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Physical Review A

Generation of monochromatic radiation by atomic ions in a magnetic field

Vladimir S. Melezhik

Published Jun 1, 1999• 1 citation
Publisher

Abstract

In the presence of a magnetic field atomic ions are shown to generate monochromatic radiation with the frequency $\ensuremath{\omega}=QB/M$, depending on the field strength B and the ion mass M and charge Q. The origin of the effect is the interaction of the bound electrons with the oscillating field of the Stark term coupling the center of mass and electronic motions of an ion due to the nonseparability of the collective and internal degrees of freedom in the system. The intensity of the radiation is defined by the velocities of the ions and the magnetic field strength.

DOI
10.1103/physreva.59.4833

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In the presence of a magnetic field atomic ions are shown to generate monochromatic radiation with the frequency \ensuremathω=QB/M\ensuremath{\omega}=QB/M\ensuremathω=QB/M, depending on the field strength B and the ion mass M and charge Q. The origin of the effect is the interaction of the bound electrons with the oscillating field of the Stark term coupling the center of mass and electronic motions of an ion due to the nonseparability of the collective and internal degrees of freedom in the system. The intensity of the radiation is defined by the velocities of the ions and the magnetic field strength.
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.
It is shown that upon the application of an external magnetic field, a gas of ionized particles may experience noninversive partial velocity amplification of radiation by ions due to their Larmor rotation. In this case, virtually all ions may be in the ground state. It may happen that approximately half the number of ions in the medium amplify the incident radiation. The integrated absorption coefficient remains positive due to the enhancement of absorption of radiation by the other half of ions. Noninversive amplification of radiation takes place when the condition ω c ≳Γ 2 / kv T is satisfied ωw c is the cyclotron frequency of ions in the magnetic field; Γ is the homogeneous half-width of the absorption line for ions, and kv T is the Doppler width). In the case of interaction of atomic ions with radiation in the optical range, this corresponds to magnetic fields B ≳600 G (for the ion mass M ∼10 amu). Noninversive partial velocity amplification of radiation is a “latent” effect in the sense that it disappears upon averaging over all velocity directions of ions. This effect is associated with the emergence of phase incursion of the induced dipole moment oscillations for ions moving in circular cyclotron orbits, which depends on the ion velocity.
For neutral particle systems in a homogeneous magnetic field, there exists a constant of motion, the pseudomomentum, which allows a complete pseudoseparation of the center-of-mass motion. For ions such a separation is not possible, and the Landau orbit of the center-of-mass and internal (electronic) motion are intimately coupled. We investigate different physical situations for which this interaction becomes strong at laboratory magnetic-field strengths. In particular, we find that the Landau orbit itself can change substantially upon this interaction.
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 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 states of the atom, determined by the motion of electrons, are stationary in the presence of all internal atomic forces and of interactions with constant external fields. When electrons interact with the field associated with electromagnetic radiation, the atomic states are no longer stationary, and the time-dependent perturbation treatment has to be applied to calculate the effect produced by the radiation, which is a function of time. Consequently, as shown in Section 9.3 , the time evolution of the atom will be described in terms of transitions between the stationary states of the unperturbed atomic system.