Annales Henri Poincaré

, Volume 11, Issue 3, pp 539–564

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

• Gianfausto Dell’Antonio
• Rodolfo Figari
• Alessandro Teta
Article

DOI: 10.1007/s00023-010-0037-4

Dell’Antonio, G., Figari, R. & Teta, A. Ann. Henri Poincaré (2010) 11: 539. doi:10.1007/s00023-010-0037-4

## Abstract

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 a2 lies on the line joining the origin with a1. The work is a fully time-dependent version of the original analysis proposed by Mott in 1929.

## Authors and Affiliations

• Gianfausto Dell’Antonio
• 1
• 2
• Rodolfo Figari
• 3
• Alessandro Teta
• 4
1. 1.Dipartimento di MatematicaUniversitá di Roma “La Sapienza”RomeItaly
2. 2.S.I.S.S.ATriesteItaly
3. 3.Dipartimento di Scienze FisicheSezione I.N.F.N. di Napoli, Università “Federico II”NaplesItaly
4. 4.Dipartimento di Matematica Pura ed ApplicataUniversità di L’AquilaL’AquilaItaly
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