He${}_2^{3+}$ and HeH${}^{2+}$ molecular ions in a strong magnetic field: the Lagrange mesh approach

Accurate calculations for the ground state of the molecular ions He${}_2^{3+}$ and HeH${}^{2+}$ placed in a strong magnetic field $B\gtrsim {10}^2$ a.u. ($\approx 2.35\times {10}^{11}$G) using the Lagrange-mesh method are presented. The Born-Oppenheimer approximation of zero order (infinitely massive centers) and the parallel configuration (molecular axis parallel to the magnetic field) are considered. Total energies are found with 9-10 s.d. The obtained results show that the molecular ions He${}_2^{3+}$ and HeH${}^{2+}$ exist at $B > 100$a\mathrm{.}u\mathrm{.}and$B > 1000$,a.u., respectively, as predicted in \cite{Tu:2007} while a saddle point in the potential curve appears for the first time at $B \sim 80$a\mathrm{.}u\mathrm{.}and$B \sim 740$ a.u., respectively.