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Linear electric field frequency shift (important for next generation electric dipole moment searches) induced in confined gases by a magnetic field gradient

The search for particle electric dipole moments (edm) represents a most promising way to search for physics beyond the standard model. A number of groups are planning a new generation of experiments using stored gases of various kinds. In order to achieve the target sensitivities it will be necessary to deal with the systematic error resulting from the interaction of the well-known $\overrightarrow{v}\times \overrightarrow{E}$ field with magnetic field gradients (often referred to as the geometric phase effect (Commins, ED; Am. J. Phys. \QTR{bf}{59}, 1077 (1991), Pendlebury, JM \QTR{em}{et al;} Phys. Rev. \QTR{bf}{A70}, 032102 (2004)). This interaction produces a frequency shift linear in the electric field, mimicking an edm. In this work we introduce an analytic form for the velocity auto-correlation function which determines the velocity-position correlation function which in turn determines the behavior of the frequency shift (Lamoreaux, SK and Golub, R; Phys. Rev \QTR{bf}{A71}, 032104 (2005)) and show how it depends on the operating conditions of the experiment. We also discuss some additional issues.