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

TL;DR

This study uses the Lagrange-mesh method to accurately calculate the ground states of He$_2^{3+}$ and HeH$^{2+}$ molecular ions in strong magnetic fields, confirming their existence at high field strengths and identifying potential energy saddle points.

Contribution

The paper provides the first accurate calculations of these molecular ions' ground states in strong magnetic fields using the Lagrange-mesh method, within the Born-Oppenheimer approximation.

Findings

He$_2^{3+}$ exists at B > 100 a.u.

HeH$^{2+}$ exists at B > 1000 a.u.

Potential saddle points appear at B ~ 80 a.u. and B ~ 740 a.u.

Abstract

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.u. 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.u. and $B \sim 740$ a.u., respectively.