The conventional description of nuclear structure relies heavily on the nuclear mass density function ρ(r) which captures the distribution of nucleons within the nucleus. Recent theoretical developments suggest that this view is incomplete because it neglects the spatial distribution of quantum informational content that arises from many–body correlations and entanglement among nucleons. In this paper we introduce the Nuclear Information Density Spectrum (NIDS), a formalism that assigns to each point inside a nucleus an information density function I(r). This function quantifies the amount of quantum information encoded at each spatial coordinate and is defined through the von Neumann entropy of reduced density matrices of local subsystems. By integrating I(r) over the nuclear volume we recover the total quantum informational content, while the shape of I(r) reflects the distribution of correlation strength throughout the nucleus. We derive explicit expressions for I(r) in terms of the two–body correlation function g2(r1,r2) and outline a strategy to extract I(r) from high–energy elastic and inelastic scattering experiments. The NIDS formalism provides a new lens to view the internal structure of nuclei, potentially redefining shell closures, deformation, and collective modes. Moreover, it offers a quantitative framework to assess the role of quantum correlations in nuclear binding, with implications for the interpretation of exotic nuclei and the equation of state of dense matter. The proposal that the nucleus contains an intrinsic information density invites fresh experimental investigations that could lead to a Nobel–level paradigm shift in nuclear physics.
The conventional description of nuclear structure relies heavily on the nuclear mass density function ρ(r) which captures the distribution of nucleons within the nucleus. Recent theoretical developments suggest that this view is incomplete because it neglects the spatial distribution of quantum informational content that arises from many–body correlations and entanglement among nucleons. In this paper we introduce the Nuclear Information Density Spectrum (NIDS), a formalism that assigns to each point inside a nucleus an information density function I(r). This function quantifies the amount of quantum information encoded at each spatial coordinate and is defined through the von Neumann entropy of reduced density matrices of local subsystems. By integrating I(r) over the nuclear volume we recover the total quantum informational content, while the shape of I(r) reflects the distribution of correlation strength throughout the nucleus. We derive explicit expressions for I(r) in terms of the two–body correlation function g2(r1,r2) and outline a strategy to extract I(r) from high–energy elastic and inelastic scattering experiments. The NIDS formalism provides a new lens to view the internal structure of nuclei, potentially redefining shell closures, deformation, and collective modes. Moreover, it offers a quantitative framework to assess the role of quantum correlations in nuclear binding, with implications for the interpretation of exotic nuclei and the equation of state of dense matter. The proposal that the nucleus contains an intrinsic information density invites fresh experimental investigations that could lead to a Nobel–level paradigm shift in nuclear physics.
The conventional description of the atomic nucleus relies heavily on the spatial distribution of nucleons, expressed by the nuclear density function ρ(r). While ρ(r) captures the average position of nucleons, it neglects the intrinsic quantum correlations that arise from the many-body wave function. In this paper, we introduce the Nuclear Information Density Spectrum (NIDS), a formalism that supplements the conventional density with an information density I(r), defined in terms of the local reduced density matrix and an entropic functional. I(r) quantifies the amount of quantum information and correlation present at each point inside the nucleus. We develop the mathematical foundations of NIDS, derive its properties, and discuss its implications for nuclear structure and scattering processes. By integrating NIDS into the analysis of scattering data, we demonstrate that it provides a more nuanced understanding of nuclear dynamics, potentially opening new avenues for precision tests of nuclear models and a deeper appreciation of the underlying quantum many-body physics.
Abstract Quantum entanglement offers a unique perspective into the underlying structure of strongly-correlated systems such as atomic nuclei. In this paper, we use quantum information tools to analyze the structure of light and medium-mass berillyum, oxygen, neon and calcium isotopes within the nuclear shell model. We use different entanglement metrics, including single-orbital entanglement, mutual information, and von Neumann entropies for different equipartitions of the shell-model valence space and identify mode-entanglement patterns related to the energy, angular momentum and isospin of the nuclear single-particle orbitals. We observe that the single-orbital entanglement is directly related to the number of valence nucleons and the energy structure of the shell, while the mutual information highlights signatures of proton–proton and neutron–neutron pairing, as well as nuclear deformation. Proton and neutron orbitals are weakly entangled by all measures, and in fact have the lowest von Neumann entropies among all possible equipartitions of the valence space. In contrast, orbitals with opposite angular momentum projection have relatively large entropies, especially in spherical nuclei. This analysis provides a guide for designing more efficient quantum algorithms for the noisy intermediate-scale quantum era.
