Scaling calculation of the scattering of super(4)He atomic beams

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 lambda while the collision cross-section is increased by lambda . 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 super(4)He- super(4)He atomic scattering cross-section sigma at low energies. Because of the existence of a very weakly bound dimer, the low energy cross-section is expected to be unusually large, approx. 1.83 x 10 super(5) angstrom super(2). In the simulation N/ lambda 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 sub(r) between approx. 2 and approx. 8 m/sec, corresponding to relative energies between approx. 1 and approx. 16 mK. By fitting sigma (v sub(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.