The atomic beam $E-H$ gradient balance method has been used to measure the polarizabilities of the alkali atoms. In this method, congruent electric and magnetic fields are established in the same region of space by applying a potential difference to pole pieces of high permeability which are insulated from their magnet yoke. The condition that atoms in a particular magnetic substate suffer no deflection in such a field region is $\frac{\alpha E\partial E}{\partial z}=\frac{{\mu }_{\mathrm{eff}}\partial H}{\partial z}$, where $\alpha$ is the atomic polarizability, ${\mu }_{\mathrm{eff}}$ is the effective magnetic moment in the field $H$, and $\frac{\partial E}{\partial z}$ and $\frac{\partial H}{\partial z}$ are the transverse components of the gradients of the electric and magnetic fields, respectively. Because of the congruence of the $E$ and $H$ fields, $\frac{\left(\frac{\partial E}{\partial z}\right)}{E}=\frac{\left(\frac{\partial H}{\partial z}\right)}{H}$, and therefore $\alpha =\frac{{\mu }_{\mathrm{eff}}H}{E^2}$ when the balance condition is satisfied. The determination of $\alpha$ is therefore independent of the velocity distribution in the beam, the field gradients and the apparatus geometry (except where it enters into the calculation of the electric field). The magnetic field $H$ is readily measured by making use of the convenient alkali zero moments. In these experiments, absolute accuracy for the $\alpha \text{'}\mathrm{s}$ is limited by the uncertainty in the determination of $E$, which is calculated from a knowledge of the applied voltage and the gap geometry.

The results in units of ${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^3$ are: Li, 20±3.0; Na, 20±2.5; K, 36.5±4.5; Rb, 40±5.0; Cs, 52.5±6.5. These are considerably higher than the values obtained in early beam experiments using electrostatic deflection techniques. They are, however, in fairly good agreement with the recent calculations of Dalgarno and Kingston and with other theoretical determinations of alkali polarizabilities.

• Received 12 June 1961

DOI:https://doi.org/10.1103/PhysRev.124.1431