Isotope effects on antiproton and muon capture by hydrogen and deuterium atoms and molecules

Abstract

Cross sections for capture of the antiproton $(\overline{p})$ and negative muon $({\ensuremath{\mu}}^{\ensuremath{-}})$ by the ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ molecules are calculated using fermion molecular dynamics (FMD). All the cross sections are significantly larger than those for capture by the corresponding atom, also evaluated by the FMD method. The largest molecular cross sections are obtained when the negative projectile mass best matches the nuclear mass in the molecular target, thus for $\overline{p}+{\mathrm{H}}_{2}.$ The vibrational degree of freedom is shown to be most important in distinguishing the four reactions, but the effects of rotations, two-center electronic charge distribution, and nonadiabaticity are also significant. The predicted initial capture fractions (i.e., not taking subsequent transfer into account) in a ${\mathrm{H}}_{2}+{\mathrm{D}}_{2}$ mixture are ${P}_{\mathrm{capt}}^{(p)}{/P}_{\mathrm{capt}}^{(d)}{=qc}_{p}{/c}_{d},$ where $q=1.585$ for $\overline{p}$ and $q=1.186$ for ${\ensuremath{\mu}}^{\ensuremath{-}}$ independent of ${c}_{p}$ and ${c}_{d}.$ The energy-dependent quantum-number distributions of the exotic atoms formed, the angular distributions of antiprotonic atoms, and the initial kinetic energies of muonic atoms are also presented.