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

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.

**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

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

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:

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:

- Properites of SIGRADUR
- Mean thickness = 2.1 mm
- Radiation length X0 = 28 cm

- 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

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

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%**

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

I | Attachment | Action | Size | Date | Who | Comment |
---|---|---|---|---|---|---|

png txt | ScatteringRadiatorAll.png scattering50.txt | manage | 14.5 3.3 K | 05 12 Jun 2007 - 08:31 12:32 | MartinJurkovic | Scatteing Total scattering and scattering in radiator for different Theta as a function of momenta at polar angle 50deg |

png txt | compareSim.png theta2length.txt | manage | 22.6 1.3 K | 29 May 12 Jun 2007 - 09:21 12:31 | MartinJurkovic | Comparision delta Path length theta (RICH - MDC) distribution of signal and conversion leptons deflection angle as a function of polar angle |

jpg | phiPos.jpg | manage | 112.7 K | 29 May 2007 - 09:24 | MartinJurkovic | Phi correlation for positive leptons (signal left, conversion right) |

png | scatteringCFK.png | manage | 7.3 K | 05 Jun 2007 - 08:25 | MartinJurkovic | scattering CFK |

png | scatteringRadiator.png | manage | 26.1 K | 05 Jun 2007 - 08:27 | MartinJurkovic | 3D scattering radiator |

png | scatteringRadiator50.png | manage | 9.9 K | 05 Jun 2007 - 08:50 | MartinJurkovic | scattering radiator @ 50deg |

png | scatteringTotal.png | manage | 28.7 K | 12 Jun 2007 - 09:26 | MartinJurkovic | Total scattering angle as a function of polar angle and momenta |

png | scatteringTotalSlice.png | manage | 17.7 K | 12 Jun 2007 - 09:27 | MartinJurkovic | Scattering angle as a function of momenta for different polar angles |

jpg | thetaPos.jpg | manage | 118.5 K | 29 May 2007 - 09:26 | MartinJurkovic | Theta correlation for positive leptons (signal left, conversion right) |

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