Occupancy for Sector 1

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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.pngMolThetaCM LUND DC limits.png

Applying the weight

MolThetaLab DClimits integral.pngCosMolThetaLab weightedDClimits.png


MolThetaCM DClimits weighted rebin integral.pngCosMolThetaCM weightedDClimits.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

CrossSectionMathematica1.png


"Integrating" with Cosine term

CrossSectionMathematica2.png

Finding the Cross Section

CrossSectionMathematicaProof.png


Performing a Riemann sum for [math]-30^{\circ} \lt \phi \lt 30^{\circ}[/math]


CrossSection60deg.png


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.pngMolThetaLabdSigmaIntegral.png

AssociatedWeights2.pngDSigmaCMLab.png

Adjust for DC Sector 1 Limits

IntegralDCLimitsdSigmaCM.pngIntegralDCLimitsdSigmaLab.png

GEMC Cross Section

Only taking GEMC hits in Sector 1 with Track ID of the mother of the FP equal to zero:

DSigmaVsThetaLabOverlay.png [math]\frac{0.009731\ barn}{0.013924\ barn}=70\%[/math]Efficiency

CorrelatedPhiThetaHits.pngPhiThetaBinsdSigma.png


LUNDPhiThetaBins.pngLUNDPhiThetaBinsWeighted.png


Taking GEMC hits with ANY Track ID of the mother of the FP :


DSigmaVsThetaLabWithAll.png[math]\frac{0.012433\ barn}{0.013924\ barn}=90\%[/math]Efficiency

CORRELATED PhiThetaHits.pngCORRELATED PhiThetaHits dSigma.png


NOTCORRELATED PhiThetaHits.pngNOTCORRELATED PhiThetaHits dSigma.png


LUNDPhiThetaBins.pngLUNDPhiThetaBinsWeighted.png

Using the Cross Section

[math]\sigma \equiv \frac{N_{scattered}}{\mathcal{L}t}=\frac{N_{scattered}}{N_{incident}\rho \ell }[/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]

Clas12monNoSolNoShield.png


FOR DC Limits

OccupancyDCLimits Unweighted.png

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]