The chemical pollution of the secondary of a cataclysmic variable by novae

We study the chemical evolution of population I and population II secondari es in cataclysmic variables (CVs) assuming that during nova explosions a pa rt of the high metallicity nova ejecta is intercepted by the secondary and mixed into its convective envelope. We derive analytic expressions for the chemical composition of the envelope of the secondary as a function of the chemical composition of the nova ejecta X-i,X-ej and the cross-section of t he secondary sigma. For population I CVs we find that the increase of the m etallicity of the secondary is comparable to its initial metallicity only i f sigma is larger by an order of magnitude than the geometrical cross-secti on. A significant accumulation is therefore possible only in those species that are highly overabundant in the nova ejecta. Because the changes in the abundances of even those species depend strongly on the poorly known cross -section a, the predictive power of our model is weak for population I CVs as long as sigma is not well determined. Tn the case of population II CVs t he accumulation of heavy elements by this process dominates over the initia l metallicity of the secondary even for values of sigma that are smaller by an order of magnitude than the geometrical cross-section. Thus, within a s hort time after turn-on of mass transfer, the relative metal abundances in the envelope of the secondary reflect those in the nova ejecta. This is nea rly independent of the cross-section sigma.