A Direct Determination of the Magnetic Moment of the Protons in Units of the Nuclear Magneton

Abstract

A direct measurement of the proton magnetic moment in units of the nuclear magneton has been made, using the method of Alvarez and Bloch. The experiment consists of comparison of the nuclear magnetic resonance frequency of protons with the orbital frequency of protons revolving in the same homogeneous field. The resonance frequency of protons in water has been measured by the method of nuclear induction; the orbital frequency has been measured by a special device: a small decelerating cyclotron operated at an odd multiple of the fundamental cyclotron frequency.The device has been operated in a field of about 5300 gauss at all odd multiples from the first to the eleventh, with a corresponding range of the dee frequency between 8.1 and 89 Mc/sec. As expected, the sharpness of the cyclotron resonance was observed to greatly increase at the higher multiples; besides this advantage for obtaining high accuracy, the comparison of the results at different multiples also furnished an important check on the reliability of the measurements.An approximate theory for the shape of the cyclotron resonance curves has been developed, and its qualitative agreement with the observations has been established. The perturbing effects of extraneous electric and magnetic fields have been investigated, both theoretically and experimentally, and found to be negligible. With the smallest relative half-width of resonance about 1/10,000, which was observed at the higher multiples, and guided by the interpretation of the resonance shape, the magnetic moment of the proton has been found to be 2.7924\ifmmode\pm\else\textpm\fi{}0.0002 nuclear magnetons.