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

Total scattering angle as a function of polar angle and momenta. |
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Total scattering angle as a function of momenta for different polar angles. |
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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 length through the material) was taken into account.

Dependance of the deflection angle on the polar angle. |
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**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

- Density: 24.61 g/cm**3 (at 20deg Celsius, 2.28bar,

Small angle scattering in RICH radiator as a function of polar angle and momenta. |
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Dependance of the particle trajectory length in the RICH radiator on the polar angle. |
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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. |
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In the following, only the **mean** deflection to the perpendicular direction of **22.25deg** was taken into account to make the pictures simple

- Properites Properties of SIGRADUR
- 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 |
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- Properties of Aluminum (reflactive (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 Aluminium. | Scattering in MgF2. |
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- Properties of CFK
- Thickness = 0.4 mm
- Radiation length X0 = 28 cm

Scattering in CFK |
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Area difference between these two cuts is:

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

I have compared the 1D distribution for (theta_rich - theta_RK) (in phi it looks similar) for electrons comming coming from conversion and the electrons comming 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

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 |

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