  We evaluate the matrix elements for the processes pi^0 K^0 -> pi^0 K^0 and
pi^- K^+ -> pi^0 K^0 in the presence of isospin breaking terms at leading and
next-to-leading order. As a direct application the releveant combination of the
S-wave scattering lengths involved in the pion-kaon atom lifetime is
determined. We discuss the sensitivity of the results with respect to the input
parameters.
