Manyparticle interactions and local structure of the metallic hydrogen   at zero pressure
  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. 
S.D. Kaim, N.P. Kovalenko, E.V. Vasiliu