Charge was calculated for signals registered by photomultipliers at both ends of scintillator (PM3 and PM4). Attenuation length can be determined by fitting function given by formula 11 [105]
to experimental points:
(11).
Fitting to experimental points determined for PM 4 is shown in Fig. 39.
0
20
40
60
80
100 120 140 160 180
20
30
40
50
60
70
Q [a.u.]
Position on strip [mm]
Figure 39 Function given by formula 11 fitted to experimental points (PM4).
72
Such shape of fitted curves is justified by appearance of two components of light
attenuation: long (λ
1
) and short (λ
2
), that can be pointed out from fitting. In short
scintillators, about 20 cm long, the short component dominates. Attenuation length is
dependent on the wavelength [9]. The obtained results refer to blue light, to which vacuum
photomultipliers are sensitive.
Function given by formula 11 was fitted also to experimental points of 25 cm long
BC-420 scintillator, and parameters λ
1
and λ
2
were determined as well. In Tab. 11 absolute
values of attenuation parameters determined for J-PET and BC-420 scintillators with pair
of photomultipliers for each strip are presented.
Table 11 Attenuation parameters for J-PET and BC-420 scintillators. Scintillator/parameter λ 1 [mm] λ 2 [mm] J-PET
10.3 ± 2.6 | 26.0 ± 5.7
158.4 ± 6.5 | 163.0 ± 3.7
BC-420
8.8 ± 2.3 | 31.7 ± 7.8
492 ± 60 | 308.6 ± 8.2
In case of BC-420, mean values of λ
1
and λ
2
are comparable with corresponding
parameters of 30 cm scintillators determined and described in [105]. For blue light, values
of short component: λ
1
in both scintillators are consistent within error bars. Therefore, light
attenuation in scintillating strips, about 20 cm long, is similar. However, the long constant:
λ
2
differs significantly in both scintillators. In case of BC-420 it is more than two times
bigger than in J-PET scintillator. This indicates that attenuation in longer J-PET
scintillators will be larger in comparison to BC-420.
The described test was carried out for blue light detected by vacuum
photomultipliers. Here it is important to note that J-PET is emitting light also in the range
between about 330 nm and 370 nm (see Fig. 16), where the attenuation is strong and where
BC-420 has no contribution. This is the region of relatively high quantum efficiency of
vacuum photomultipliers but not silicon ones. The experiment does not describe
attenuation of light of the targeted wavelength, but shorter ones.
Moreover, J-PET plastic scinitllators are prepared from monomer containing
inhibitor of polymerization: 4-tert-butylcatechol, in amount of 50 ppm. It is brown solid,
yellowish when dissolved, what may cause slight yellowing of polymer. Even such low
amount may affect the light propagation and attenuation length in the scintillating material.
73
J-PET scintillators will be eventually utilized with silicon photomultipliers,
sensitive to light of larger wavelength. Maximum of emission of J-PET scintillators is
shifted towards longer wavelengths, for which attenuation is lower. Therefore in long
J-PET scintillators strips the attenuation length should be larger than in BC-420 of the
same length.