A novel approach to the observation of the condensate fraction in superfluid helium four

We present a phenomenological analysis of an experiment to observe the condensate fraction of helium four by firing low energy pulses of helium atoms at suspended droplets of the superfluid and observing the resulting emission of helium atoms from the fluid. The analysis shows that two kinds of process will result in such emission: In a conventional process in which rotons are produced and propagate to the other side of the droplet, causing reemission of helium atoms, the cross-section scales quadratically with the geometrical area of the incoming beam. In another process depending on the existence of the condensate fraction, a lowest order calculation predicts that the cross-section scales with the fourth power of the area of the incoming beam. However a preliminary calculation of the matrix elements suggests that the first order calculation may not be adequate for the experimental conditions envisioned. We briefly discuss possible consequences of this.