⚛️ nuclear theory

Modeling quasielastic lepton-nucleus interactions with ab initio spectral functions from infinite nuclear matter

This paper presents a quasielastic lepton-nucleus scattering model within the local density approximation that utilizes ab initio spectral functions from infinite nuclear matter, interpolated by neural networks and incorporating final-state interactions, demonstrating good agreement with experimental data for various nuclei while assessing theoretical uncertainties.

Original authors: Alma L. Cavallin, Francesco Marino, Joanna E. Sobczyk

Published 2026-08-25

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CC BY 4.0

Original authors: Alma L. Cavallin, Francesco Marino, Joanna E. Sobczyk

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

To understand how the universe works at its most fundamental level, scientists often fire beams of tiny, ghostly particles called neutrinos at atomic nuclei. These neutrinos are elusive; they rarely interact with matter, but when they do, they can reveal secrets about the structure of the atom and the forces that hold it together. Next-generation experiments designed to study these particles need to know exactly what happens during these collisions to avoid mistakes in their measurements. The challenge lies in the complexity of the target: an atomic nucleus is not a simple, solid ball, but a crowded room of protons and neutrons moving in a chaotic, quantum dance. When a neutrino strikes one of these particles, it doesn't just knock it out; the remaining particles rearrange themselves, and the ejected particle often bumps into its neighbors on the way out. Predicting the outcome of this messy interaction requires a map of the nucleus's internal landscape, a task that has long been difficult to perform with high precision.

A team of researchers has now created a new, highly detailed map of this internal landscape to improve how scientists model these collisions. They focused on a specific type of interaction called quasielastic scattering, where a lepton (a particle like an electron or a neutrino) hits a nucleon (a proton or neutron) and knocks it out of the nucleus. To build their model, they started with the theoretical description of an infinite, uniform soup of nuclear matter, calculating exactly how the particles within it behave using advanced quantum mechanics. However, real atomic nuclei are finite and have varying densities, so the researchers had to translate their infinite calculations into a form that could describe specific atoms like carbon, oxygen, and calcium. To bridge this gap, they trained artificial neural networks—computer programs designed to recognize patterns—to act as a translator, interpolating their complex data so it could be applied to any point inside a nucleus.

The researchers tested their new framework by simulating how electrons and neutrinos scatter off these nuclei. They found that their model, which accounts for the interactions of the ejected particle with the rest of the nucleus as it escapes, matched experimental data remarkably well for a wide range of collision energies. When they ignored these final interactions, the model failed to predict the correct energy and direction of the outgoing particles, shifting the results by significant amounts. By including the full picture of how the particles interact, the team was able to reproduce the experimental observations for carbon-12, oxygen-16, and calcium-40 with high accuracy. They also calculated the total probability of neutrinos interacting with carbon-12, a crucial measurement for current neutrino experiments, and found their results aligned closely with existing data from the Liquid Scintillator Neutrino Detector.

One of the key strengths of this work is its ability to quantify how uncertain the predictions are. The researchers showed that their model is reliable for collisions where the momentum transfer is moderate, but as the energy of the collision increases, the predictions become less certain because the underlying assumptions of their method begin to stretch. They also demonstrated that their results are robust, meaning they do not change drastically depending on which specific version of the nuclear force equations they used. This consistency gives scientists confidence that the model captures the essential physics of the nucleus. While the current approach works best for nuclei with equal numbers of protons and neutrons, the researchers have laid the groundwork to extend their method to more complex, asymmetric nuclei, which are the targets of future large-scale experiments.

The implications of this work extend beyond a single experiment. By providing a more accurate and consistent way to describe how particles interact with nuclei, this new framework helps reduce the systematic errors that currently limit the precision of neutrino research. This is vital for experiments aiming to determine the fundamental properties of neutrinos, such as their mass hierarchy and whether they violate the symmetry between matter and antimatter. The researchers noted that their method can be easily expanded to include other physical processes, such as the production of pions, which occur at higher energies. This flexibility means the model can grow alongside the experiments, offering a unified tool to interpret data across different energy scales and target materials. Ultimately, this work provides a clearer window into the quantum world, turning a previously blurry picture of nuclear interactions into a sharp, reliable image that scientists can use to explore the deepest questions in physics.

Technical Summary: Modeling Quasielastic Lepton-Nucleus Interactions with Ab Initio Spectral Functions

Problem Statement
Next-generation neutrino oscillation experiments (e.g., DUNE, T2HK) require precise theoretical modeling of neutrino-nucleus interactions to control systematic uncertainties. A central challenge is the consistent treatment of different interaction channels and final-state interactions (FSI) within a single framework. While spectral function (SF) formalisms are widely used, FSI are often neglected or treated approximately (e.g., via optical potentials). Furthermore, existing microscopic calculations of electroweak cross-sections have been limited to inclusive observables using Green's function Monte Carlo or coupled-cluster theory, often lacking a consistent treatment of FSI in the particle sector. There is a need for a framework that incorporates ab initio spectral functions for both the initial (hole) and final (particle) states to improve the description of quasielastic (QE) scattering, particularly in the low-to-medium momentum transfer regime relevant for neutrino experiments.

Methodology
The authors propose a framework based on the Local Density Approximation (LDA) and the Impulse Approximation (IA) to model inclusive lepton-nucleus scattering.

