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

Classical trajectory and quantum calculations of helium three-body recombination are compared. The energies treated range from the ultracold up to the thermal regime. Quantum calculations are performed for the $J^{\Pi}$ = $0^{+}$ symmetry of the three-body recombination rate in order to compare with the classical results for zero angular momentum, yielding a good agreement for $E\sim$ 1 K. The classical calculations are treated as a scattering process in $n=6$-dimensions, and the results emerge from trajectory calculations. 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 for a hard hypersphere that resembles the well-known shadow scattering in two-body collisions.