Calculation of electronic energies and vibrational levels of molecular ions from the Hamilton-Jacobi equation: H2+, D2+, T2+, HD+ and DT+

Starting with the Hamilton-Jacobi equation we apply Hylleraas' method in association with the series established by Wind-Jaffe, to H2+, D2+, T2+, HD+ and DT+ molecular ions in order to calculate the electronic energies as well as vibrational levels. In the later it is necessary to have the exact value of the electronic energy as a function of the nuclear distance. The dissociation of these molecular ions is important to study proton injection in magnetic mirrors and in Tokomak leading to the controlled thermonuclear fusion.