  We study a realistic Kondo model for crystal field quartet ground states
having magnetic and non-magnetic (quadrupolar) exchange couplings with
conduction electrons, using the numerical renormalization group method. We
focus on a local effect dependent on singlet excited states coupled to the
quartet, which reduces the non-magnetic coupling significantly and drives
non-Fermi liquid behavior observed in the calculated quadrupolar
susceptibility. A crossover from the non-Fermi liquid state to the Fermi liquid
state is characterized by a small energy scale very sensitive to the
non-magnetic coupling. On the other hand, the Kondo temperature observed in the
magnetic susceptibility is less sensitive. The different crystal-field
dependence of the two exchange couplings may be related to the different $x$
dependence of quadrupolar and magnetic ordering temperatures in
Ce$_x$La$_{1-x}$B$_6$.
