The repulsive Coulombic forces exerted between proton wave particles in electrochemical and physical systems are examined, together with the attractive ion-induced dipole forces between protons and neighboring neutral particles, e.g. neutrons in the case of physical systems (nuclei). It is shown that when protons and neutrons are treated as harmonic oscillators with the same kinetic and potential energy, then two roots exist for their vibrational velocity. One root corresponds to negligible relativistic corrections (nu/c << 1) and unstable nuclei, the other to significant relativistic corrections (nu/c approximate to 1) and to formation of stable nuclei. It is shown that the first root corresponds to protons in chemical-electrochemical systems and the second (relativistic) root corresponds to protons in nuclei. In the latter case the formation of stable nuclei is due to the attractive ion-induced dipole forces and to the pronounced increase in mass and gravitational forces. The latter, together with the ion-induced dipole forces, counterbalance the strong repulsive Coulombic forces. This leads to the analytical computation of the energy of formation of the He-4 and H-2 nuclei and of the gravitational constant. All three computed values are in quantitative agreement with experiment. (c) 2006 Elsevier Ltd. All rights reserved.