  Recently, a series of noncentrosymmetric superconductors has been a subject
of considerable interest since the discovery of superconductivity in CePt_3Si.
In noncentrosymmetric materials, the degeneracy of bands is lifted in the
presence of spin-orbit coupling. This will bring about new effects in the Kondo
effect since the band degeneracy plays an important role in the scattering of
electrons by localized spins. We investigate the single-impurity Kondo problem
in the presence of spin-orbit coupling. We examine the effect of spin-orbit
coupling on the scattering of conduction electrons, by using the Green's
function method, for the s-d Hamiltonian, with employing a decoupling
procedure. As a result, we obtain a closed system of equations of Green's
functions, from which we can calculate physical quantities. The Kondo
temperature T_K is estimated from a singularity of Green's functions. We show
that T_K is reduced as the spin-orbit coupling constant \alpha is increased.
When 2\alpha k_F is comparable to or greater than k_BT_K(\alpha=0), T_K shows
an abrupt decrease as a result of the band splitting. This suggests a Kondo
collapse accompanied with a sharp decrease of T_K. The log T-dependence of the
resistivity will be concealed by the spin-orbit interaction.
