  We analyze non-Fermi liquid (NFL) properties along a line of critical points
in a two-channel Anderson model with phonon-assisted hybridizations. We succeed
in identifying hidden nonmagnetic SO(5) degrees of freedom for
valence-fluctuation regime and analyze the model on the basis of boundary
conformal field theory. We find that the NFL spectra along the critical line,
which is the same as those in the two-channel Kondo model, can be alternatively
derived by a fusion in the nonmagnetic SO(5) sector. The leading irrelevant
operators near the NFL fixed points vary as a function of Coulomb repulsion U;
operators in the spin sector dominate for large U, while those in the SO(5)
sector do for small U, and we confirm this variation in our numerical
renormalization group calculations. As a result, the thermodynamic singularity
for small U differs from that of the conventional two-channel Kondo problem.
Especially, the impurity contribution to specific heat is proportional to
temperature and bipolaron fluctuations, which are coupled electron-phonon
fluctuations, diverge logarithmically at low temperatures for small U.
