Matter effects in oscillations of neutrinos traveling short distances in matter

It is well known that when the distance t traveled by neutrinos in matter i s short, matter effects in oscillations of neutrino flavour are small and d ecrease with decreasing t more rapidly than the oscillations effects themse lves. We discuss the reason for this and demonstrate that under certain cir cumstances this statement is no longer correct. In particular, we show that if neutrinos propagate significant distances in vacuum before entering mat ter (or after exiting it), matter effects in short-t neutrino oscillations can be significantly enhanced. Implications for oscillations of solar and a tmospheric neutrinos with nearly horizontal trajectories inside the Earth a nd for accelerator experiments are considered. We also comment on neutrino oscillations in matter due to flavour changing neutral currents. (C) 2001 P ublished by Elsevier Science B.V.