A long-standing goal of nuclear theory is to explain how the structure and dynamics of atomic nuclei and neutron-star matter emerge from the underlying interactions among protons and neutrons. Achieving this goal requires solving the nuclear quantum many-body problem with high accuracy across a wide range of length scales and density regimes. In this review, we discuss how artificial neural network representations of the nuclear many-body wave function have significantly extended the capabilities of continuum quantum Monte Carlo methods. In particular, neural network quantum states enable calculations of larger systems than were previously accessible and provide a flexible framework for capturing phenomena that challenge conventional approaches, including the emergence of nuclear clusters and superfluid phases in dense matter. We highlight recent applications to finite nuclei, infinite nuclear and neutron matter, and dynamical processes relevant to lepton-nucleus and nucleus-nucleus scattering. We also discuss conceptual and methodological connections with condensed matter physics, emphasizing developments in neural network quantum states that bridge strongly correlated systems across disciplines. Together, these developments demonstrate how neural-network methods open new avenues toward unified and accurate descriptions of nuclear structure, matter, and reactions.
This study introduces a quantum information perspective to analyze the internal structure of atomic nuclei, focusing on the quantum entanglement between α clusters in the 0+ state of 8Be. A wave function based on angular momentum coupling is developed to transform the two-cluster wave function from the conventional center of mass and relative coordinate basis (HRc.m.⊗Hr) into the individual particle basis (H1⊗H2), which is essential for a precise quantification of entanglement. Within this method, the von Neumann entropy is employed to quantify the entanglement arising from the mixing of angular momentum channels. Additionally, we introduce the concept of spatially resolved entropy, which measures entanglement as a function of the radial separation between clusters. Our analysis reveals that the entanglement is strongly correlated with the spatial configuration at the femtometer scale. As the inter cluster separation vanishes, the system approaches a separable S-wave state, indicating that entanglement is dynamically generated during the spatial separation of the clusters. This research provides a new tool for investigating nonlocal quantum correlations in nuclear structure, complementing existing descriptions.
The properties of one-body and two-body density matrices of a nucleus as a nonrelativistic system are studied. Unlike the usual procedure applied in the theory of infinite systems, for a nucleus of A nucleons these quantities are determined as the expectation values of A-body multiplicative operators that depend on the relative coordinates and momenta (Jacobi variables) and affect the intrinsic wave functions. The translational invariance of these operators is thus ensured. An algebraic technique based on the Cartesian representation is developed for handling such operators. Within this technique, the coordinate and momentum operators are linear combinations of production and annihilation operators $$\hat \vec a^ + $$ and $$\hat \vec a$$ with commutation relations for bosons (oscillators). Each of the multiplicative operators reduces to the normally ordered product of two exponents, one of which depends on set $$\left\{ {\hat \vec a^ + } \right\}$$ only and is located to the left of the second, which depends on $$\left\{ {\hat \vec a} \right\}$$ only. This procedure offers a new view of the origin of the so-called Tassie–Barker factors and other model-independent results. In addition, the proposed method yields a fair description of the available experimental data and can easily be extended to investigate the role of short-range nucleon-nucleon correlations within these translationally invariant calculations of nucleon density and momentum distributions in light nuclei.
Efforts to describe nuclear structure and dynamics from first principles have advanced significantly in recent years. Exact methods for light nuclei are now able to include continuum degrees of freedom and treat structure and reactions on the same footing, and multiple approximate, computationally efficient many-body methods have been developed that can be routinely applied for medium-mass nuclei. This has made it possible to confront modern nuclear interactions from Chiral Effective Field Theory, that are rooted in Quantum Chromodynamics with a wealth of experimental data. Here, we discuss one of these efficient new many-body methods, the In-Medium Similarity Renormalization Group (IMSRG), and its applications in modern nuclear structure theory. The IMSRG evolves the nuclear many-body Hamiltonian in second-quantized form through continuous unitary transformations that can be implemented with polynomial computational effort. Through suitably chosen generators, we drive the matrix representation of the Hamiltonian in configuration space to specific shapes, e.g., to implement a decoupling of low-and high-energy scales, or to extract energy eigenvalues for a given nucleus. We present selected results from Multireference IMSRG (MR-IMSRG) calculations of open-shell nuclei, as well as proof-of-principle applications for intrinsically deformed medium-mass nuclei. We discuss the successes and prospects of merging the (MR-)IMSRG with many-body methods ranging from Configuration Interaction to the Density Matrix Renormalization Group, with the goal of achieving an efficient simultaneous description of dynamic and static correlationsin atomic nuclei.