Detailed discussion of a linear electric field frequency shift induced in confined gases by a magnetic field gradient: Implications for neutron electric-dipole-moment experiments

The search for particle electric dipole moments (EDM’s) is one of the best places to look for physics beyond the standard model of electroweak interaction because the size of time reversal violation predicted by the standard model is incompatible with present ideas concerning the creation of the baryon-antibaryon asymmetry. As the sensitivity of these EDM searches increases more subtle systematic effects become important. We develop a general analytical approach to describe a systematic effect recently observed in an electric dipole moment experiment using stored particles [J. M. Pendlebury et al., Phys. Rev. A 70, 032102 (2004)]. Our approach is based on the relationship between the systematic frequency shift and the velocity autocorrelation function of the resonating particles. Our results, when applied to well-known limiting forms of the correlation function, are in good agreement with both the limiting cases studied in recent work that employed a numerical and heuristic analysis. Our general approach explains some of the surprising results observed in that work and displays the rich behavior of the shift for intermediate frequencies, which has not been studied previously.

Figure 1

The position-velocity correlation function $R\left(\tau \right)=2h\left(\tau \right)$ as a function of cell radius $R$ parametrized in terms of the mean free path $\lambda$ for different degrees of specularity as parametrized by the angular spread of the final angle compared to the incident angle. The plots for a given $R$ are for angular spreads on reflection of 0°, 45°, 90°, and 180°, with the latter representing diffuse reflection. Increased angular spread causes the correlation function to decay more rapidly in all cases. For $R\gtrsim 2.5\lambda$, there was practically no effect due to the degree of specularity, as expected.

Figure 2

The position-velocity correlation function when $\lambda$ is very small. This represents the limit for slow diffusion.

Figure 3

Results of numerically applying Eq. (37) to numerical calculations of the correlation function, for varying $\lambda$ with $R$ fixed.

Figure 4

Plot of Eq. (68). Solid line: first term. Dashed line: sum of first five terms.