Geometric Optimization of a Neutron Detector for In-Flight Measurement of the Neutron Lifetime

The recent measurement of the lifetime of the free neutron using the beam method has an 8.7 s (4$σ$) discrepancy with UCN measurements. The goal of the BL3 experiment is to improve the statistical error of this measurement and help rule out systematic uncertainties as an explanation for the discrepancy. A well-characterized neutron flux detector with flat response is essential, since the neutron flux enters linearly into the neutron lifetime. I will present a new detector geometry optimization with uniform acceptance up to sixth order in neutron position.