Theory of magnetically induced anions

A general quantum theory is presented for unconventional anionic states supported by the presence of an external magnetic field. The theory applies to atomic anions and allows for straightforward extensions to anions formed in magnetic fields by other species, e.g., by clusters or small molecules. A special focus of the theory is on the coupling of the anion’s motion across the magnetic field to the motion of the attached electron. Neglecting this coupling, the magnetically induced anionic states are known to constitute an infinite manifold of bound states. In reality, the number of bound anionic states is finite. Typically, the quantized motion of the anion in the field results in sequences of excitations. These might include, depending on properties of the anion and on the magnetic field strengths, a few or a substantial number of states. Explicit results obtained by quantum ab initio calculations are presented and discussed on bound states and radiative transitions for some experimentally relevant atomic anions.

Figure 1

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 the extrapolations of the solid lines towards zero energy. Arrows point to the minimum values of the field strength (indicated near the arrows) required to support a bound state.

Figure 2

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 motional states 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 (10.2). The numbers of the bound motional states along the branches are indicated in parentheses. Near the solid and dashed lines we also indicate the corresponding ratios of the effective masses to the net anionic masses.

Figure 3

Energies of the magnetically induced states of the anion ${\mathrm{Cs}}^{-}$ moving in a magnetic field of $100\mathrm{T}$. The branches $s=1,2,3$ of the motional states are shown. Dots show the quantum levels for $s=1$, $s=2$ and different values of $J$. 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 4

Transition energies (solid lines) and oscillator strengths (dashed lines) for the bound-ion cyclotron transitions along the branches of motional states presented in Fig. 3. The transition energies and oscillator strengths are shown in units of the corresponding quantities of a single charged particle with the charge and mass of the entire anion. Also indicated are the estimates involving the effective masses of the bound anion.