  On the basis of the perturbation expansion for 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 pair ions 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 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 deep potential well for fourth ion at
interionic separation corresponding interproton separation in molecule $H_{2}$.
The quasiclassical probability of ion transition into this well is evaluated.
The life time of metallic phase of hydrogen relative to the tunneling
nucleation of the $H_{2}$ molecules is estimated.
