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Vanwdani at 15:01, 30 May 2017

2017-05-30T15:01:23Z

Vanwdani at 14:56, 30 May 2017

2017-05-30T14:56:52Z

Vanwdani at 14:35, 30 May 2017

2017-05-30T14:35:37Z

Vanwdani at 14:33, 30 May 2017

2017-05-30T14:33:55Z

Vanwdani at 14:27, 30 May 2017

2017-05-30T14:27:11Z

Vanwdani: Created page with " Using the theoretical differential cross section from previous $\frac{d\sigma}{d\Omega}=\frac{ \alpha^2 }{4E^2}\frac{ (3+cos^2\theta)^2}{si…"$

2017-05-30T14:13:08Z

Created page with " Using the theoretical differential cross section from previous <center><math>\frac{d\sigma}{d\Omega}=\frac{ \alpha^2 }{4E^2}\frac{ (3+cos^2\theta)^2}{si…"

New page

[[Converting_to_barns| Using the theoretical differential cross section from previous]]
<center><math>\frac{d\sigma}{d\Omega}=\frac{ \alpha^2 }{4E^2}\frac{ (3+cos^2\theta)^2}{sin^4\theta}</math></center>

<center><math>\alpha ^2=5.3279\times 10^{-5}</math></center>

<center><math>E\approx 53.013 MeV</math></center>

We can take the Moller electron distribution of Theta in the Center of Mass frame, and multiply each given angle Theta by the expected differential cross section.

<center>[[File:MolThetaCM_spread.png]]</center>

This causes the Moller Theta distribution in the Center of Mass frame to directly follow the theoretical differential cross section.

<center>[[File:MolThetaCMWeightedTheory_LH2_11GeV.png]]</center>

The Lab frame distribution of Theta can also be weighted similarly. However, instead of having it be a differential cross section, [[Converting_to_barns|we can find the necessary number of particles.]]

<center><math>\frac{d\sigma}{d\Omega} = \frac{\left(\frac{number\ of\ particles\ scattered/second}{d\Omega}\right)}{\left(\frac{number\ of\ incoming\ particles/second}{cm^2}\right)}=\frac{dN}{\mathcal L\, d\Omega} =differential\ scattering\ cross\ section</math></center>

<center><math>\frac{d\sigma}{d\Omega} =\frac{dN}{\mathcal L\, d\Omega} =\frac{dN}{\Phi \rho \ell\, d\Omega}</math></center>

<center><math>\Rightarrow \int \frac{d\sigma}{d\Omega} \rho\ \ell \Phi d\Omega=\int dN</math></center>

Checking versus the given Luminosity for the experiment

<center><math>\mathcal L = \frac{1.33 \times 10^{35}}{cm^2\cdot s} \times \frac{10^{-24} cm^2}{barn}=1.33\times 10^{11} barns^{-1}s^{-1}</math></center>

<center><math>\mathcal L \int \frac{d\sigma}{d\Omega} d\Omega = 1.33 \times 10^{11} barns^{-1} \times 2\pi\ \int \frac{d\sigma}{d\Omega}\ \sin{\theta} d\theta=N</math></center>

Limiting the range of Theta to within 5 to 40 degrees in the Lab frame:

<center>[[File:DetectorRangeLab.png]]</center>

We can find the corresponding angular range in the CM frame:
<center>[[File:DetectorRangeCM.png]]</center>

Integrating the differential cross-section over the solid angle:
<center>[[File:DetectorIntegrationXSect_LH2_11GeV.png]]</center>
<pre>
IntegralDiffXSect->Integral()
</pre>

4.97493824519086629e+04 barns

Multiplying by the Luminosity, we find:

<center><math>4.97\times 10^{4} barns \times\frac{1.35\times 10^{11}}{barns\cdot s}=6.71\times 10^{15}\frac{electrons}{s}</math></center>

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 <center><math>\textbf{\underline{Navigation}}</math>
-[[VanWasshenova_Thesis#Determining_wire-theta_correspondence|<math>\vartriangleleft </math>]]
+[[Lorentz_Transformation_to_Lab_Frame|<math>\vartriangleleft </math>]]
-[[VanWasshenova_Thesis#Determining_wire-theta_correspondence|<math>\triangle </math>]]
+[[VanWasshenova_Thesis#Weighted_Isotropic_Distribution_in_Lab_Frame|<math>\triangle </math>]]
 [[CED_Verification_of_DC_Angle_Theta_and_Wire_Correspondance|<math>\vartriangleright </math>]]
 </center>

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	<center><math>4.97\times 10^{4} barns \times\frac{1.35\times 10^{11}}{barns\cdot s}=6.71\times 10^{15}\frac{electrons}{s}</math></center>		<center><math>4.97\times 10^{4} barns \times\frac{1.35\times 10^{11}}{barns\cdot s}=6.71\times 10^{15}\frac{electrons}{s}</math></center>
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@@ Line 1: / Line 1: @@
 <center><math>\textbf{\underline{Navigation}}</math>
-[[VanWasshenova_Thesis#Determining_wire-theta_correspondence|<math>\vartriangleleft </math>]]
+[[Lorentz_Transformation_to_Lab_Frame|<math>\vartriangleleft </math>]]
 [[VanWasshenova_Thesis#Weighted_Isotropic_Distribution_in_Lab_Frame|<math>\triangle </math>]]
 [[CED_Verification_of_DC_Angle_Theta_and_Wire_Correspondance|<math>\vartriangleright </math>]]

@@ Line 2: / Line 2: @@
 [[VanWasshenova_Thesis#Determining_wire-theta_correspondence|<math>\vartriangleleft </math>]]
-[[VanWasshenova_Thesis#Determining_wire-theta_correspondence|<math>\triangle </math>]]
+[[VanWasshenova_Thesis#Weighted_Isotropic_Distribution_in_Lab_Frame|<math>\triangle </math>]]
 [[CED_Verification_of_DC_Angle_Theta_and_Wire_Correspondance|<math>\vartriangleright </math>]]

@@ Line 1: / Line 1: @@
 [[Converting_to_barns| Using the theoretical differential cross section from previous]]
 <center><math>\frac{d\sigma}{d\Omega}=\frac{ \alpha^2 }{4E^2}\frac{ (3+cos^2\theta)^2}{sin^4\theta}</math></center>
@@ Line 66: / Line 78: @@
 <center><math>4.97\times 10^{4} barns \times\frac{1.35\times 10^{11}}{barns\cdot s}=6.71\times 10^{15}\frac{electrons}{s}</math></center>