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A bash script to run the GEMC simulations is created. tcsh scripts to run root2evio on lds2 is called using sshpass. The lds2 scripts use sshfs
The main script on lds3:
BUILD_GEMC_SIMULATION.sh
The 3 scripts on lds2:
first_commands.tcsh
second_commands.tcsh
last_commands.tcsh
LUND File Output
0.1 degree spacing in the Lab frame. CM Frame is not evenly spaced.
![MolThetaLab LUND DC limits.png](/./images/f/f1/MolThetaLab_LUND_DC_limits.png)
Applying the weight
![MolThetaLab DClimits integral.png](/./images/f/f3/MolThetaLab_DClimits_integral.png)
![MolThetaCM DClimits weighted rebin integral.png](/./images/a/a5/MolThetaCM_DClimits_weighted_rebin_integral.png)
Looking at the angles and the associated weight, we can find the sums
Once_Angles_and_weight=3399.930890560805437
Total_Angles_and_weight=1023379.198058736044914
Checking with Mathematica
"Integrating" with Cosine term
Finding the Cross Section
Performing a Riemann sum for [math]-30^{\circ} \lt \phi \lt 30^{\circ}[/math]
The cross section should be equal between both frames since the number of particles is an invariant. The differential cross section must differ between frames since the solid angle does vary.
[math]\sigma_{(CM)}=\sigma{(Lab)}[/math]
[math]\frac{d\sigma}{d\Omega}_{(CM)} d\Omega_{(CM)}=\frac{d\sigma}{d\Omega}_{(Lab)} d\Omega_{(Lab)}[/math]
[math]\frac{d\sigma}{d\Omega}_{(CM)} \sin \theta_{(CM)}\ d\theta_{(CM)}\ d\phi=\frac{d\sigma}{d\Omega}_{(Lab)} \sin \theta_{(Lab)}\ d\theta_{(Lab)}\ d\phi[/math]
[math]\rightarrow \frac{d\sigma}{d\Omega}_{(Lab)}=\frac{d\sigma}{d\Omega}_{(CM)} \frac{\sin \theta_{(CM)}\ d\theta_{(CM)}\ d\phi}{ \sin \theta_{(Lab)}\ d\theta_{(Lab)}\ d\phi}[/math]
[math]\rightarrow d\sigma_{(Lab)}=\frac{d\sigma}{d\Omega}_{(CM)} \frac{\sin \theta_{(CM)}\ d\theta_{(CM)}\ d\phi}{ \sin \theta_{(Lab)}\ d\theta_{(Lab)}\ d\phi}\sin \theta_{(Lab)} d\theta_{(Lab)}\ d\phi[/math]
![MolThetaCMdsigmaIntegral.png](/./images/3/33/MolThetaCMdsigmaIntegral.png)
![AssociatedWeights2.png](/./images/b/b3/AssociatedWeights2.png)
Adjust for DC Sector 1 Limits
![IntegralDCLimitsdSigmaCM.png](/./images/7/74/IntegralDCLimitsdSigmaCM.png)
GEMC Cross Section
Only taking GEMC hits in Sector 1 with Track ID of the mother of the FP equal to zero:
[math]\frac{0.009731\ barn}{0.013924\ barn}=70\%[/math]Efficiency
![CorrelatedPhiThetaHits.png](/./images/8/8c/CorrelatedPhiThetaHits.png)
![LUNDPhiThetaBins.png](/./images/7/7f/LUNDPhiThetaBins.png)
Taking GEMC hits with ANY Track ID of the mother of the FP :
[math]\frac{0.012433\ barn}{0.013924\ barn}=90\%[/math]Efficiency
![CORRELATED PhiThetaHits.png](/./images/d/d8/CORRELATED_PhiThetaHits.png)
![NOTCORRELATED PhiThetaHits.png](/./images/8/81/NOTCORRELATED_PhiThetaHits.png)
![LUNDPhiThetaBins.png](/./images/7/7f/LUNDPhiThetaBins.png)
Using the Cross Section
If we make the assumption that the beam of incoming electrons is a flux over an area,
[math]N_{incident}=\Phi\ A_{beam}\rightarrow dN_{incident}=\Phi\ dA_{beam}\rightarrow \frac{dN_{incident}}{ dA_{beam}}=\Phi[/math]
Using the definition of the differential cross section:
[math]\frac{d\sigma}{d\Omega}\equiv \frac{ \Biggl(\frac{dN_{scattered}}{d\Omega} \Biggr)}{\Biggl(\frac{dN_{incident}}{dA}\Biggr)}\rightarrow \frac{d\sigma}{d\Omega}\Biggl(\frac{dN_{incident}}{dA}\Biggr)=\Biggl(\frac{dN_{scattered}}{d\Omega} \Biggr)[/math]
Substituting using the flux
[math] \frac{d\sigma}{d\Omega}\Biggl(\frac{dN_{incident}}{dA}\Biggr)=\Biggl(\frac{dN_{scattered}}{d\Omega} \Biggr)\rightarrow \frac{d\sigma}{d\Omega}\Phi=\Biggl(\frac{dN_{scattered}}{d\Omega} \Biggr)[/math]
[math]\rightarrow dN_{scattered}= \frac{d\sigma}{d\Omega}\Phi d\Omega= \frac{d\sigma}{d\Omega}\Phi\sin \theta\ d\theta\ d\phi[/math]
Since the differential cross section is known in the Center of Mass frame of reference, but measurements are taken in the Lab Frame, a transformation must occur.
