Comparison of classical and quantal calculations of helium three-body recombination

Abstract

A general method to study classical scattering in $n$-dimension is developed. Through classical trajectory calculations, the three-body recombination is computed as a function of the collision energy for helium atoms, as an example. Quantum calculations are also performed for the $J^{\Pi }$ = $0^{+}$ symmetry of the three-body recombination rate in order to compare with the classical results, yielding good agreement for $E\gtrsim$ 1 K. The classical threshold law is derived and numerically confirmed for the Newtonian three-body recombination rate. Finally, a relationship is found between the quantum and classical three-body hard hypersphere elastic cross sections which is analogous to the well-known shadow scattering in two-body collisions.

13 pages, 6 figures

References in corpus (4)

• Adiabatic hyperspherical study of triatomic helium systems
• Rate of three-body recombination of hydrogen molecules during primordial star formation
• Sturmian theory of three-body recombination: application to the formation of H${}_2$ in primordial gas
• New Calculations of Recombination Rates for Cold ${}^4$He Atoms and Determination of Universal Scaling Functions

Cited by in corpus (18)

• Universal few-body physics and cluster formation
• Energy scaling of cold atom-atom-ion three-body recombination
• Universal temperature dependence of the ion-neutral-neutral three-body recombination rate
• Cold chemistry: a few-body perspective on impurity physics of a single ion in an ultracold bath
• Three-body recombination in physical chemistry
• Ozone formation in ternary collisions: Theory and experiment reconciled
• Three-body recombination near a narrow Feshbach resonance in ${}^6$Li
• On the formation of van der Waals complexes through three-body recombination
• Classical threshold law for the formation of van der Waals molecules
• Vibrational quenching and reactive processes of weakly bound molecular ion-atom collisions at cold temperatures
• Three-Body Recombination of Ultracold Microwave-Shielded Polar Molecules
• Ion-atom-atom three-body recombination: from the cold to the thermal regime
• Energy-scaling of the product state distribution for three-body recombination of ultracold atoms
• Ion-atom-atom three-body recombination in cold hydrogen and deuterium plasmas
• Hyperradial distribution function of few-body problems: a new arena for extreme value theory
• Observation of quantum capture in an ion-molecule reaction
• Classical Grand Angular Momentum in N-Body Problems
• Universality in Ionic Three-body Systems Near an Ion-atom Feshbach Resonance