Angular Resolution of Electrons in Gaseous Targets

Low-energy electron recoils are of interest in several planned and proposed future nuclear and particle physics experiments. The topology and directions of such recoils provide important particle identification and kinematical constraints, and are experimentally accessible in gaseous targets. Electron recoils have complex trajectories, and the angular resolution that can be achieved has not been well understood. We have developed a method for estimating and optimizing this angular resolution, considering contributions from both multiple scattering and detection. First, we clarify that the formula commonly used for multiple scattering through small angles is actually a fit to Moliere theory for heavy particles. We revise this formula so that it is applicable to electrons in gas. Next, we combine this with an effective point resolution contribution, which accounts for diffusion and detector effects, to obtain an approximation for the angular resolution. We identify the optimal fit length and the corresponding optimal angular resolution. The result is a simple formula to estimate the best achievable angular resolution for electrons in gaseous detectors, given the electron energy and basic gas and detector properties. Our model's predictions show good agreement with simulations. This approach can assist in the design of future experiments and the development of analysis techniques. Given the widespread use of gaseous detectors, this work is relevant to many scientific communities.