The stability of the $1u$ state of H$_{2}^{+}$ in magnetic fields with arbitrary orientations

Abstract

The existence and stability of the van der Waals $1u$ state of the molecular ion \ppe with fixed centers (infinitely massive nuclei) in the presence of a magnetic field with arbitrary orientations in the range of strengths $0 \le B \le 10\,$ a.u. (1 a.u. $\equiv 2.35\times10^{9}\,$G) is studied within the non-relativistic framework. The study is based on the variational method with physical relevant trial functions. A particular emphasis to the gauge optimization through variational parameters is incorporated. It is shown that, for all the magnetic fields studied, the potential energy curve has a pronounced minimum for finite internuclear distances and the optimal configuration of minimal total energy is realized when the molecular axis is oriented along the magnetic field lines (parallel configuration). We found a domain of magnetic fields $0 \leq B \lesssim 6.6$ a.u. where the $1u$ state in parallel configuration is stable towards dissociation \hbox{\ppe $\nrightarrow$ H + p}. The maximal stability is found to be at magnetic field $B\sim 2\,$a.u. where the potential well supports one vibrational state below the dissociation limit.