Short-Range Correlations in Nuclei

• Short-range correlations (SRCs) are high-momentum, nucleon–nucleon pairs induced by repulsive cores and tensor forces, leading to universal high-momentum tails in nucleon distributions.
• Experimental signatures include plateau scaling in electron scattering cross section ratios and a dominant presence of neutron–proton pairs over same-isospin pairs.
• SRC insights influence nuclear structure studies, inform astrophysical equations of state, and advance computational models addressing dense matter dynamics.

Short-range correlations (SRCs) in nuclei are high-momentum, short-distance nucleon–nucleon configurations that manifest as deviations from the independent-particle shell model paradigm. They arise primarily due to the strongly repulsive core and tensor components of the nucleon–nucleon force at separations ≲1 fm, inducing universal high-momentum tails in single-nucleon momentum distributions and dominating certain regions of scattering cross sections. SRCs display remarkable empirical regularity, notably in the scaling ratios observed in inclusive electron scattering, exhibit strong isospin dependence favoring neutron–proton pairs, and are quantitatively linked to bulk nuclear properties and astrophysical phenomena.

1. Universal Properties and Theoretical Foundation

Nuclear SRCs emerge from the short-range (≈0.5–1 fm) repulsive and tensor components of the nucleon–nucleon (NN) interaction. This leads to a significant fraction (≥20–30%) of nucleons in medium and heavy nuclei carrying momenta well above the nuclear Fermi momentum ($k_F \approx 250$ MeV/c). The shell model's mean-field approach fails to account for the high-momentum tail in the single-nucleon momentum distribution $n_A(k)$, which is universally observed across nuclei. Empirically, for $k > k_F$: $n_A(k) \sim C(A)\,n_D(k)$ where $n_D(k)$ is the deuteron momentum distribution and $C(A)$ is a nucleus-dependent scaling factor (Nguyen et al., 2020, Vanhalst et al., 2012, Fomin, 2012). This is a manifestation of the universal character of SRC-induced high-momentum tails, which for large $k$ aligns with a $n(k)\sim C/k^4$ behavior, with $C$ the "contact" parameter encoding SRC strength (Bulgac, 2022, Fomin et al., 14 Jan 2026).

In microscopic theory and factorized frameworks such as Generalized Contact Formalism (GCF), the many-body wave function or cross-section factors into universal two-body functions and "contacts" $C_\alpha$ specifying the number or strength of SRC pairs in a given spin–isospin channel $\alpha$ (Sharp et al., 25 Jan 2025, Fomin et al., 14 Jan 2026).

2. Experimental Signatures and Scaling Ratios

Inclusive quasielastic electron scattering $(e,e')$ at large four-momentum transfer ($Q^2>1.5$ GeV$^2$) and Bjorken $x = Q^2/(2m\nu) > 1$ provides direct access to SRCs. In the region $1.5 < x < 2$, where nucleon initial momentum must exceed $k_F$, the per-nucleon cross-section ratio between a nucleus $A$ and deuterium displays a flat "plateau" (Ye et al., 2018, Fomin, 2012, Nguyen et al., 2020): $$a_2(A) = \frac{[\sigma_A(x,Q^2)/A]}{[\sigma_D(x,Q^2)/2]}, \qquad (1.5 < x < 2)$$ The value of $a_2(A)$ rises rapidly for $A < 12$, then saturates near 4–5 for heavier nuclei. This quantifies the relative SRC abundance compared to the deuteron and demonstrates the dominance of two-nucleon SRCs (2N-SRCs). Triple-coincidence $(e,e'pN)$ knock-out experiments further reveal a striking preference for $pn$ over $pp$ or $nn$ pairs, with $pp/pn \sim 5$–6% (Fomin et al., 14 Jan 2026, Ryckebusch et al., 2014).

Three-nucleon SRCs (3N-SRCs) are theoretically predicted to arise at $x>2$, $Q^2 \gtrsim 2.5$ GeV$^2$ or light-cone momentum fraction $\alpha_{3N}\gtrsim1.6$, but experimental isolation is challenging due to kinematic smearing, final-state interactions, and limited statistics. Where identified, the 3N-SRC ratio scales quadratically with the 2N-SRC probability, $a_3(A) \sim a_2(A)^2$ (Sargsian et al., 2019).

3. Isospin Structure and Pair Dominance

A central result in SRC studies is the strong isospin dependence, with $pn$ (isosinglet, spin-1) pairs dominating over $pp$ or $nn$ pairs (isotriplet, spin-0). Recent high-precision inclusive measurements on isotopic pairs, such as $^{48}$Ca/$^{40}$Ca, exploit the different neutron/proton composition to disentangle np versus pp/nn contributions. The SRC plateau ratio: $$R_{48/40}(x) = \frac{[\sigma_{48Ca}(x,Q^2)/48]}{[\sigma_{40Ca}(x,Q^2)/40]}$$ in SRC-dominated kinematics ($1.5 < x < 2$) yields $R_{SRC} = 0.971 \pm 0.012$ (Nguyen et al., 2020); this is consistent with complete $np$-pair dominance and statistically rejects an isospin-independent scenario at $>3\sigma$.

