A Scaling Calculation of the Scattering of ⁴He Atomic Beams

Abstract

We describe a simulation of the scattering in beams of helium atoms. The number of atoms N in the beams is reduced by a large scaling factor λ while the collision cross-section is increased by λ. This leaves the rate of scattering for each particle unchanged. As an example, we predict the outcome of a low temperature atomic beam experiment to measure the ⁴ He- ⁴ He atomic scattering cross-section σ at low energies. Because of the existence of a very weakly bound dimer, the low energy cross-section is expected to be unusually large, ∼1.83 × 10 ⁵ Å ² . In the simulation N/λ is small enough for the trajectories of all the scaled atoms to be calculated numerically. The simulation shows that the experiment is quite practicable. The proposed apparatus is just over 20 cm long, and a few centimeters wide, small enough to fit in a dilution refrigerator. The heaters and bolometers are assumed to be similar to those used in previous low temperature scattering experiments. We show that, using low intensity beams, the cross-section can be measured as a function of the relative velocity v _r between ∼2 and ∼8 m/sec, corresponding to relative energies between ∼1 and ∼16 mK. By fitting σ(v _r) one can determine the scattering length and effective range of the interaction. We predict that, at high intensity where multiple scattering is very important, the two beams coalesce into one.