2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/198084Transverse ionization cooling of muons is modeled as a Brownian motion of the muon beam as it traverses a Li or Be rod. A Langevin like equation is written for the free particle case (no external transverse magnetic field) and for the case of a harmonically bound beam in the presence of a focusing magnetic field. We demonstrate that the well known muon cooling equations for short-absorbers can be extrapolated to the useful case of a long absorber rod with a focusing magnetic field present.Latex uses revtex, 9 pages; submitted to Phys. Rev EAccelerator Physicstext