Exclusive and semi-exclusive measurements, as well as photon- and hadron-induced SRC probes, confirm that $pn$ contacts outnumber $pp$ (or $nn$) by factors of 3–5 in heavy nuclei and up to $\sim20$ in the relevant momentum regime (Ryckebusch et al., 2014, Sharp et al., 25 Jan 2025).

4. Phase-Space Localization and Bulk Nuclear Effects

SRCs are strongly localized in the nuclear interior (for $r\lesssim2$ fm) and produce high-momentum tails in $n(k)$ up to $k\sim 5$ fm$^{-1}$ (Cosyn et al., 2021). Explicit Wigner phase-space mapping shows that the kinetic energy per nucleon is almost doubled in the nuclear core; e.g., $T(r)$ increases from $\sim 16$ MeV (mean field) to $\sim 30$ MeV (with SRCs) for $r \lesssim 2$ fm. The high-momentum components ($k > 2$ fm$^{-1}$), while carrying large kinetic energy, only marginally affect rms radii due to spatial localization.

In neutron-rich nuclei ($N>Z$), SRCs produce a "kinetic energy inversion" where proton kinetic energy per nucleon exceeds that of neutrons. SRCs also partially quench neutron skins, e.g., in $^{48}$Ca, by up to 10% (Cosyn et al., 2021, Ryckebusch et al., 2014, Cai et al., 2017).

5. Connections to Nuclear Structure, EMC Effect, and Astrophysics

SRCs are intimately linked to modifications in nuclear structure, such as the EMC effect, where deep-inelastic structure functions of bound nucleons are altered compared to free nucleons. Quantitative studies reveal a robust linear correlation between the SRC scaling ratio $(a_2-1)$ and the EMC slope $dR_{EMC}/dx$ across the nuclear chart (Fomin, 2012, Vanhalst et al., 2012, Ye et al., 2018). This supports the view that high-local-density configurations (SRC pairs) drive in-medium quark distribution modifications.

In heavy-ion collisions, direct measurement of SRCs via bremsstrahlung gamma-ray emission provides independent confirmation of the SRC fraction $(20 \pm 3)\%$ in $^{124}$Sn, matching electron- and hadron-induced determinations and offering new access to quark-level nuclear dynamics (Xu et al., 14 Apr 2025).

Astrophysically, SRCs are a crucial ingredient in dense matter equations of state (EOS), neutron-star structure, cooling, and nuclear pasta formation. Inclusion of SRC-induced high-momentum tails modifies kinetic energy contributions, symmetrizes the EOS, lowers tidal deformability and direct Urca thresholds, and even alters the geometry and existence of non-spherical phases in neutron-star crusts (Cai et al., 29 Dec 2025, Souza et al., 2020, Souza et al., 2020, Pelicer et al., 2022).

6. Quantification, Computational Models, and Scaling Laws

SRCs are quantitatively characterized by the number of correlated nucleon pairs and triples, typically extracted via cluster expansions, counting of zero relative angular momentum pairs, or via scaling ratios in experimental cross sections (Vanhalst et al., 2012, Ma et al., 5 Jun 2025). For two- and three-body SRCs, empirical scaling with nuclear mass follows a soft power law:

Correlation Type	Per Nucleon Scaling	Abundance (Heavy Nuclei)
2N SRC	$N_{2N}(A)/A \sim A^{0.35}$	$a_2(A) \sim 4$–$5$
3N SRC	$N_{3N}(A)/A \sim A^{0.58}$	$a_3(A) \sim a_2(A)^2 \sim 7$–$8$

SRCs also manifest in the single-nucleon momentum distribution's $1/k^4$ tail, with "contact" $C$ setting the overall strength. In asymmetric matter, the SRC fraction above $k_F$ is strongly isospin dependent due to tensor forces, yielding increased depletion and momentum-space "proton skin" in neutron-rich nuclei (Cai et al., 2017, Cai et al., 29 Dec 2025).

7. Open Questions, Future Experiments, and Theoretical Advances

Outstanding issues include the precise extraction and momentum structure of 3N-SRCs, the density and isospin dependence of SRCs at supranuclear densities, the role of SRCs in modifying nucleon structure and parton distributions, and the impact on neutron-star astrophysical observables (Fomin et al., 14 Jan 2026, Fomin et al., 2023, Sargsian et al., 2019, Cai et al., 29 Dec 2025). Planned and ongoing experiments target mirror nuclei, triple-coincidence knockout of three-nucleon clusters, photon-induced tests of probe factorization, and multimessenger constraints from gravitational-wave and X-ray observations (Nguyen et al., 2020, Sharp et al., 25 Jan 2025, Ye et al., 2018).

On the computational side, further integration of ab initio quantum Monte Carlo, cluster expansions with realistic NN+3N forces, and advanced correlations in density functional frameworks are expected to refine both SRC quantification and predictions for nuclear, astrophysical, and QCD-scale observables. The emerging theoretical consensus emphasizes universality, factorization, and contact-driven scaling, while remaining open to explicit medium-modification and non-nucleonic dynamics in extreme environments.