Theoretical Foundation:
- Spectral Functions (SFs): The study utilizes ab initio spectral functions for infinite symmetric nuclear matter (NM) derived from Self-Consistent Green's Functions (SCGF) theory using the Gorkov framework. These calculations employ realistic nuclear Hamiltonians from chiral effective field theory (specifically $\Delta$ N2LOGO(394), $\Delta$ N2LOGO(450), and N2LOsat(450)) and the Algebraic Diagrammatic Construction (ADC) method at the "ADC(3)-D" truncation level.
- LDA Implementation: Finite nuclei ( $^{12}$ C, $^{16}$ O, $^{40}$ Ca) are modeled by integrating the infinite NM SFs over the nuclear density profile $\rho(r)$ . The framework includes both the hole SF ( $S_h$ ), describing the initial bound nucleon, and the particle SF ( $S_p$ ), accounting for FSI.
- Two Models: Two kinematical regimes are considered:
  - IA+FSI: Uses ab initio NM SFs for both hole and particle sectors.
  - PWIA (Plane Wave Impulse Approximation): Uses ab initio hole SFs but replaces the particle SF with a relativistic Fermi gas model (accounting only for Pauli blocking), suitable for higher momentum transfers where the non-relativistic ab initio SFs become unreliable.
Neural Network Interpolation:
- Since SCGF calculations provide SFs at discrete points in energy, momentum, and density, the authors developed artificial neural networks (ANNs) to interpolate these data continuously.
- Six separate networks were trained (one for each combination of three Hamiltonians and two isospins: proton/neutron).
- The input features are energy ( $E$ ), momentum ( $|p|$ ), density ( $\rho$ ), and a smoothing factor ( $\Gamma$ ). The output is the spectral function value.
- A physics-informed loss function was employed, incorporating a penalty term to enforce the normalization sum rule ( $\int dE S(E) = 1$ ).
Cross-Section Calculation:
- The hadron tensor is constructed by integrating the product of hole and particle SFs over the nuclear volume.
- The framework calculates electromagnetic (EM) responses and charged-current (CC) responses, including flux-averaged total cross-sections for neutrino scattering.

Key Contributions

Consistent FSI Treatment: The paper introduces a consistent treatment of FSI using the particle spectral function derived ab initio, rather than relying on phenomenological optical potentials.
Neural Network Interpolation: The development of ANNs to interpolate high-dimensional ab initio spectral function data, enabling their use in cross-section calculations for arbitrary kinematic variables.
Benchmarking: The model is benchmarked against experimental electron scattering data for $^{12}$ C, $^{16}$ O, and $^{40}$ Ca, as well as against ab initio LIT-CC (Lorentz Integral Transform with Coupled-Cluster) calculations for $^{16}$ O.
Neutrino Predictions: The framework is applied to predict charged-current responses for $^{16}$ O and the flux-averaged total $\nu_\mu$ - $^{12}$ C cross-section, comparing results with LSND experimental data.

Results

Electron Scattering:
- For $^{12}$ C, the IA+FSI model shows remarkable agreement with Rosenbluth-separated experimental data for the longitudinal response ( $R_L$ ) at $\omega \lesssim \omega_{QE}$ across various momentum transfers.
- The inclusion of FSI corrects the peak position and strength compared to the PWIA model, which tends to shift the QE peak to higher energies and overestimate strength.
- The transverse response ( $R_T$ ) is systematically underestimated, consistent with the exclusion of two-body currents in the calculation.
- For $^{16}$ O, the IA+FSI results agree well with LIT-CC calculations near the QE peak, though the LDA approach lacks the detailed shell-structure threshold effects seen in the LIT-CC results.
- For $^{40}$ Ca, the model reproduces experimental data well, showing good agreement in both longitudinal and transverse channels.
Neutrino Scattering:
- The flux-averaged total $\nu_\mu$ - $^{12}$ C cross-sections calculated with the IA+FSI model are consistent with LSND experimental data.
- The PWIA model yields cross-sections approximately 20% lower than IA+FSI, attributed to the shift of the QE peak outside the integration window at lower momenta.
- Theoretical uncertainties (from Hamiltonian choice and smoothing factor $\Gamma$ ) are assessed to be around 7–15% at the QE peak for momentum transfers $|q| \approx 0.2\text{--}0.6$ GeV.

Significance and Claims
The authors claim that their framework provides a "good agreement with experimental data within the range of validity of our approximations" (specifically low-to-medium momentum transfers). The significance lies in:

Improved Consistency: Providing a microscopic, ab initio description of both initial and final states within the LDA, which is particularly well-suited for neutrino oscillation experiments where the broad energy flux smears out detailed shell structures.
Extensibility: The framework is designed to be readily extended to include additional dynamical mechanisms (such as in-medium pion production) and other nuclear Hamiltonians.
Validation: The successful benchmarking against electron data and LIT-CC calculations validates the approach for inclusive observables in isospin-symmetric nuclei.

The paper modestly notes limitations: the LDA sacrifices detailed shell structure (making it less suitable for exclusive $(e, e'p)$ data), and the model breaks down at very high momentum transfers where relativistic corrections and mechanisms beyond QE (like pion production) become dominant. Future work is outlined to extend the SCGF calculations to isospin-asymmetric matter (relevant for $^{40}$ Ar in DUNE) and to combine the framework with intranuclear cascade models.

Technical Summary: Modeling Quasielastic Lepton-Nucleus Interactions with Ab Initio Spectral Functions

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