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

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