Multinucleon Final-States Overview

• Multinucleon final-states are reaction outcomes where two or more nucleons are simultaneously detected, evidencing complex many-body dynamics and short-range correlations.
• Advanced frameworks like RMSGA and spectral function approaches model these states, capturing both initial and final state interactions in scattering experiments.
• Accurate treatment of final-state interactions and energy redistribution is crucial for interpreting precision data in neutrino, electron, and heavy-ion reactions.

Multinucleon final-states describe the ensemble of reaction outcomes in which two or more nucleons (or, in some contexts, mesons or hyperons in conjunction with nucleons) are detected in coincidence following an initial interaction with a nucleus by a probe such as an electron, photon, neutrino, or another hadron. These final-states emerge from processes that often reflect the correlated many-body dynamics of the nuclear medium, short-range correlations, multinucleon transfer mechanisms, pair emission, or complex nuclear excitations. Their correct theoretical description is both a fundamental test of nuclear many-body theory and an essential component for the interpretation of precision experiments in nuclear and particle physics.

1. Theoretical Frameworks for Multinucleon Final-States

Two central theoretical methodologies underpin modern descriptions of multinucleon final-states: the relativistic multiple-scattering Glauber approximation (RMSGA) and spectral function (SF) approaches.

In high-energy exclusive scattering (e.g., A(e,e′p), A(e,e′pp), A(p,2p)), the RMSGA incorporates both initial- and final-state interactions (ISI and FSI) within a relativistic eikonal framework. The amplitude for a reaction is modified by the Glauber phase factor: $$\mathcal{G}(\mathbf{b}, z) = \prod_{\alpha_{\text{occ}} \neq \alpha} \int d\mathbf{r}'\, \left|\phi_{\alpha_{\text{occ}}}(\mathbf{r}')\right|^2 \left[1 - \theta(z - z')\Gamma_{pN}(\mathbf{b}' - \mathbf{b})\right] \prod_{i}\left[1 - \theta(z'_i - z_i)\Gamma_{iN}(\mathbf{b}'_i - \mathbf{b}_i)\right]$$ where $\Gamma_{iN}$ characterizes the effective profile of hadron–nucleon scattering and is parameterized by total cross sections, slope, and ratio of real to imaginary parts of the amplitude (Cosyn et al., 2010).

The SF approach, often implemented in Monte Carlo event generators (e.g., NuWro (Ankowski et al., 13 Aug 2025)), provides a natural avenue for describing both mean-field and multinucleon (short-range correlated) final-states: $$P_{\text{corr}}(p,E) = \int d^3h\, \delta(E-E_{\text{thr}}-T_{A-1})\, n_{\text{cm}}^{pn}(|\mathbf{p}+\mathbf{h}|)\, n_{\text{rel}}^{pn}\left(\left|\frac{\mathbf{p}-\mathbf{h}}{2}\right|\right)$$ allowing explicit generation of two-nucleon final-states and validation against inclusive and exclusive lepton-nucleus cross sections.

Accurate treatments of FSI are achieved by convoluting the plane-wave response with a folding function directly connected to the particle spectral function, capturing both the energy shift and redistribution due to rescattering (Benhar, 2013): $$S(q,\omega) = \int d\omega' S_0(q,\omega') F_q(\omega-\omega')$$ with $F_q(\omega) = P_p(q, \omega + E_q)$.

For heavy-ion multinucleon transfer, time-dependent density functional theory (TD-DFT) and covariant (relativistic) extensions, supplemented by angular momentum projections and entanglement analysis, have elucidated the dynamics of nucleon exchange, intrinsic spin generation, and quantum correlations (Li et al., 28 Mar 2024, Zhang et al., 16 Jul 2025).

