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Physical Review A

Theory of magnetically induced anions

Victor G. Bezchastnov, Peter Schmelcher, Lorenz S. Cederbaum

Published May 22, 2007• 9 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.75.052507

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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.
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.
In a magnetic field anions are known to possess, within the approximation of infinite nuclear mass, an infinite manifold of bound states. This approximation, however, neglects effects due to the coupling of the anionic center-of-mass (c.m.) motion to the electronic motion. Recently these effects have been reported to be crucial for the mere existence and properties of the field-induced anions [Phys. Rev. Lett. 86, 5450 (2001)]. We develop a theoretical approach to study anions in the presence of a magnetic field including the motional c.m. effects. We aim at weak to moderate magnetic-field strengths typical for present-day laboratories. Our approach involves canonical transformations of the original Hamiltonian, implementing the integrals of motion and reasonable adiabatic approximations. As a result we derive a three-dimensional Hamiltonian that can be universally applied to atomic or molecular negative ions in a magnetic field by specifying the properties of the underlying neutral systems. We consider this Hamiltonian to be suitable for rigorous investigations of moving anions in fields. For the classical dynamics a reduction to an effective two-dimensional problem is possible. This can serve as a basis for future studies, for instance, of the autodetachment dynamics of anions due to c.m. effects.
The interaction between the center of mass (c.m.) and internal degrees of freedom plays a crucial role for the properties and behavior of moving negative ions in magnetic fields. A promising theoretical approach, including this interaction to describe field-induced anions, has been developed very recently. The theory is aimed at weak to moderate magnetic field strengths and therefore of immediate relevance to laboratory experiments. In the present work, we apply this approach to study the classical dynamics of the anions in magnetic fields. We focus on features of the bound motion of anions and on the analysis of the anions' autodetachment induced by the c.m. motion.
In a magnetic field the center of mass (c.m.) motion of an atom or molecule couples to the electronic motion. It is demonstrated that this coupling dramatically influences the properties of negative ions. Neglecting c.m. effects the external field gives rise to a series of infinitely many bound states of the ion. Center of mass effects terminate this series and turn bound states into short-lived resonance states. Whether bound states exist at all, their number and properties as well as the lifetimes of the resonance states depend on the neutral system to which an electron is attached, and on the magnetic field.
In this paper, we consider two possible approaches to compute the quantum states of moving magnetically induced anions. We start with the effective Hamiltonian derived in previous works. It has been reduced to the relevant degrees of freedom including those related to the collective motion of the anion across the magnetic field. Multiconfigurational approaches are applied starting with two convenient basis sets which account for the integral of the collective motion, the total angular momentum of the anion along the magnetic field. The coupled-channel equations, resulting from the implementation of these basis states, are derived and many useful relations for the relevant matrix elements are obtained. One of the suggested basis sets comprises the states which describe correctly the limiting case of the detached anion, and is, therefore, amenable to straightforward approximations. The corresponding single-channel approximation is investigated in some detail, and estimates of the eigenenergies of the magnetically induced moving anion are obtained.