Three-Particle Interactions Fully Mapped with Novel Scattering Technique

Researchers Romain Guérout at the University Paris-Saclay and colleagues are presenting calculations utilising the configuration-space Faddeev formalism to investigate the scattering of three particles, with a specific focus on scenarios where all particles are initially and finally in free, unbound states, a condition known as the double continuum. The methodology consolidates all possible scattering processes, encompassing transitions between single-particle and two-particle continua, into a single, comprehensive matrix. This provides a more efficient and systematic approach to analysing these complex interactions. Application of this technique to the benchmark system of neutron-deuteron scattering is intended to refine our understanding of the underlying nuclear forces.

Improved coordinate separation enhances three-body scattering precision near π/2

A substantial five-fold enhancement in the precision of three-body scattering calculations has been demonstrated, reducing uncertainties in the determination of breakup amplitudes to within 5% in the vicinity of a critical polar angle of π/2. Prior to this work, calculations suffered from limited precision in this crucial angular region due to slow convergence behaviour in the asymptotic region, that is, at large inter-particle separations. This improvement arises from a sophisticated refinement of the method used to separate two-particle and three-body contributions within the double continuum. The researchers employ a combination of Jacobi and polar coordinates to meticulously describe the interactions between the constituent particles. Jacobi coordinates are particularly useful for transforming the three-body problem into an equivalent two-body problem, simplifying the mathematical treatment, while polar coordinates facilitate the description of angular distributions. This combined approach allows for a more accurate modelling of the intricate dynamics of nuclear interactions, and analysis of the resulting scattering matrix revealed that the coupling term in the double continuum channel decays as 1/y^3/2 as the separation variable, y, approaches infinity.

This slower convergence rate, in comparison to calculations involving only single continua, previously posed a significant limitation on the achievable accuracy. The three-body reduced mass, denoted as 2μ_3B, has been rigorously validated across various Jacobi coordinate arrangements, confirming the robustness and consistency of the computational method. The reduced mass is a crucial parameter in the three-body problem, representing the effective mass of two particles orbiting a third, and its invariance under coordinate transformations is a key indicator of the reliability of the formalism. A 3×3 transition matrix, effectively linking elastic scattering, breakup processes (where one particle dissociates from the other two), and three-body recombination processes (where all three particles bind temporarily), was successfully calculated using the unified matrix approach to collect all scattering events. The elements of this matrix represent the probabilities of transitioning between these different outcomes.

This allows for a detailed examination of the complex interplay between these fundamental nuclear processes, providing insights into how energy and momentum are exchanged during collisions. Future research will focus on investigating how this transition matrix evolves as different nuclear configurations and interaction strengths are considered. Such investigations are expected to yield a deeper understanding of the intricate relationships between these fundamental nuclear reactions and the underlying strong nuclear force. Accurate modelling of three-particle interactions is of paramount importance for furthering our understanding of the strong nuclear force, the fundamental interaction responsible for binding protons and neutrons together within atomic nuclei. The strength and range of this force dictate the stability of nuclei and the properties of nuclear matter.

The unification of processes where particles remain bound together and those where they break apart into a single, cohesive framework provides scientists with a clearer and more comprehensive picture of these collisions. Like many approaches in this field, the current formalism still relies on approximations to simplify the inherently complex mathematics involved in solving the three-body Schrödinger equation. Further research will likely concentrate on extending this formalism to encompass heavier nuclei, which present significantly greater computational challenges, and more intricate interactions, potentially including relativistic effects. This refined computational approach offers a single, unified framework to study both two-fragment and three-fragment breakup scenarios, simplifying calculations that were previously hindered by imprecise separation of these outcomes. Establishing the independence of the three-body reduced mass from the choice of coordinate arrangement serves as a strong validation of the technique’s reliability and opens up exciting possibilities regarding its application to systems beyond those consisting of three identical nucleons. This could potentially allow for the investigation of more complex nuclear species and interactions, such as those involving different types of nucleons (protons and neutrons) or the inclusion of many-body forces, ultimately leading to a more complete and accurate description of nuclear phenomena.

The researchers successfully developed a unified mathematical framework to study the scattering of three particles, demonstrated using neutron-deuteron interactions. This approach combines processes where particles remain bound with those where they break apart, offering a more complete understanding of these collisions. Accurate modelling of these interactions is important for improving knowledge of the strong nuclear force, which binds protons and neutrons within atomic nuclei. The authors intend to extend this formalism to heavier nuclei and more complex interactions, potentially refining the description of nuclear phenomena.