Formation rate of muonic molecules in an alloy of deuterium and tritium.

Abstract

For the purpose of understanding how the interaction between target molecules affects the resonant formation mechanism of muonic molecules and, as a result, how the density dependence of the formation rate deviates from the linearity observed in a dilute gas of targets, we examine a rather exotic problem of the muonic-molecule formation in a metallic phase of a mixture of deuterium and tritium. As the mechanism in the alloy we can enumerate multiphonon, plasmon, and electron-hole pair excitations, each of which plays a role of an absorber of the energy released as a weakly bound muonic molecule forms. The calculated normalized formation rate for the multiphonon excitation process takes values of the order of ${10}^{8}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at ${r}_{s}$=1.2 bohrs and much larger ones with increasing density of the alloy. The rate for the pair excitation is nearly ${10}^{8}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, almost independently of the density. These values should be compared with (0.3--0.5)\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ predicted for a dilute mixture of deuterium and tritium on the basis of the screened-dipole-interaction mechanism. On the other hand, the plasmon excitation process turns out to contribute little to the rate.