Fabrication of silica aerogel with $n$ = 1.08 for $e^{+}\mathrm{/}{\mu }^{+}$ separation in a threshold Cherenkov counter of the J-PARC TREK/E36 experiment

This study presents the development of hydrophobic silica aerogel for use as a radiator in threshold-type Cherenkov counters. These counters are to be used for separating positrons and positive muons produced by kaon decay in the J-PARC TREK/E36 experiment. We chose to employ aerogel with a refractive index of 1.08 to identify charged particles with momenta of approximately 240 MeV/$c$, and the radiator block shape was designed with a trapezoidal cross-section to fit the barrel region surrounding the kaon stopping target in the center of the TREK/E36 detector system. Including spares, we obtained 30 crack-free aerogel blocks segmented into two layers, each layer having a thickness of 2 cm and a length of 18 cm, to fill 12 counter modules. Optical measurements showed that the produced aerogel tiles had the required refractive indices and transparency.