# Total scattering in RICH

Total scattering was calculated using the formula:

Theta_0 = 13.6MeV/(beta*c*p) 13.6 MeV/(beta*c*p) * Z * sqrt(SUM) * {1 + 0.038 * ln(SUM)}
where SUM = sum(x_i / X0_i)
Taking into account electrons electrons, than beta = Z = 1 `=> beta =` Z == 1

Total scattering angle as a function of polar angle and momenta. Total scattering angle as a function of momenta for different polar angles. In the calculation, the polar angle dependant deflection between the perpendicular direction to the surface of the RICH components (shortest distance through the materials) and particle incident angle (real particle path lengt through the material) was taken into account.

Dependance of the deflection angle on the polar angle. # Small Angle Scattering devided in all RICH components

### Scattering in the radiator gasC4F10

• Properties of C4F10
• Density: 24.61kg/m**3 24.61 g/cm**3 (at 20deg Celsius, 2.28bar, gas phase)
• Density: 1516kg/m**3 1516 g/cm**3 (at 20deg Celsius, liquid phase)
• Radiation Length X0 = 34.52g/cm**2 34.52 g/cm**2 = 3200cm 3200 cm in the gas phase at atmospheric pressure

Dependance of the length of the radiator on the emmision angle:

Small angle scattering in RICH radiator as a function of polar angle and momenta. Small angle scattering as a function of momentum and emmision angle: Dependance of the particle trajectory length in the RICH radiator on the polar angle. Momentum dependance of the small scattering angle for different emmision angles: Scattering angle in RICH radiator as a function of momenta for different polar angles.Scattering angle in RICH radiator as a function of momenta for polar angle Theta = 50deg.  Momentum dependance of the small scattering angle for emmision angle Theta = 50deg: ### Scattering in the carbon shell

In the following, only the mean deflection to the perpendicular direction of 22.25deg was taken into account to make the pictures simple

• Properites of CFK
• Mean thickness = 2.1mm
• Radiation length X0 = 30cm

Dependance of the small scattering ang le on momentum: # Eliptic vs rectangular matching cut

• Mean thickness = 2.1 mm
• Radiation length X0 = 28 cm
Scattering angle in RICH mirror substrate material SIGRADUR as a function of momenta for mean deflection angle 22.25deg ### Scattering in the mirror reflective and protection layer

• Properties of Aluminum (reflactive layer)
• Thickness = 20 ug/cm**2
• Density = 2.7 g/cm**3
• Radiation length X0 = 24.01 g/cm**2 = 8.9 cm
• Properties of MgF2 (protection layer)
• Thickness = 11 ug/cm**2
• Density = 3.0 g/cm**3
• Radiation length X0 = 29.32 g/cm**2 = 9.77 cm
Scattering in Aluminium.Scattering in MgF2.  ### Scattering in the carbon shell (CFK)

• Properties of CFK
• Thickness = 0.4 mm
• Radiation length X0 = 28 cm
Scattering in CFK # Eliptic (circular) vs rectangular matching cut

Area difference between these two cuts is:

• Rectangular cut: (2*D_phi)*(2*D_theta) = 4*D_theta*D_phi
• Eliptic cut: pi * D_theta * D_phi
• Difference = (4 - pi)/4 = 22%

# Conversion / Signal from PLUTO simulation

I have compared the 1D distribution for (theta_rich - theta_RK) (in phi it looks similar) for electrons comming from conversion and the electrons comming from all other sources. the conversion signal I have chosen according to the following condition: "pid.genInfo1==7001 || pid.genInfo1==17001 || pid.genInfo1==52001", the "real" signal is negation of the previous condition. the determination of the mean and sigma of the distribution was done with the "standard" 2-gaussian fit for momentum bins (0,150>; (150,350> and (350,1000>

in the picture "compareSim.png" you can see mean and sigma of the delta_theta distributions for the 3 momenta bins. the upper two pictures are done for electrons and positrons separately (red color "real" signal, blue conversion signal). in the lowest picture the comparision between electrons and positrons for the "real" signal is done.

as one can see, the differences in the simulation are only minor. the yields for signal and conversion are comparable (almost 1:1) for momenta (0,150>, it drops to 2:1 for momenta (350,1000> (see thetaNeg.jpg)

The sigma of the delta_theta distributions for negative tracks is:

• Signal: 0.96, 0.74, 0.54
• Conversion: 1.01, 0.81, 0.62

The sigma of the delta_theta distributions for positive tracks is:

• Signal: 1.18, 0.79, 0.60
• Conversion: 1.12, 0.88, 0.60

`==================================================`

in phi are the distributions much more narrower:

The sigma of the delta_phi distributions for negative tracks is:

• Signal: 0.55, 0.47, 0.47
• Conversion: 0.40, 0.53, 0.56

The sigma of the delta_phi distributions for positive tracks is:

• Signal: 0.57, 0.49, 0.50
• Conversion: 0.46, 0.51, 0.40

At this point i have to add, that i set following limits for the fit parameters: for signal is sigma in the range (0.4; 2.0) and for the background (2.0; infinity), which you can see in the fits not very well describing the distributions. in the most cases, the background had sigma of 2.0 in few cases just a touch higher than 2.0! (not a very good model :-(...), since for experimental data this limits worked very well, i decided not to introduce new limits for the fits.

I hope, the selection of the conversion was done properly (according to the documentation i hope i have not overseen something...)

-- MartinJurkovic - 29 May 2007

• Comparision delta theta (RICH - MDC) distribution of signal and conversion leptons: • Phi correlation for positive leptons (signal left, conversion right): • Theta correlation for positive leptons (signal left, conversion right): • Total scattering angle as a function of polar angle and momenta: • Scattering angle as a function of momenta for different polar angles: -- MartinJurkovic - 29 May 2007

IAttachmentActionSizeDateWhoComment  png txt ScatteringRadiatorAll.png scattering50.txt manage14.5 3.3 K 05 12 Jun 2007 - 08:31 12:32 MartinJurkovicScatteing Total scattering and scattering in radiator for different Theta as a function of momenta at polar angle 50deg  png txt compareSim.png theta2length.txt manage22.6 1.3 K 29 May 12 Jun 2007 - 09:21 12:31 MartinJurkovicComparision delta Path length theta (RICH - MDC) distribution of signal and conversion leptons deflection angle as a function of polar angle jpgphiPos.jpgmanage 112.7 K 29 May 2007 - 09:24MartinJurkovic Phi correlation for positive leptons (signal left, conversion right) pngscatteringCFK.pngmanage 7.3 K 05 Jun 2007 - 08:25MartinJurkovic scattering CFK pngscatteringRadiator.pngmanage 26.1 K 05 Jun 2007 - 08:27MartinJurkovic 3D scattering radiator pngscatteringRadiator50.pngmanage 9.9 K 05 Jun 2007 - 08:50MartinJurkovic scattering radiator @ 50deg pngscatteringTotal.pngmanage 28.7 K 12 Jun 2007 - 09:26MartinJurkovic Total scattering angle as a function of polar angle and momenta pngscatteringTotalSlice.pngmanage 17.7 K 12 Jun 2007 - 09:27MartinJurkovic Scattering angle as a function of momenta for different polar angles jpgthetaPos.jpgmanage 118.5 K 29 May 2007 - 09:26MartinJurkovic Theta correlation for positive leptons (signal left, conversion right)

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