  We present tunneling and rattling motions of an off-center guest atom in cage
referring to a clathrate crystal La_3Pd_{20}Ge_6. The elastic constant C_{44}
of La_3Pd_{20}Ge_6 shows a Debye-type dispersion around 20 K obeying a
relaxation time tau = tau_0exp(E/k_{B}T) with an attempt time tau_0 =
2.0*10^{-12} sec and an activation energy E = 197 K. At low temperatures below
3 K down to 20 mK, the C_{44} shows a softening of C_{44} =
C_{44}^0(T-T_C^0)/(T-Theta) with T_C^0 = -337.970 mK and Theta = -338.044 mK.
These facts are attributed to two different types of the off-center motions
with Gamma_5 symmetry in 4a-site cage of La_3Pd_{20}Ge_6, a thermally activated
rattling motion over the potential hill and a tunneling motion through the
potential hill at low temperatures.