2. Experimental Manifestations and Reaction Mechanisms

Multinucleon final-states are accessed through a diverse array of reactions:

• Direct Two-Nucleon Removal. The sudden approximation describes reactions where pairs of nucleons are removed in a single step, with the residue observed in a specific final state. The momentum distributions of these residues are primarily sensitive to the total orbital angular momentum of the removed pair, $L$, rather than merely their coupled spin $I$ (Simpson et al., 2010). Dalitz plot analyses of correlated three-body systems (core + 2p) provide direct information on spatially and spin-correlated pair removal (Wimmer et al., 2012).
• Knockout and Pion Production. A(e,e′p), A(e,e′pp), A(p,2p), and $A(e,e′\pi)$ reactions, especially in the GeV regime, systematically probe the spatial extent of nucleon correlations. For example, double knockout with $\gamma, pp$ preferentially samples the nuclear interior, making it a selective probe of high-density SRCs (Cosyn et al., 2010).
• Inclusive and Exclusive Channels in Electron and Neutrino Scattering. Differential cross sections, reconstructed final-state hadronic kinematics, and correlations (e.g., transverse momentum imbalance in T2K (Abe et al., 2018)) clearly demonstrate the role of 2p–2h (two-particle–two-hole) and even 3p–3h mechanisms, with multinucleon event rates essential for interpreting cross-section enhancements originally observed in MiniBooNE (Benhar et al., 2015, Sobczyk et al., 2020).
• Heavy-Ion Multinucleon Transfer (MNT) and Isospin Equilibration. In near-barrier heavy-ion collisions, multinucleon final-states correspond to the set of projectile- and target-like fragments resulting from the transfer of several nucleons. TD-DFT and quantum molecular dynamics (QMD) reveal complex evolution of N/Z in the fragments, sequential neutron-then-proton flow through the dynamical neck, and pathways to isospin equilibration (Scamps et al., 2015, Li et al., 2018).

3. Final-State Interactions (FSI): Attenuation, Correlations, and Mass Dependence

FSI crucially shape observed multinucleon yields through attenuation, energy loss, and deflection processes:

• Attenuation and Nuclear Transparency. The survival probability of pairs (quantified by transparency $T_A^{pN}$) decreases with nuclear mass; for exclusive two-nucleon knockout, $T_A^{pN} \sim A^{-\lambda}$ with $0.4 \lesssim \lambda \lesssim 0.5$ (Colle et al., 2015). FSI reduce, but only modestly distort, the momentum-space features that represent SRC—momentum distributions and opening angles remain reliable tracers of underlying correlations in the initial state.
• Single-Charge Exchange (SCX) and Meson Rescattering. In addition to attenuation from elastic rescattering, SCX mechanisms in which a nucleon changes identity, or meson rescattering affecting pion production, provide additional albeit usually sub-dominant contributions (Dieterle, 2011, Colle et al., 2015).
• FSI Effects beyond Quasielastic Regime. The convolution approach, allowing the folding of the response with an empirically or microscopically computed FSI function, enables the connection between one- and two-nucleon observables, and directly ties the FSI modification to the underlying spectral function (Benhar, 2013, Ankowski et al., 13 Aug 2025).
• Energy-Broadening and Kinetic Energy Sharing. In neutrino-nucleus scattering, multinucleon emission results in a distinct sharing of kinetic energy and asymmetric nucleon momentum distributions, which differ markedly from those predicted by phase-space-only MC generator implementations and affect calorimetric energy reconstruction (Sobczyk et al., 2020).

4. Multinucleon Transfer and Many-Body Quantum Dynamics

Multinucleon transfer (MNT) reactions in heavy ions provide both a testbed for quantum many-body dynamics and new isotopic production:

• Coupled-Channels and Quantum Molecular Dynamics. Semi-classical and quantal coupled-channels models incorporate transfer channels (0n, 1n, 2n, …), direct versus sequential transfer, and absorption. High-fidelity reproduction of one- and two-neutron transfer cross sections, and their dependence on geometric and dynamical variables, necessitates inclusion of direct pair transfer and quantum tunneling (Scamps et al., 2015).
• Isospin Equilibration and Symmetry Energy. Dynamical modeling, e.g., using ImQMD, shows that isospin flows—first by neutron transfer along the low-density neck, later by protons—are driven by symmetry energy coefficients, with rapid N/Z variation signaling approach to equilibration (Li et al., 2018). Fully equilibrated fragments are found in events with large mass transfer, often associated with symmetric fission-like events.
• Entanglement and Quantum Information. The description of multinucleon final-states extends naturally to entanglement observables: in TD-DFT, the von Neumann entropy of fragments provides a measure of quantum correlations, and is linearly bounded by nucleon-number fluctuations, i.e. $L \approx 8\ln2\cdot \Delta N^2$ (Li et al., 28 Mar 2024). Mutual information analyses clarify the onset and fate of spin–spin correlations in the fragments (Zhang et al., 16 Jul 2025).

