Gianfausto Dell'Antonio, "Mott's problem: tracks in a cloud chamber"

I will in the first part of the talk (which will be as little technical as possible) introduce the zero-range interactions and and explain which sort of interactions they mimick (short range, large scattering lenght). I shall give at least some elements of the role zero energy resonances and the reason why the Birman kernel comes into play (I will not give the proof of resolvent convergence as it is in the book of Albeverio et al.). I will point out the connection between Krein's extension and the presence of a resonance. I will briefly comment on the three particles case (Efimov effect versus "fall to the centre" of Minlos and Faddaev). In the second part of the talk I will use the zero range interaction (as solvable model in which everything is explicit) to discuss the Mott problem (particle-like tracks in a cloud chamber as a result of the interaction of a wave (the "alfa-wave" produced in a decay) with the atoms in the chambers), and the need of the "reduction postulate".