower in the spectrum. The ordering of some sd-shell intruder levels can also be understood. The success of this simple model supports the idea that one-pion exchange is the dominant force controlling the structure of light nuclei.