Measurement of thegFactor of Free, High-Energy Electrons

Abstract

100-kev electrons in 0.1-μsec bunches are sent into a gold foil. The part of the electron bunch which is scattered at right angles, and which, consequently, is partially polarized, is trapped in a magnetic field and held for a measured length of time (up to 300 μsec). The bunch is then released from the trap and allowed to strike a second gold foil. Counters receive the electrons scattered at plus and minus approximately 90°. The cycle is repeated 1000 times per sec. The asymmetry in intensity in the two directions depends upon the final direction of polarization. A plot of the intensity asymmetry vs trapping duration is a cosine curve, whose frequency is the difference between the orbital frequency and the spin precession frequency. This is related to the $g$ factor as follows: $\frac{{\omega }_D{m}_{0}c}{\mathrm{Be}}=a$, where $g$ is $2(1+a)\mathrm{}$. Thus the "anomaly," $a$, is measured directly. The determination of $B$ presents some difficulty because the field must be slightly nonuniform in order to trap the electrons. The spatial variation in $B$ from the center of the trap to the ends is only 0.3%, and the time average of $B$ which applies to the trapped electrons is evaluated to 0.1%. Measurements made at other electron energies, down to 50 kev, showed a slight dependence of $a$ upon energy. The dependence is attributed to electrostatic charges on the surfaces in the trapping region. The final standard error quoted is, however, purposely made large enough so that the variation of $a$ with energy is bracketted. The result is $a=0.0011609\mathrm{}\pm 0.0000024$.