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

Abstract

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 sigma_i.sigma_j tau_i.tau_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 alpha 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.

20 pages, 7 figures

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• Neutrinoless double beta decay matrix elements in light nuclei
• Chiral Effective Field Theory Calculations of Weak Transitions in Light Nuclei
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• Electromagnetic structure of light nuclei