Shock-Tube Measurement of the Polarizability of Atomic Hydrogen

Abstract

The electric polarizability of atomic hydrogen has been measured at optical frequencies by shock heating a gaseous mixture of argon and molecular hydrogen to temperatures causing nearly complete dissociation of the latter. Application of Mach-Zehnder interferometry to the shock-heated gas gave measurements of fringe shift across the shock front which were subsequently reduced to obtain the polarizability of the ground state of atomic hydrogen. The resultant value is ${\alpha }_H=(4.61\mathrm{}\pm 0.07){a_0}^3$, for a wavelength of 5870 Å, where $a_0$ is the first Bohr radius and the error assignment is purely statistical. The shock waves employed were in the Mach number range 10 to 12 in a $\frac{2}{3} \mathrm{Ar}-\frac{1}{3} {\mathrm{H}}_2$ mixture (by volume) and produced temperatures of the order of 4600°K at densities high enough to ensure thermal equilibrium. Under these conditions there was negligible ionization or excitation of the argon diluent. In contrast to earlier experiments reported in the literature, the present result is in good agreement with the predictions of the quantum-mechanical time-dependent perturbation theory which gives a value of ${\alpha }_H=(4.66\mathrm{}\pm 0.01){a_0}^3$ for the same wavelength as that used in the experimental work.