  Based on the many-body theory of metals in the third order of the
perturbation expansion in electron-ion interaction pseudopotential, the
potentials of pair and three-ion interactions are calculated in liquid lead,
aluminium and beryllium at their melting temperatures. The reducible and
irreducible three-ion interactions have an attractive nature on distances
approximately equal to an average distance between ions in metals. It results
in the shortening of average interatomic distance in an equilibrium state of
metal. The potential landscapes created by a pair of fixed ions relative to the
third ion are constructed. It is shown that with increasing of an electronic
density the contribution as reducible, that and irreducible three-ion
interaction is increased. It is shown also that the influence of reducible
three-ion interaction on a potential landscape in a cluster of three ions is
considerably larger than influence of irreducible three-ion interaction.
