  We have studied Pb thin films as a function of the thickness up to 60
monolayers (MLs) using ab initio first principles and model calculations. Magic
heights corresponding to a modulated oscillatory pattern of the energy of
Pb(111) films have been measured up to about 30 MLs. We demonstrate that this
behaviour continues even for higher thickness due to an extra second modulation
pattern in the energetics of the metal film as a function of the number of
atomic layers. The origin of this second modulation is the nesting of two close
values of the Fermi wavelength in the (111) direction.
