Results of Integration Cube Type

Performance of Integration Cube type (Fig.22(b)) has been investigated as well. Position dependences is studied in horizontal direction ($x$) at y = 0. Photoelectron yield of each PMT and sum of two PMT's are plotted in Fig.31. Unlike the Belle type, Integration Cube type gives very flat distribution. With Belle type, decrease by a factor of $\sim$ 5 is seen in propagation of 10 cm, but with Integration Cube type, decrease of only $\sim$ 10 % is seen.¹ Total yield of photoelectron (sum of two PMT's) at the center is about 19, which is about 20 % smaller than that of Belle type.

Uniform photoelectron yields are demonstrated in Fig.32. Sum of two PMT's are plotted as a function of $x$ for $y = -3, 0, 3$ [cm]. The photoelectron yields are found to be stable within 10%.

図 31: Position dependence of $N_{pe}$ as a function of $x$ at $y = 0$ cm for Integration cube type.

図 32: Position dependence of $N_{pe}^{sum}$ as a function of $x$ at $y = -3, 0, 3$ cm for Integration cube type.

For further study of this type, Integration Cube types with other geometries have been studied. In fig.33, effects of integration cube volume are studied. Depth of Integration Cube is reduced from 12 cm (solid circle) to 6 cm (solid square). By reducing the integration volume by a factor of 2, photoelectron yields increases from 19 to 22 while slight position dependence is appeard.

When the width of the counter is doubled, namely changing from $12 \times 12 {\rm cm}^2$ to $24 \times 12 {\rm cm}^2$, while keeping the same thickness of aerogel, the photoelectron yield decreses from 19 to 10. Thus, there is strong correlation between the volume or surface area of Integration Cube and photon yields.

図 33: Position dependence of $N_{pe}$ summed from both PMTs as a function of x for Integration Cube type with different geometries. The thickness of aerogel is fixed to be 12 cm.

図 34: Position dependence of $N_{pe}$ as a function of x at different y for Mirror type. The PMT is located at -6 cm. The low values of points at x = 5 cm are accidental due to an air gap between the aerogel and the wall.

In the stacking configuration of Integration Cube type counters (Fig.16), every other cells are stacked in reverse direction in order to eliminate dead space and having the aerogel at the same radius. In this configuration, some particles enter in reverse direction. Effects of direction of particle injection have been studied. Integration Cube type counter has been rotated by 90, 180 and 270 degrees and photoelectron yields are compared. Path length of particle trajectory along the aerogel has been kept the same for comparison. As listed in Table. 2, photoelectron yield decrease by $\sim 20 \%$ when particles enter from the back to front. This rather small difference suggests that most of photons in the integration cube do not have directionality already, which is again consistent with the diffusive optical property of the aerogel.

表 2: $N_{pe}$ obtained in different beam directions for Integration Cube type. The beam was injected through the center of aerogel volume.

Beam direction	$N_{pe}$ (left)	$N_{pe}$ (right)	$N_{pe}$ (sum)
Normal (from front to back)	9.8	8.9	18.7
Reverse (from back to front)	8.2	7.3	15.5
Sideward (from the side)	8.4	7.9	16.3