The effects of indiscernibility can be observed in scattering experiments. Let us consider an elastic collision between a helium nucleus (also called an a-particles) and an oxygen nucleus. We look at the collision in the centre-of-mass frame, in which the particles have antiparallel velocities both before and after the collision. Suppose that a counter D is placed on an axis perpendicular to the initial trajectory of the particles. If we repeat the experiment many times and measure sparately the rate Fa of a-particles scattered into D and the rate FOXY of oxygen nuclei also scattered into D, we find FOXY = Fa. This result is easily understood taking into account the fact that for each oxygen nucleus scattered into D, an a-particle is scattered in the opposite direction. But since the direction pointing D is perpendicular to the initial trajectory, also the oppisite direction is. Therefore, for symmetry reasons, the rate of a-particles scattered in this opposite direction must equal Fa. Hence FOXY = Fa. The total rate of particles counted by D (disregarding whether they are helium or oxygen) is therefore FTOT = Fa+ FOXY = 2Fa. We can repeat the experiment by changing the target particle (for example replacing oxygen by carbon or beryllium): we always get FTOT = 2Fa . But now suppose that the target particles are themselves a-particles. In this case, we find FTOT = 4Fa; in other words, FTOT is increased by a factor 2!
It must be stressed that this result has nothing to do with some special feature of helium. What really matters is the indiscernibility of the targets and the projetiles. In effect, if instead of using the same helium isotope for both the projectile and the target, we use for example 4He projectiles and 3He targets, the enhancement of FTOT is not observed. In fact, the projectile (4He) and the target (3He) are now distinguishable, so we recover the result found with oxygen.
An explanation of this phenomenon is provided by the indiscernibility principle. Since the colliding particles are now indiscernible, there are two indistinguishable paths leading to the detection of one particle in D (see Figure 2). Like in the double-slit experiment, the proobability amplitudes corresponding to these two indiscernible possibilities interfere.
a-particles are bosons. What now if we repeat the experiment with two identical fermions, for example with two electrons with parallel spin? The result is even more amazing. Again the value of FTOT is different from what is expected for distinguishable particles, but this time FTOT = 0. In other words, no perpendicular scattering is observed.
