Motion of the Center of Mass of Atoms and Molecules

The motion of the center of mass of atoms and molecules is described in the presence of external fields. In the case of electromagnetic radiation whose wavelength is much larger than the atom or molecule, we find that there will be a very small change in the component of the momentum of the center of mass which is in the direction of the polarization of the light. For ions we show that the integral over the perturbing potential yields $-Nqv$, where $N$ is the degree of ionization, $q$ is the elementary charge, and $v$ is the velocity of the center of mass in the direction which the light wave travels. If the wavelength of the light is large when compared with the size of the vessel which contains ionized atoms or molecules, the equation describing the motion of the center of mass is that of a damped harmonic oscillator. We show that in an external homogeneous electric field, the wave function of the center of mass of an ionized atom or molecule is an Airy function. In an external homogeneous magnetic field, we show that the motion of the center of mass of a neutral molecule is that of a harmonic oscillator with a frequency of $\omega ={\left(\frac{N_e{q}^2{H}^2}{4Mm{c}^2}\right)}^{\frac{1}{2}}$, where $N_e$ is the number of electrons in the atom or molecule, $H$ is the magnetic field strength, $M$ is the total mass, $m$ is the electronic mass, and $c$ is the velocity of light. If an oscillatory field polarized perpendicular to the steady field is introduced, we show that the transitions are restricted by the usual harmonic-oscillator selection rules, and that the emission rate for spontaneous emission is about ${10}^{-3\mathrm{}}$ ${\sec }^{-1\mathrm{}}$ for the lighter atoms.