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.

Figures (4)

• Figure 1: Calculating the probability of having a different isospin (left) and a same isospin SRC pair in a $r_{\mathrm{src}}$ cell. $P_2$ is the probability of having two nucleons in the cell and p the reduction for spin anti-parallel pairs. See text for details.
• Figure 2: Mass (A) dependence of the number of np (top panel) and pp (bottom panel) SRC pairs of nucleus A relative to $^{12}$C. Data (small full squares with error bars) are as extracted in Colle2015 from the measured CLAS A(e,e$^\prime$p) and A(e,e$^\prime$pp) cross-section ratios EMC2011Fomin2012 after correcting for FSI. Error bars include the estimated uncertainty on the cross-section ratios and the FSI corrections. The empty crosses denote the result of the ZRA calculation of ref Colle2015 Our model calculations in the relevant ranges of the adjustable parameters ($p$, $r_{\mathrm{src}}$) are presented as a band (red online).
• Figure 3: Number of SRC pairs as calculated by us as a function of A. The band (red online) represents the range of adjustable parameter as discussed above. The nominal value (black line) is calculated using the nominal parameters $r_{\mathrm{src}}=1\ \mathrm{fm}$ and $p=0.22$, which are obtained by requiring (pp/np)=$7.5\%$ and $\#$pairs/A=$17.5\%$.
• Figure 4: The predicted 3N-SRC/A ratio as a function of the mass number. The calculations assumes that the 3N-SRC triplets are due to 2N forces only and that the force between any two nucleons is independent of other nucleons in the nucleus.See text for details.