Molecular effects in low-energy muon transfer from muonic hydrogen to oxygen

Abstract

In the present study we determine from the available experimental data the cross section of muon transfer to molecular oxygen at low energies with account of the oxygen molecule structure. Building on an earlier work, the results highlight the role of the molecular structure effects and signifcantly improve the agreement with theoretical calculations of the muon transfer rate. An effcient computational model of the kinetics of processes involving muonic hydrogen atoms in gaseous mixture of H2 and O2 is developed and analyzed. The model is applied in the description of the FAMU experiment for the measurement of the hyperfine splitting in muonic hydrogen and the Zemach radius of the proton.

Figures (7)

• Figure 1: The ratio of the stationary energy distribution of the muonic hydrogen atoms to the Maxwell-Boltzmann energy distribution $\mathbf{n}^{\rm(st)}(T)/\mathbf{n}^{\rm MB}(T)$ for H$_2$-O$_2$ gas target temperatures $T=$80, 104, 177, and 300 K. The values of the ratios at the mean thermal energies $E_T=3k_BT/2$, marked with circles, turn out to be very close to 1. Near epithermal states are overpopulated at the expense of subthermal and higher energy states.
• Figure 2: The kernels $\overline{g}(v;T)$ for the experimentally investigated temperature range, calculated with the $p\mu$ velocity distribution $\overline{f_A}$ of Eq. (\ref{['eq:nst']}) (solid lines), and extrapolated for higher temperatures (short-dashed lines). The thick dashed line represents the profile of the muon transfer cross section $\sigma(v)$.
• Figure 3: Values of the cross section $\sigma(v)$ of muon transfer from a $p\mu$ atom to an oxygen nucleus, calculated from Eq. (\ref{['eq:linsys']}) for a discrete set of relative velocities, corresponding to the nodes of Gauss-Hermite quadratures of rank $n_G=32$, 48, and 80. The error bars represent the statistical error due to the experimental uncertainty of the FAMU data. The solid line is a cubic interpolation of the discrete data points. The shadowed area illustrates the uncertainty related to the lack of data at higher temperatures. The vertical lines link the lower (velocity) and upper (energy) scales.
• Figure 4: Rate of muon transfer from muonic hydrogen to oxygen, obtained in the present work (solid), and its statistical uncertainty (shadowed area). For comparison: the theoretical curve of Ref. romanov22, variant C (dashed), the local peak positions and values, calculated in dupays1cdlin, and the energy dependence determined from experiment in ours without accounting for the oxygen molecular effects (dash-dotted). All rates are normalized to LHD.
• Figure 5: Comparison of the kernels $\overline{g}(v;T)$, calculated for temperatures $T=80$, 177, and 300 K with account of the oxygen nucleus motion described by the velocity distribution $\overline{f_N}$ (solid), and for frozen oxygen nuclei (dashed).