  Using the numerical renormalization group method, we investigate an extended
Anderson model, in which correlated electrons with the
$\Gamma_1$(singlet)-$\Gamma4$(triplet) f$^2$ crystalline-electric-field (CEF)
configuration hybridize with conduction electrons of $\Gamma_7$(doublet) and
$\Gamma_8$ (quartet) under cubic $O_h$ symmetry, from a strong spin-orbit
interaction limit. For the case of the parameters relevant to PrFe4P12, the
system is under competition between the CEF singlet fixed point and the
multichannel
  Kondo non-Fermi liquid fixed point arising from the quadrupolar coupling
between the impurity with pseudospin 1 and the conduction electron with
pseudospin 3/2 . We consider that this result reveals the origin of the
heaviness of the effective mass and non-Fermi liquid behavior of the Pr- based
filled skutterudite compounds.
