Modeling Short-Range Nucleon Pair and Triplet Abundances in Atomic Nuclei

Abstract: Short-range correlated (SRC) nucleon pairs provide a sensitive probe of the short-distance structure of atomic nuclei and the underlying nucleon-nucleon (NN) interaction. We present a simple numerical method to estimate the number of two- and three-nucleon SRC clusters using an independent-particle shell model with a harmonic-oscillator basis. The relative abundances of proton-neutron (pn), proton-proton (pp), and neutron-neutron (nn) SRC pairs are calculated for Al, Fe, and Pb nuclei, normalized to carbon, and compared with existing analytical predictions and available extractions from experimental data. We extend the analysis to the isotopes 40Ca, 48Ca, and 54Fe (collectively, the CaFe nuclei), which have been recently measured but whose SRC results are not yet published. These isotopes provide insight into the role of 1f7/2 shell occupancy in SRC pair formation. Finally, we present a reference baseline for three-nucleon SRC cluster abundances across the studied nuclei, assuming 3N clusters originate from independent two-nucleon interactions. The predicted baseline is about 2.5% 3N-SRC/2N-SRC ratio for all medium and heavy nuclei. Deviations from this baseline may indicate the presence of additional short-range nuclear dynamics.