Schrödinger Equation Solution Reproduces Nuclear Cluster Radii and Binding Energies

Understanding the structure of light atomic nuclei and their exotic counterparts, hypernuclei, remains a fundamental challenge in nuclear physics, and researchers are now providing new insights into these complex systems. Jiaxing Zhao, from the Institute for Theoretical Physics at Johann Wolfgang Goethe Universität, along with colleagues including Joerg Aichelin and Elena Bratkovskaya, have calculated the Wigner phase-space densities for a range of nuclear clusters and hypernuclei, offering a detailed picture of their internal structure. By solving the Schrödinger equation with realistic interactions between nucleons, the team accurately reproduces known properties like size and binding energy, and importantly, provides data that will refine methods used to identify these clusters in the aftermath of heavy-ion collisions. This improved understanding of cluster formation promises to advance our knowledge of matter under extreme conditions, relevant to both astrophysics and the study of the strong force.

Researchers have solved the Schrödinger equation for few-body systems, determining the wave function for light nuclear clusters and hypernuclei ranging from deuterium to ⁵ΛΛHe. This work utilizes realistic interactions between nucleons to accurately model these systems and projects the solutions onto a mathematical framework called hyperspherical harmonic basis states, allowing the team to calculate density matrices and Wigner densities, which describe the distribution of particles in both position and momentum. The method successfully reproduces experimentally measured sizes and binding energies of these clusters, validating its accuracy.

Realistic Few-Body Interactions and Nuclear Matter Equation of State

This research develops a sophisticated theoretical framework for studying systems with a small number of protons and neutrons, providing fundamental insights into the behavior of larger nuclei and dense nuclear matter. The core focus lies in employing realistic interactions between nucleons, crucial for making accurate predictions about nuclear systems, and determining the equation of state of nuclear matter at various densities, relevant to understanding neutron stars and the conditions created in heavy-ion collisions. The framework also models and explains nuclear reactions. The team’s approach is based on solving the complex many-body problem using hyperspherical harmonics and extending it to larger systems, connecting with established techniques like Coupled Cluster and the No-Core Shell Model for cross-validation.

The framework includes methods for calculating high-order corrections to improve accuracy and optimizes computational efficiency, enabling calculations with realistic interactions for larger systems, and explores the use of machine learning to accelerate calculations. The work utilizes nucleon-nucleon and three-nucleon interactions derived from chiral effective field theory, employing specific potentials like Argonne v18 and various chiral potentials with consistent regularization schemes. This research calculates ground state properties of light nuclei, predicts scattering observables for nucleon-nucleon and nucleon-alpha scattering, and determines the energy spectra of few-body systems, aiming to constrain the properties of neutron stars and provide insights into heavy-ion collisions, while also investigating alpha-cluster phenomena in light nuclei. The combination of realistic interactions, advanced theoretical methods, and high-performance computing makes this a valuable contribution to the field.

Wigner Density Calculations Bridge Theory and Experiment

Researchers have made a significant advance in understanding the formation of light nuclei and exotic hypernuclei, bridging the gap between fundamental calculations of nuclear structure and observations from high-energy heavy-ion collisions. They have developed a method to accurately calculate the Wigner density, a quantum mechanical description of a cluster’s distribution in both position and momentum, directly from the solution of the Schrödinger equation, representing a substantial improvement over previous approaches. The team’s calculations employ realistic interactions between nucleons, accounting for both attractive and repulsive forces, and utilize a sophisticated mathematical framework known as hyperspherical harmonics to solve the complex many-body problem. By accurately determining the Wigner density, researchers can now predict the probability of cluster formation in heavy-ion collisions with greater precision, moving beyond models that require tuning to match experimental data, particularly for understanding the formation of hypernuclei, which contain strange quarks and provide insights into matter at extreme densities. The results demonstrate excellent agreement with experimentally measured properties of light nuclei, validating the accuracy of the computational approach, and offer a pathway to explore the role of strangeness in nuclear interactions and address long-standing puzzles in nuclear astrophysics, providing a rigorous, parameter-free framework for studying cluster production and linking the intrinsic quantum properties of the clusters to their observed yields.

Wigner Densities Reveal Nuclear Cluster Structure

This research presents a detailed solution to the Schrödinger equation for light nuclear clusters and hypernuclei, employing realistic interactions between nucleons and accurately reproducing experimentally known properties of these clusters, including their binding energies and root mean square radii, offering a comprehensive description of the complex many-body problem inherent in nuclear physics. The key contribution lies in the calculation of Wigner densities, which represent the phase-space distribution of nuclear clusters, and are expected to improve current methods used to identify clusters formed in heavy-ion collisions, offering a more refined understanding of the matter created in these extreme conditions. By accurately modelling the internal structure of these clusters, the research provides a crucial theoretical foundation for interpreting experimental results, while acknowledging limitations due to neglecting genuine three-body potentials, and opening avenues for exploring the dynamics of cluster formation and decay, potentially leading to new insights into the equation of state of nuclear matter.