On the Energy Dependence of the Rate of Muon Transfer from Proton to Oxygen

Experimental determination of the energy dependence of the rate of the muon transfer reaction from muonic hydrogen to oxygen for collision energies up to 0.1 eV

“…While the results in Refs. [24,25,29] are in qualitative agreement with each other, the remaining significant quantitative discrepancy only reaffirms the need of such reliable references.…”

“…There are no evidences of threshold phenomena or processes that would give rise to discontinuities or singularities of λ pO (E) in the considered range of collision energies. The theoretical calculations in [24,25,29] also predict a smooth energy dependence. We therefore restrict our search to the class of C ∞ trial functions.…”

“…In analogy, one may expect that the "flat behavior" of λ pO (E) is displayed in the energy range below E W < ∼ 10 −7 ε µ ∼ 10 −3 eV, where ε µ = m µ c 2 α 2 ∼ 5 keV denotes the "µ-atomic unit of energy"; the numerical results of Refs. [24,25,29] point at even slightly higher values of E W . We therefore impose the constraint…”

“…within the method of perturbed stationary states [23,24], and in the hyperspherical approach [25][26][27][28][29][30]. On the experimental side, the scarce amount of muonic hydrogen atoms (as compared with charge transfer experiments with electronic atoms), and the short lifetime of the muon, required the use of techniques inspired by experimental particle physics, such as the analysis of the time evolution of the characteristic X-ray spectra.…”

“…The interest in the subject was revived a few years later in relation to the projects to measure the hyperfine splitting in the ground state of muonic hydrogen [42][43][44][45][46], and extract out of it the value of the electromagnetic Zemach radius of the proton [47,48]. In a series of advanced theoretical calculations [24,25,29] significant progress was achieved in the quantitative description of the process (3) for energies up to 10 eV, but these theoretical results necessitate experimental verification. The breakthrough came with the recent results of the FAMU collaboration [49,50], which performed the first experimental investigation of the temperature dependence of the rate of muon transfer from hydrogen to oxygen.…”