Classical-quantal coupling in the capture of muons by hydrogen atoms

Abstract

The authors describe a self-consistent semiclassical approach to the problem of muon capture by hydrogen atoms. The dynamics of the heavier muon and proton are treated classically, and the electron quantally, with the potentials for both being self-consistently determined. Their numerical results are compared to classical-trajectory Monte Carlo (CTMC) and adiabatic ionisation (AI) results. Their capture cross sections are larger at low energy but fall more rapidly to zero. Their results provide the corrections to the dynamics beyond the adiabatic picture, which were missing in other approaches; interesting questions concerning the quantal nature of the events are discussed.

Long-lived states of antiprotonic lithiump¯Li+produced inp¯Sakimoto1 2011Phys. Rev. A61180View full textAdd to dashboardCite

“…Another possibility of performing a reasonable study for such cases is to employ a semiclassical (SC) approximation, in which the electron motion is described by quantum mechanics, and the heavy particle motion is assumed to be classical. 1 The SC calculations of the capture process were carried out for a H target by Kwong et al [18] and the present author [19,20]. Although the SC method succeeded in reproducing the total capture cross sections obtained by previous QM calculations [20], it was unable to provide the product-state distribution.…”

Protonium formation in collinear collisions between antiprotons and hydrogen molecular ions: Quantum-classical hybrid method versus adiabatic approximation

“…In the QC method, there is no unique way to determine the time dependence of the classical variables R͑t͒ and r͑t͒. Here, we adopt common trajectories as in previous studies [14,18] by using the equations of motion…”

Adaptive Estimation of Intravascular Shear Rate Based on Parameter Optimization

“…The FMD method has been successfully applied to a number of problems involving capture of heavy negative exotic particles (muon µ − with mass 207m e , pion π − with mass 273m e , kaon K − with mass 966m e and antiprotonp with mass 1836m e ) by atoms, molecules and ions [7]. Though experimental results and accurate quantum-mechanical calculations for these problems are scarce, the FMD results [8] for capture of µ − andp by the hydrogen atom are in excellent agreement with quantum-mechanical [9,10] and hybrid quantum-classical calculations [11,12]. Also, FMD results are in excellent agreement with an experiment on π − capture in mixtures of the H 2 , D 2 and HD molecules [13], and in reasonably good agreement with capture ratios obtained in experiments with various mixtures of the noble gas atoms He, Ne, Ar, Kr and Xe [14,15].…”