Electrostatic models of charged hydrogenic chains in a strong magnetic field

Abstract

Simple one-dimensional electrostatic models of one-(two) electron molecular systems H$_2^{+}$, H$_3^{2+}$, H$_4^{3+}$ and H$_2$, H$_3^{+}$, H$_4^{2+}$ in a strong magnetic field are proposed to estimate the binding-(ionization) energy of the corresponding ground states. The study is carried out in the range of magnetic fieds $B=10^2-10^6\,$ a.u. The models are inspired (and based) on the quasi one-dimensional form of the ground state electronic distribution function which is obtained by precise variational calculations in the Born-Oppenheimer approximation in a non-relativistic framework. It is shown that the models give, for all magnetic fields considered, a very good description of the binding-(ionization) energy of the one-electron molecular systems H$_2^{+}$, H$_3^{2+}$, H$_4^{3+}$, being accurate in $2.5%$, $5%$ and $5%$ respectively, and $15%$ for the two-electron systems H$_3^{+}$, H$_4^{2+}$ ($30%$ for H$_2$) as compared with the corresponding variational calculations.