On the basis of the perturbation expansion for the electron gas energy in the third order to the electron{ion potential the pair and irreducible three{ion interaction potentials in metallic hydrogen are calculated. The irreducible potential of three{ion interaction has attractive nature at short interionic separation and oscillates at large ones. The anisotropic character of the three{ion interaction is shown. The potential relief of the ions pair relative to the third ion is constructed. This relief has some potential wells and valleys which connect them. The important role of the irreducible three{ion interaction in the formation of the local order in three-and four{ion clusters is shown. The potential relief of an equiangular ion triplet relative to the fourth ion is calculated. This relief has a deep potential well for the fourth ion at interionic separation corresponding to the interproton separation in the H2 molecule . The quasiclassical probability of the ion transition into this well is evaluated. The life time of the metallic phase of hydrogen relative to the tunneling nucleation of the H2 molecules is estimated.

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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.

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