Short-range correlated pairs from nucleon density profiles as a new probe of the nuclear equation of state
We investigate to what extent the observed nuclear systematics of Short-Range Correlations (SRCs) can be described by the geometry of the underlying proton and neutron density distributions. Building on previous connections between nuclear SRC contacts and one-body densities, we formulate an explicit density-overlap representation in which proton--proton, proton--neutron, and neutron--neutron SRC source terms are constructed from the full spatial density profiles obtained with Energy Density Functionals (EDFs). The framework contains two global parameters describing the overall SRC pair formation strength and the relative contribution of the spin-singlet channel, while the nucleus-dependent evolution is generated by the density-overlap integrals. The framework simultaneously reproduces several independent experimental SRC observables, including proton--proton to proton--neutron pair ratios, relative SRC pair abundances, and proton and neutron high-momentum double ratios. A comparison between relativistic and Skyrme-type EDF families demonstrates the sensitivity of these observables to the underlying density geometry and allows the effect of the complete density profiles to be distinguished from simple radius-based geometrical estimates. Applied to neutron-rich oxygen isotopes, the framework predicts a pronounced evolution of the neutron--neutron pair abundance. Comparison with an independent calculation based on occupied harmonic-oscillator wave functions and an explicit finite-distance criterion supports the predicted isotopic evolution in neutron-rich oxygen isotopes. This agreement identifies the proton--proton to neutron--neutron SRC pair ratio as a promising experimental probe of neutron-skin thicknesses in neutron-rich nuclei and, through their connection to the symmetry energy, of the nuclear equation of state.