[math]\rightarrow dN_{scattered}= \frac{d\sigma}{d\Omega_{Lab}}\Phi \sin \theta_{Lab}\ d\theta_{Lab}\ d\phi_{Lab}[/math]
[math]\frac{d\sigma}{d\Omega_{Lab}}\sin \theta_{Lab}\ d\theta_{Lab}\ d\phi_{Lab}=\frac{d\sigma}{d\Omega_{CM}}\sin \theta_{CM}\ d\theta_{CM}\ d\phi_{CM}[/math]
[math]\frac{d\sigma}{d\Omega_{Lab}}=\frac{d\sigma}{d\Omega_{CM}}\frac{\sin \theta_{CM}\ d\theta_{CM}\ d\phi_{CM}}{\sin \theta_{Lab}\ d\theta_{Lab}\ d\phi_{Lab}}[/math]
[math]\rightarrow dN_{scattered}=\frac{d\sigma}{d\Omega_{CM}}\frac{\sin \theta_{CM}\ d\theta_{CM}\ d\phi_{CM}}{\sin \theta_{Lab}\ d\theta_{Lab}\ d\phi_{Lab}}\Phi \sin \theta_{Lab}\ d\theta_{Lab}\ d\phi_{Lab}[/math]
If we divide both sides by time
[math]\rightarrow \frac{dN_{scattered}}{t}=\frac{d\sigma}{d\Omega_{CM}}\frac{\sin \theta_{CM}\ d\theta_{CM}\ d\phi_{CM}}{\sin \theta_{Lab}\ d\theta_{Lab}\ d\phi_{Lab}}\frac{\Phi}{t} \sin \theta_{Lab}\ d\theta_{Lab}\ d\phi_{Lab}[/math]
Occupancy
LH2_NOSol_0Tor_11GeV_IsotropicPhi_v2_6_ShieldOut
Run
./BUILD_GEMC_SIMULATION.sh
DVMacro
Clas12Mon
Create hipo file
Move hipo file to clas12mon folder
mv LH2_NOSol_0Tor_11GeV_IsotropicPhi_v2_6_ShieldOut.hipo ~/clas12mon
Run monitor program
./README
Load hipo file
"Press H for hipo"
"Press play"
"Switch to
For [math]5^{\circ}\gt \theta\lt 40^{\circ}\ -30^{\circ}\gt \phi\lt 30^{\circ}[/math]
FOR DC Limits
Calculating
[math]\sigma_{Moller\ (\theta_{lab} = 5^{\circ}-40^{\circ})}=0.86\ barn[/math]
[math]t_{simulated}=\frac{N_{events}}{\sigma_{events} \Phi \rho \ell}=\frac{96105\ barn \cdot s}{7.87\times 10^{-2} \cdot 1.33\times 10^{11}\ barn}=9.3\times 10^{-6} s[/math]
[math]N_0=\Delta t \cdot R_{events}=\Delta t \cdot \frac{N_{events}}{t_{simulated}}=250\times 10^{-9}\ s \cdot \frac{98181}{9.3\times 10^{-6}\ s}=2639[/math]
[math]Occupancy=\frac{N_{hits}}{N_0}=\frac{N_{hits}}{\Delta t \cdot R_{events}}=\frac{t_{simulated}\cdot N_{hits}}{N_{events}\cdot \Delta t}=[/math]