Three-body recombination of helium atoms from ultracold to thermal energies: classical trajectory vs. quantal calculations*

A general method to study classical scattering in $n$-dimensions is developed. Through classical trajectory calculations the new method is applied to compute the three-body recombination rate 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 $E\sim$ 1 K. The classical threshold law is derived and numerically confirmed for the three-body recombination rate. Finally, a relationship is found between the quantum and classical three-body elastic cross section which exhibits a similarity to the well-known shadow scattering in two-body collisions.\\[4pt] [1] J. P\'{e}rez-R\'{i}os et al., J. Chem. Phys. {\bf 140}, 044307 (2014).