We review the design, simulation, and tests of a detection system for measuring the energy distribution of daughter nuclei recoiling from the $\beta$ decay of laser trapped neon isotopes. This distribution is sensitive to several new physics effects in the weak sector. Our “decay microscope” relies on imaging the velocity distribution of high-energy recoil ions in coincidence with electrons shaken off in the decay. We demonstrate by way of Monte Carlo simulation that the nuclear microscope increases the statistical sensitivity of kinematic measurements to the underlying energy distribution and limits the main systematic bias caused by discrepancy in the trap position along the detection axis.

• Received 2 November 2019
• Revised 4 January 2020
• Accepted 19 February 2020

DOI:https://doi.org/10.1103/PhysRevC.101.035501