Quantum States of Magnetically Induced Anions

In a magnetic field, an atom (or molecule) can attach an extra electron to form an unconventional anionic state which has no counterparts in field-free space. Assuming the atom to be infinitely heavy, these magnetically induced anionic states are known to constitute an infinite manifold of bound states. In reality, the species can move and its motion across the magnetic field couples to the motion of the attached electron. We treat this coupling, for the first time, quantum mechanically, and show that it makes the number of bound anionic states finite. Explicit numerical quantum results are presented and discussed.

Figure 1

Energies of the motional magnetically induced anions formed by atoms which do not form anions in field-free space. Dashed lines show the $s=0$ branches of excitations for $B=10\mathrm{T}$. Dots show the quantum levels with $s=1$ and different values of $J$ for $B=100\mathrm{T}$, and are connected by solid lines for visualization of the analytical approximation (8). Also indicated in the figure are the numbers of the bound motional states along the branches (in parentheses) and the effective anionic masses (near the solid and dashed lines).

Figure 2

The energy of the lowest bound state of the anion ${\mathrm{He}}^{-}$, i.e., $s=0$, $J=0$, and of the state $s=1$, $J=-1$ of ${\mathrm{Mg}}^{-}$, as a function of the magnetic field strength (solid lines). Dashed lines show the corresponding energies of the infinitely heavy anions. Dots correspond to polynomial extrapolations of the solid lines towards the detachment threshold (zero energy). Arrows point to the minimum values of the field strength (indicated near the arrows) required to support a bound state.