A torsion pendulum having masses with -loZ2 and -10" polarized electrons is used to search for an anomalous spin interaction of macroscopic range. Competition from magnetic forces is reduced by using Dy-Fe masses (which exhibit orbital compensation of the electron intrinsic spin), combined with light magnetic shielding, so that the sensitivity is better than one-tenth of a percent of the gravitational force. Fluctuations set the overall experimental limit at about 8 times this level. Interpretation of our null result sets limits on electron spin interactions and on moments which are not of electromagnetic origin. In terms of a standard dipole-dipole form the result is (1.6+6.9)X l o 1 * of the interaction strength between the magnetic moments of the electrons. Comparisons are made with theoretical predictions for very light exchange particles. 42 977-

Measuring the period of torsion pendulums with precision has long been a formidable challenge in gravitation experiments, particularly those measuring the Newtonian gravitational constant G. An alternative method to fitting the position signal of the pendulum to a sine wave is the use of the power spectrum generated by the fast Fourier transform (FFT) as the source of information from which the period of oscillation can be determined. There are, however, known limitations to the use of a FFT to measure the period of a physical oscillator with precision. These limitations include two effects due to the finiteness of the duration of the sinusoidal data record and one effect due to the uncertainty of the starting phase of the oscillator relative to the window imposed by this duration. We have done a phenomenological study of the FFT using a desktop computer to imitate a precision oscillator having the physical characteristics of a finite damping constant and drift in the zero potential-energy position. Also, we have taken extensive data with a torsion pendulum, and analyzed them in this way. These studies show that for a real oscillator, such as the classical torsion pendulum, the FFT is a useful tool for determining the period of oscillation with the precision usually associated with larger, more complex, fitting algorithms. With good signal-to-noise ratio and under conditions appropriate to a torsion pendulum, the FFT method can measure the frequency or period to five parts in 106 or better.

The torsion balance has been the experimental apparatus of choice for centuries, both in precision measurements of the Newtonian gravitational constant and in searches for weak anomalous interactions outside of gravity. If the form of the interaction is modeled, it is often possible to optimize the interacting bodies so that the apparatus has the greatest sensitivity to the interaction under study. Other researchers have applied this strategy in the case of the gravitational interaction between cylinders, and between a cylinder and sphere. Whereas their work focused on developing an analytical expression for the force between the masses, we present here a numerical method−Monte Carlo integration−which is general enough to aid in the design of bodies interacting under arbitrary potentials and with any desired geometric shape (as long as an accurate absolute value of the force is not needed). This numerical method is used to compute the gravitational torsion constant produced between an external hollow cylinder and sphere, and demonstrates the behavior studied previously through analysis. However, the main purpose for which we have used this numerical technique is in the design of interacting bodies used in a torsion-pendulum search for interactions that depend on net intrinsic spin. We demonstrate how the method may be used to determine the optimum aspect ratio (l/r) of the polarized test masses, as well as the most sensitive orientation of the masses. Two different interactions are considered: the dipole–dipole interaction between two polarized bodies, and the monopole–dipole interaction between a polarized and unpolarized body. In the case of the monopole–dipole interaction, we also show how the numerical method can indicate which orientation between test bodies is most susceptible to a false signal caused by gravity.