Zeros in Bosonic Wave-Function Result in Local Anti-Bunching: Refining Feynman's argument

The effect of boson bunching is frequently mentioned and discussed in the literature. This effect is the manifestation of bosons tendency to "travel" in clusters. One of the core arguments for boson bunching was formulated by Feynman in his well-known lecture series and has been frequently used ever since. By comparing the scattering probabilities of two bosons and of two non-identical particles, Feynman concluded: "We have the result that it is twice as likely to find two identical Bose particles scattered into the same state as you would calculate assuming the particles were different." [1]. Indeed, in most scenarios, this reasoning is valid, however, as it is shown in this paper, there are cases, even in the most ordinary scattering scenarios, where this reasoning is invalid, and in fact the opposite occurs: boson anti-bunching appears. Similarly, it is shown that at exactly the same scenarios, fermions bunch together.