Does the Mott problem extend to Geiger counters?

Abstract

Abstract The Mott problem is a simpler version of the quantum measurement problem that asks: Is there a microscopic physical mechanism – based (explicitly or implicitly) only on Schroedinger’s equation – that explains why a single alpha particle emitted in a single spherically symmetric s-wave nuclear decay produces a manifestly nonspherically symmetric single track in a cloud chamber? I attempt here to generalize earlier work that formulated such a mechanism. The key ingredient there was identification of sites at which the cross section for ionization by a passing charged particle is near singular at ionization threshold. This near singularity arose from a Penning-like process involving molecular polarization in subcritical vapor clusters. Here, I argue that the same Mott problem question should be asked about Geiger counters. I then define a simple experiment to determine if ionization physics similar to the cloud chamber case takes place in the mica window of a Geiger counter and explains the collimation of wavefunctions that are spherically symmetric outside the counter into linear ion tracks inside. The experiment measures the count rate from a radioactive point source as a function of source-window separation. I have performed a proof of concept of this experiment; results are reported here and support the near-singular-ionization picture. These results are significant in their own right, and they may shed light on physical mechanisms underlying instances of the full quantum measurement problem. I illustrate this for the Stern–Gerlach experiment and a particular realization of superconducting qubits. I conclude by detailing further work required to flesh out these results more rigorously.