Muonium formation via electron transport in solid nitrogen

Abstract

Muon spin rotation $(\ensuremath{\mu}\mathrm{SR})$ techniques have been used to investigate the diamagnetic and paramagnetic states of energetic positive muons stopped in solid molecular nitrogen. The paramagnetic signal arises from muonium $(\mathrm{Mu}\mathrm{}={\ensuremath{\mu}}^{+}{+e}^{\ensuremath{-}})$ atoms and reflects both ``prompt'' epithermal Mu formation and ``delayed'' thermal Mu formation. The latter is shown to be due to convergence of the thermalized ${\ensuremath{\mu}}^{+}$ with an electron liberated in its ionization track. Measurements in external electric fields of up to 10 kV/cm applied along and antiparallel to the initial muon momentum reveal a large anisotropy in the spatial distribution of muon-electron pairs: the ${\ensuremath{\mu}}^{+}$ is shown to thermalize ``downstream'' of the ionization products of its track. The characteristic muon-electron distances in $\ensuremath{\alpha}\ensuremath{-}{\mathrm{N}}_{2}$ and $\ensuremath{\beta}\ensuremath{-}{\mathrm{N}}_{2}$ and liquid nitrogen are estimated to be approximately 500 \AA{}, 250 \AA{}, and 300 \AA{}, respectively. The dependence of delayed Mu formation upon electron mobility offers a method for determining such mobilities on a microscopic scale. Electron drift mobilities are shown to differ by several orders of magnitude in the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ phases of solid nitrogen. Excess electrons from the muon track are apparently delocalized in orientationally ordered $\ensuremath{\alpha}\ensuremath{-}{\mathrm{N}}_{2};$ electron localization in orientationally disordered $\ensuremath{\beta}\ensuremath{-}{\mathrm{N}}_{2}$ is discussed in terms of the formation of a small polaron due to electron interaction with the rotational degrees of freedom of ${\mathrm{N}}_{2}$ molecules. The diamagnetic signal in condensed nitrogen is ascribed to the ${\mathrm{N}}_{2}{\ensuremath{\mu}}^{+}$ molecular ion; in $\ensuremath{\beta}\ensuremath{-}{\mathrm{N}}_{2}$ it consists of two components, one relaxing slowly due to random fields from nuclear dipole moments and the other relaxing up to two orders of magnitude faster, due to very delayed Mu formation as the muon captures low-mobility electrons.