The quantum diffusion of interstitial muonium atoms in solid methanes (CH4
and CD4) has been studied in the temperature range from 10 to 90 K using th
e technique of muonium spin relaxation in transverse magnetic field. In the
high temperature crystalline phase, which is characterized by rotating mol
ecules, muonium dynamics becomes bandlike with decreasing T. At low tempera
tures, slowing down of molecular rotation and molecular freezing in the ori
entationally ordered phase render adjacent tunneling sites inequivalent, re
sulting in strong particle localization. [S0031-9097(99)08729-3].