 Solution

The radiation length $X_0$ is the characteristic length for high-energy electron energy loss by bremsstrahlung; smaller $X_0$ means more radiative loss for the same traversed thickness. To limit that loss, minimize $x/X_0$, choosing less material or a larger $X_0$, rather than minimizing $X_0$ itself. At reactor Positron energies of a few MeV, ionization and subsequent annihilation matter more than high-energy bremsstrahlung. A sufficiently large scintillation counter measures the deposited energy, so containment of the Positron and annihilation photons, light yield and calibration are the relevant design issues.^[ref]