# Total scattering in RICH

Total scattering was calculated using the formula:

Theta_0 = 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, than beta = Z = 1

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 length through the material) was taken into account.

# Small Angle Scattering divided in all RICH components

### Scattering in the radiator gas C4F10

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

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

### Scattering in SIGRADUR (mirror substrate material)

• Mean thickness = 2.1 mm
• Radiation length X0 = 28 cm

### Scattering in the mirror reflective and protection layer

• Properties of Aluminum (reflective 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 the carbon shell (CFK)

• Properties of CFK
• Thickness = 0.4 mm
• Radiation length X0 = 28 cm

# Elliptic (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
• Elliptic 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 coming from conversion and the electrons coming 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...)

• 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):

-- MartinJurkovic - 29 May 2007
Topic attachments
I Attachment Action Size Date Who Comment
txt scattering50.txt manage 3.3 K 12 Jun 2007 - 12:32 MartinJurkovic Total scattering and scattering in radiator as a function of momenta at polar angle 50deg
txt theta2length.txt manage 1.3 K 12 Jun 2007 - 12:31 MartinJurkovic Path length and deflection angle as a function of polar angle
Topic revision: r7 - 14 Jun 2007, MartinJurkovic

 Български _jméno_jazyka Dansk Deutsch English Español Suomi Français Italiano 日本語 한글 Nederlands Norsk Polski Português Português brasileiro Русский Svenska 简体中文 正體中文
Copyright © by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding Hades Wiki? Send feedback
Imprint (in German)