1. Aerogel detector revisited Sokolov Oleksiy, UNAM, progress report, 20 Sept 2006 E int = M – wall reflectivity є – PMT relative area Belle geometry (traditional): uses a lignt integration box, detects scattered Cherenkov photons. Light collection efficiency:

2. Light collection efficiency Teflon- covered walls, reflectivity = 0.9..0.95 Box size:13x13cm, PMT diameters: 1.5“(1), 3.0“(2) E int 1=8..15% E int 2 =26..41%

3. Fresnel lens geometry (proposed): detects both unscattered and scattered photons. Unscattered light is focused on the PMT with the fresnel lens. F lens = distance to PMT. Clearly provides an advantage!

4. Geometry: Aerogel refraction index n=1.0304 Cherenkov cone half-opening angle: Θ=acos(1/n)=14° For lens of 6” focal length, diameter of the ring is d ≈ 3”,

5. Geometry: Aerogel refraction index n=1.0304 Cherenkov cone half-opening angle: Θ=acos(1/n)=14° For lens of 6” focal length, diameter of the ring is d ≈ 3”, but PMT of d=1.5” was used!! => Focused light was entirely missing the PMT!!!

6. What to do? Change geometry, so that the ring is smaller than the PMT diameter  2 Fresnel lenses have been purchased, with focal length F_1=2.8”, d=1.39” (for 1.5” PMT) F_2=5.0”, d=2.48” (for 3.0” PMT) Cover the box with another layer of teflon to increase reflectivity (up to 0.95)

7. What performance to expect? Number of detected photons: N det = N dir +N scat = N Ĉh ·a·E PMT +N Ĉh · (1-a) ·E int ·E PMT = = N Ĉh ·E PMT [a+(1-a)E int ] a – fraction of photons that pass aerogel block without Rayleigh scattering. a=L Ray /(L·n) ·[1-exp(-n·L/L Ray )] L – box size, L RAY – Rayleigh length N Ĉh =2παL[1-1/(nβ) 2 ](1/λ 1 -1/λ 2 )

8. Rayleigh length PMT spectral range: 300nm - 650nm, peak 420 nm Rayleigh length for aerogel depends on the wavelength, Measurements with 2 laser beams of different wavelength gave: λ=473 nm, L RAY ≈ 2.5cm, a=0.18; λ=405 nm, L RAY ≈ 1.0cm, a=0.07; Total number of detected photons: for 1.5” PMT: N Ĉh ≈ 422 Emitted N scat ≈ 5 Detected diffused N Dir ≈ 7.5 Detected unscattered