An experimental search for an electric dipole moment (EDM) of the neutron has been carried out at the Institut Laue-Langevin, Grenoble. Spurious signals from magnetic-field fluctuations were reduced to insignificance by the use of a cohabiting atomic-mercury magnetometer. Systematic uncertainties, including geometric-phase-induced false EDMs, have been carefully studied. The results may be interpreted as an upper limit on the neutron EDM of |d(n)|< 2.9 x 10(-26)e cm (90% C.L.).

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Theories are developed to evaluate Larmor frequency shifts, derived from geometric phases, in experiments to measure electric dipole moments (EDM's) of trapped, atoms, molecules, and neutrons. A part of these shifts is proportional to the applied electric field and can be interpreted falsely as an electric dipole moment. A comparison is made between our theoretical predictions for these shifts and some results from our recent experiments, which shows agreement to within the experimental errors of 15%. The comparison also demonstrates that some trapped particle EDM experiments have reached a sensitivity where stringent precautions are needed to minimize and control such false EDM's. Computer simulations of these processes are also described. They give good agreement with the analytical results and they extend the study by investigating the influence of varying surface reflection laws in the hard-walled traps considered. They also explore the possibility to suppress such false EDM's by introducing collisions with buffer gas particles. Some analytic results for frequency shifts proportional to the square of the E field are also given and there are results for the averaging of the B field in the absence of an E field.

A general review of conventional magnetic shielding is presented. Several possible definitions of the term 'shielding factor' are given, taking into account the ferromagnetic nature of shielding materials. An alternative treatment of single-layer axial shielding for a cylindrical shield is presented and compared to a previous approximation. A new algorithm for calculating multi-layer axial shielding factors is derived and shown to be an improvement on existing methods when applied to some assemblies, including one reported for the first time.

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