Universal laws for nuclear contacts

TL;DR

This work extends the YPB universal laws linking short-range nucleon-nucleon correlations to mean-field radii by combining the generalized contact formalism with Skyrme Hartree-Fock-Bogolyubov densities and AV18-based two-body inputs. It demonstrates that spin-zero $pp$ and $nn$ nuclear contacts obey $C^A_{0,pp} = L^0_{pp} \frac{Z^2}{R_p^3}$ and $C^A_{0,nn} = L^0_{nn} \frac{N^2}{R_n^3}$ with global Levinger constants $L^0_{pp} \approx 0.0163$ fm$^3$ and $L^0_{nn} \approx 0.0166$ fm$^3$ across $40 < A < 240$, up to modest isospin-breaking and Coulomb corrections. This provides a robust, practical framework to infer nuclear SRCs from bulk radii measurements and suggests a deep connection between SRC abundance, neutron skin, and the equation of state for dense matter, with implications for neutron-star physics. Tensor-force effects do not alter these leading-order relations, and the approach extends the applicability of the YPB laws to a wide swath of the nuclear chart.

Abstract

The nuclear contact characterizes the nucleon-nucleon pairs in close proximity and serves as an important tool for studying the short-range correlations (SRCs) within atomic nuclei. While they have been extracted for selected nuclei, the investigation of their behavior across the nuclear chart remains limited. Very recently, Yankovich, Pazy, and Barnea have proposed a set of universal laws (YPB laws) to describe the correlation between nuclear contacts and nuclear radii and tested their laws for a small number of nuclei by using the Woods-Saxon mean-field model~[R.\ Yankovich, E.\ Pazy, and N.\ Barnea, arXiv:2407.15068 (2021)]. In this Letter, we extend their study to a majority part of the chart of nuclides within the framework of the Skyrme Hartree-Fock-Bogolyubov model, which incorporates several essential beyond-mean-field features and offers a more accurate description of the bulk properties of atomic nuclei. Our results suggest that the YPB laws hold as a good approximation for different nuclear mass regions, with minor deviations attributed to, e.g., isospin-breaking effects. Our work lays a firm foundation for future applications of the YPB laws in finite nuclei and provides new evidence for the long-range nature of the relative abundance of short-range pairs.

Figures (6)

• Figure 1: Nuclear contacts for Pb isotopes versus RMS radii of nucleon density distributions for (a) $pp$ pairs and (b) $nn$ pairs. The results are shown for nuclei with neutron numbers ranging from $N=96$ to $N=138$. The fitted lines follow the expressions $C^A_{0,pp}=L^0_{pp}\frac{82^2}{R_p^3}$ and $C^A_{0,nn}=L^0_{nn}\frac{N^2}{R_n^3}$. The corresponding point-nucleon density distributions are given by the Skyrme HFB method with SIII, SKM*, SLY4, SKI3, and SKX parameter sets.
• Figure 1: The $pp$ contacts $C^A_{0,pp}$ for Pb isotopes versus mass number $A$. The corresponding point-proton density distributions are given by the Skyrme HFB method with SIII, SKM*, SLY4, SKI3, and SKX parameter sets. The vertical dashed line marks $A=208$.
• Figure 2: Generalized Levinger constant for $nn$ pairs $L^0_{nn}$ across the chart of nuclides. The three images below display an enlarged view of the pattern. The corresponding $nn$ contacts and RMS radii of neutron density distributions are calculated with the HFB point-neutron density distributions using the SLY4 parameter set.
• Figure 2: Nuclear contacts for $N=82$ isotones versus RMS radii of nucleon density distributions for (a) $pp$ pairs and (b) $nn$ pairs. The results are shown for nuclei with proton numbers ranging from $Z=48$ to $Z=72$. The fitted lines follow the expressions $C^A_{0,pp}=L^0_{pp}\frac{Z^2}{R_p^3}$ and $C^A_{0,nn}=L^0_{nn}\frac{82^2}{R_n^3}$. The corresponding point-nucleon density distributions are given by the Skyrme HFB method with SIII, SKM*, SLY4, and SKP parameter sets. The generalized Levinger constant is determined to be $L^0_{nn} = 0.01653$ fm$^3$ for $nn$ pairs, while for $pp$ pairs, the values of $L^0_{pp}$ range from 0.01618 to 0.01633 fm$^3$ across different data sets.
• Figure 3: Generalized Levinger constant for $pp$ pairs $L^0_{pp}$ across the chart of nuclides. The three images below display an enlarged view of the pattern. The corresponding $pp$ contacts and RMS radii of proton density distributions are calculated with the HFB point-proton density distributions using the SLY4 parameter set.