| software | GEANT3.21 |
| hadron package | GHEISHA / FLUKA+MICAP |
| incident particle | n |
| momentum distribution | Uniform on (100.,800.) MeV/c |
| orientation | Uniform on (-0.45,0.45),(0.,0.15π/0,85π,1.15π/1.85π,2&pi), for cosθ,φ |
| generated event number | 107 |
| target center | (-0.3,0.,1.3):E549 |
| x/y generation point distribution | 4.0 cm sigma Gaussian centered at (x,y)=(-0.3,0.) |
| z generation point distribution | uniform |
| multiple scattering | on(Moliere) |
| energy loss straggling | on(Gauss/Landau/Vavilov are internally selected adequately) |
| nuclear reaction of n and secondaries | on(GHEISHA/FLUKA) |
| Birk's coefficient for plastic scintillator | 0.013/(MeV/cm) |
| energy resolution of scintillators | infinite |
| thresholds | 0/3/5/7/10 MeVee |
| segentation of scintillators | properly treated(initial layer) |
| momentum resolution | infinite |
γ,p,n,d,t,3He,4He are generated and transported.
Nuclear residuals are neglected.
Ex: In the n + 12C -> α + 9Be reaction, only &alpha particle is transported to contribute the light output, and 9Be is neglected.
ichset=1: n + p -> n + p (proton elastic)
ichset=3: n + 12C -> n + 12C (Carbon elastic)
ichset=5: n + 12C -> α + 9Be
ichset=6: n + 12C -> n + 3α
ichset=7: n + 12C -> p + 12B
ichset=7: n + 12C -> p + n + 11B
ichset=7: n + 12C -> n + n + 11C
ΔE' = R ΔE, R=(1+C1δ+C2δ2), δ=dE/dx * 1/ρ (MeV g-1 cm2),
where ΔE is the energy deposit (MeV) on a step, dE/dx is the ionization energy loss (MeV/cm), ρ is the density of the material (g/cm3). C1=0.013 g MeV-1 cm-2 and C2=9.6E-06 g2 MeV-2 cm-4, which are user-defined. If the particle is with Z>1, C1 is automatically replaced by ~0.5714C1 to get better description. The ΔE' is integrated over the every steps and charged particles passing through the segment. See, J.B.Birks, "The Theory and Practice of Scintillation Counting." Pergamon Press, 1964. In the analysis, the evaluated ΔE' value is refered to with the "MeVee" unit. Therefore, the MeVee values are linearly dependent on the detected photon number, and the value is defined by the equivalent depositted energy of ideal particle with no saturation for every incident particles. Therefore, the value is defined for all particles over the full energy range just with observed pulse height (ADC value) regardless of the source of the photons.
Detected photon number is translated into the electron energy value which produces the same photon number. The electron energy value is refered to by "MeVee" unit. The transformation formula for proton is given below:
ΔEe = a1ΔEp/α-a2(1-exp(-a3ΔEp/αa4)),
where coefficients ai (i=1~4), are evaluated for p and α, separately, being optimized for each of scintillators as tabulatted below. See, R. Madey et. al., Nucl. Instr. and Meth. 151 (1978) 445, R. A. Cecil et. al., Nucl. Instr. and Meth. 161 (1979), K. Nakayama et. al., Nucl. Instr. and Meth. 190 (1981) 555 .
| Particle | Scintillators | Coefficients a1/a2/a3/a4 |
|---|---|---|
| p | NE-102=BC-400(plastic) | 0.95/8.0/0.1/0.90 |
| p | NE-213=BC-501(liquid) | 0.83/2.82/0.25/0.93 |
| p | NE-224=BC-505(liquid) | 1.0/8.2/0.1/0.88 |
| p | NE-228/NE-228A=BC-513(liquid) | 0.95/8.4/0.1/0.90 |
| alpha; | all | 0.41/5.9/0.065/1.01 |
In the application to the data, we meet several difficluties:
1. The formula does not give any relationship between ΔEe and detected pulse height. Therefore, we have no way to convert detected pulse height to ΔEe, and we cannot help assuming Birks law additionally to calibrate.
2. The depositteed energy by electron is dominated by the Bremsstrahlung - therefore, depositted energy VS detected energy relationship for electron may depend on the dimensions, shape of the scintillator used. This may introduce additional uncertainty - since the Te VS Tp relationship may valid only in the experiment measured it, the relationship cannnot be used commonly.
3. Since the fit is obtained for the proton with 2.43~19.55 MeV, the application should be limited to the region, while the full stop proton on our segement is with ~395 MeV/c momentum (~80 MeV kinetic energy).
4. The relationship is obtained for stopped proton within the scintillator. For fast protons escape from the segment, the relation should underestimate the light output assuming the Birks law.
5. The responce function is different by, say, ~10% each other even within BC5xx, as shown below. Therefore, the adoption of NE102(attenuation length : 160 cm) parameters for the BC408 (:210 cm) would not be justified, even for lower energy protons.
Because of these uncertainties, the definition is unacceptable as it is for our usage.
The difference between GEANT- and DEMONS-definition is demonstrated below:
The data always gives smaller output by ~10%, than the simulation assuming Birks factor 0.013 g MeV-1 cm-2. This may be caused either the larger Birks factor or the nonlinearity (saturation) of the H6410 PMT output.