5. Spin Distributions and Intrinsic Angular Momentum Generation

MNT processes involving substantial nucleon transfer and frictional dissipation induce characteristic broad distributions of intrinsic spin (S) in the outgoing fragments:

• Conversion Mechanism. The partitioning $\vec{J} = \vec{S}_L + \vec{S}_H + \vec{\Lambda}$ (total angular, PLF, TLF, and residual orbital angular momenta) reflects how macroscopic relative orbital motion is redistributed via friction (sliding/rolling) mechanisms into intrinsic rotations (Zhang et al., 16 Jul 2025).
• Impact Parameter and Dynamical Pathways. A decrease in impact parameter enhances nucleon exchange and friction, increasing both mean and width of $S$ distributions. Ratios such as $S_{\text{PLF}}/S_{\text{TLF}}$ are found intermediate between sticking and rolling limits, indicative of mixed-mode dissipation.
• Mutual Information and Correlations. Mutual information between spin observables of the fragments increases under strong friction/nucleon exchange but remains moderate, indicating only weak correlations in intrinsic spins under typical MNT conditions.

6. Applications, Validation, and Implications

Multinucleon final-states are critical in multiple contexts:

• Validation of Nuclear Many-Body Models. Residue momentum distributions, opening angle correlations, and event-by-event kinematical analyses (e.g., Dalitz plots) provide stringent benchmarks for shell–model, ab initio, and EDF-based nuclear structure models (Simpson et al., 2010, Wimmer et al., 2012).
• Neutrino-Nucleus Interaction Modeling. Correct treatment of multinucleon ejection is vital for neutrino oscillation experiments. Models omitting correlated 2p–2h/3p–3h strength substantially underestimate experimental cross sections and energy reconstruction accuracy (Benhar et al., 2015, Sobczyk et al., 2020, Ankowski et al., 13 Aug 2025).
• Nuclear Structure and Production of Exotic Isotopes. Isospin equilibration and transfer reactions enable routes to neutron-rich nuclei production and probe the density dependence of the symmetry energy and pairing.
• Quantum Correlations and Entanglement. Quantum information observables provide new tools for dissecting many-body dynamics, establishing links between entanglement measures and directly measurable nucleon-number fluctuations (Li et al., 28 Mar 2024).
• Limits for Kaonic and Hypernuclear States. The inclusion of multinucleon absorption in $K^-$ optical potentials leads to widths exceeding binding energies and negates the existence of experimentally observable narrow kaonic nuclear states (Hrtankova et al., 2017).

7. Summary Table: Notable Multinucleon Final-State Phenomena and Modeling Approaches

Observable/Process	Key Modeling Tool	Distinctive Feature/Result
2N knockout residue momentum	RMSGA, SF, LS-coupling shell model	Distribution width traces total pair OAM $L$
Transparency (e,e′pN)	RMSGA, toy geometric models	$T_A^{pN} \sim A^{-0.4 \ldots -0.5}$, SRC features robust
2p–2h/3p–3h in $\nu$-nucleus	SF, MC, MEC+correlation interference	Explains observed cross section excess (MiniBooNE)
Heavy-ion MNT fragment $S$	TD-CDFT + angular momentum projection	Broad $S$, friction converts $\Lambda \to S$
Entanglement entropy vs. $\Delta N$	TD-CDFT, von Neumann vs. Shannon	$L \sim (8\ln2)\Delta N^2$ (linear bound)

The theoretical, computational, and experimental treatment of multinucleon final-states is a cornerstone of contemporary nuclear reaction and structure physics. From modeling short-range nucleon-nucleon correlations and mediating FSI, to mapping spin and entanglement in transfer reactions, the field presents ongoing challenges and opportunities for deeper understanding of quantum many-body dynamics in nuclei.