  The creation of lepton pairs ($e^+e^-$ and $\mu^+\mu^-$) via multiphoton
absorption in collisions of ultrarelativistic ion beams with ultrashort
high-frequency laser pulses is considered. Both the free and the bound-free
production channels are addressed, where in the latter case the negatively
charged lepton is created in a bound atomic state. It is shown that these
nonlinear QED processes are observable when a table-top source of intense xuv
or x-ray laser radiation is operated in conjunction with the LHC. We discuss
the relative effectiveness of protons versus Pb ions and specify for each pair
production channel the most suitable collision system.
