Annales Henri Poincaré

, Volume 11, Issue 3, pp 539-564

First online:

A Time-Dependent Perturbative Analysis for a Quantum Particle in a Cloud Chamber

  • Gianfausto Dell’AntonioAffiliated withDipartimento di Matematica, Universitá di Roma “La Sapienza”S.I.S.S.A
  • , Rodolfo FigariAffiliated withDipartimento di Scienze Fisiche, Sezione I.N.F.N. di Napoli, Università “Federico II”
  • , Alessandro TetaAffiliated withDipartimento di Matematica Pura ed Applicata, Università di L’Aquila Email author 

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We consider a simple model of a cloud chamber consisting of a test particle (the α-particle) interacting with two quantum systems (the atoms of the vapor) initially confined around \({a_1, a_2 \in \mathbb{R}^3}\) . At time zero, the α-particle is described by an outgoing spherical wave centered in the origin and the atoms are in their ground state. We show that, under suitable assumptions on the physical parameters of the system and up to second order in perturbation theory, the probability that both atoms are ionized is negligible unless a 2 lies on the line joining the origin with a 1. The work is a fully time-dependent version of the original analysis proposed by Mott in 1929.