  We investigate the enhancement of the Kondo effect in quantum dots with an
even number of electrons, using a scaling method and a mean field theory. We
evaluate the Kondo temperature $T_K$ as a function of the energy difference
between spin-singlet and triplet states in the dot, $\Delta$, and the Zeeman
splitting, $E_Z$. If the Zeeman splitting is small, $E_Z \ll T_K$, the
competition between the singlet and triplet states enhances the Kondo effect.
$T_K$ reaches its maximum around $\Delta=0$ and decreases with $\Delta$ obeying
a power law. If the Zeeman splitting is strong, $E_Z \gg T_K$, the Kondo effect
originates from the degeneracy between the singlet state and one of the
components of the triplet state at $-\Delta \sim E_Z$. We show that $T_K$
exhibits another power-law dependence on $E_Z$. The mean field theory provides
a unified picture to illustrate the crossover between these regimes. The
enhancement of the Kondo effect can be understood in terms of the overlap
between the Kondo resonant states created around the Fermi level. These
resonant states provide the unitary limit of the conductance $G\sim 2e^2/h$.
