H^+_2$ in a strong magnetic field described via a solvable model

TL;DR

This paper models the hydrogen molecular ion in strong magnetic fields using a solvable one-dimensional approximation, and improves accuracy with perturbative corrections, also predicting the existence of $He_2^{3+}$ under certain conditions.

Contribution

It introduces a solvable model for $H^+_2$ in strong magnetic fields and demonstrates how to accurately compute its properties with perturbative corrections.

Findings

Correct equilibrium distance and binding energy obtained with second-order perturbation.

The model predicts the existence of $He_2^{3+}$ at high magnetic fields.

The effective Hamiltonian simplifies to a one-dimensional form with delta function potentials.

Abstract

We consider the hydrogen molecular ion $H^+_2$ in the presence of a strong homogeneous magnetic field. In this regime, the effective Hamiltonian is almost one dimensional with a potential energy which looks like a sum of two Dirac delta functions. This model is solvable, but not close enough to our exact Hamiltonian for relevant strenght of the magnnetic field. However we show that the correct values of the equilibrium distance as well as the binding energy of the ground state of the ion, can be obtained when incorporating perturbative corrections up to second order. Finally, we show that $ He_2^{3+}$ exists for sufficiently large magnetic fields.