Difference between revisions of "October 22, 2008"

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Line 1: Line 1:
 +
[http://wiki.iac.isu.edu/index.php/October_Fission_HRRL_Measurements_2008 go back]
 +
 +
 
Unpolarized Measurents:
 
Unpolarized Measurents:
  
Line 26: Line 29:
 
<math>HV_{Det_C}</math> =
 
<math>HV_{Det_C}</math> =
  
−
==Run 234==
+
==Run 168 ( 234.lst) ==
  
 
[[Image:Run234_Nai_Spectrum.gif|300px|thumb|NaI spectrum monitoring the photon flux during run 234]]
 
[[Image:Run234_Nai_Spectrum.gif|300px|thumb|NaI spectrum monitoring the photon flux during run 234]]
Line 77: Line 80:
 
You create your histograms, loop over the ntuple entries , and perform histogram operations in the file [[Media:PhotoFis.C.txt]]
 
You create your histograms, loop over the ntuple entries , and perform histogram operations in the file [[Media:PhotoFis.C.txt]]
  
−
==Run 229==
+
==Run 164 (229.lst)==
  
 
[[Image:Run229_Nai_Spectrum.gif|300px|thumb|NaI spectrum monitoring the photon flux during run 229]]
 
[[Image:Run229_Nai_Spectrum.gif|300px|thumb|NaI spectrum monitoring the photon flux during run 229]]
Line 112: Line 115:
 
=H20 runs=
 
=H20 runs=
  
−
==run 140==
+
==Run 140 (199.lst)==
 
Det A on top
 
Det A on top
  
 
uses file 199.lst
 
uses file 199.lst
  
−
The spectrum below shows the Time of Flight spectrum for Detectors "A" and "C".  The bottom figures represent the energy calculated from the time of flight when a neutron is assumed as the detected particle.  Events beyond 50 MeV are from the photon peak.  In order to determine the time of flight the average ToF for a photon (140 ns) was used as the start time.  Photon events above this average will appear at energies beyond 50 MeV and photon events below this average will have negative times and appear as Underflows in histogram AupNErun199.  There are 7640  events in Histogram Auprun199 above 146 ns correspond to the (15050-7410=7640) events shown in AupNErun199 histogram.   
+
The spectrum below shows the Time of Flight spectrum for Detectors "A" and "C".  The bottom figures represent the energy calculated from the time of flight when a neutron is assumed as the detected particle.  Events beyond 15 MeV are from the photon peak (phtotons are misidentified as neutrons).  In order to determine the time of flight the average ToF for a photon (140 ns) was used as the start time.  Photon events above this average will appear at energies beyond 15 MeV and photon events below this average will have negative times and appear as Underflows in histogram AupNErun199.  There are 7640  events in Histogram Auprun199 above 146 ns correspond to the (15050-7410=7640) events shown in AupNErun199 histogram.   
  
 
[[Image:Run140_RawToF.gif | 200 px]]
 
[[Image:Run140_RawToF.gif | 200 px]]
  
−
Neutrons from the target should have energies  below 14 MeV.  The spectrum below were normalized by the number of NaI events observed during the run.
+
Neutrons from the target should have energies  below 14 MeV.  The spectra below were normalized by the number of NaI events observed during the run.
  
 
[[Image:Run140_NormNeutronEspectrum.gif | 200 px]]
 
[[Image:Run140_NormNeutronEspectrum.gif | 200 px]]
  
−
==run 136 ==
+
==Run 136 (194.lst) ==
  
 
Det A on side
 
Det A on side
Line 188: Line 191:
 
  AsideNormRun234->Sumw2();
 
  AsideNormRun234->Sumw2();
 
   
 
   
−
  TH1F DetAdiffH20= ( AupNormRun199-AsideNormRun194);
+
  TH1F DetAdiffH20= ( *AupNormRun199 - *AsideNormRun194);
 +
DetAdiffH20->SetName("DetAdiffH20");
 +
 
 +
TH1F DetAup_D2OsubH20= ( *AupNormRun229 - *AupNormRun199);
 +
DetAup_D2OsubH20->SetName("DetAup_D2OsubH20");
 +
TH1F DetAside_D2OsubH20= ( *AsideNormRun234 - *AsideNormRun194);
 +
DetAside_D2OsubH20->SetName("DetAside_D2OsubH20");
 +
TH1F DetAdiff= (DetAup_D2OsubH20 - DetAside_D2OsubH20);
 +
  DetAdiff->SetName("DetAdiff");
 +
DetAdiffH20->Write();
 +
TH1F DetAsum= (DetAup_D2OsubH20 + DetAside_D2OsubH20);
 +
  DetAsum->SetName("DetAsum");
 +
DetAsumH20->Write();
  
−
  TH1F DetAup_D2OsubH20= ( AupNormRun229-AupNormRun199);
+
  DetAup_D2OsubH20->Write();
−
  TH1F DetAside_D2OsubH20= ( AsideNormRun234-AsideNormRun194);
+
  DetAside_D2OsubH20->Write();
−
  TH1F DetAdiff= (DetAup_D2OsubH20-DetAside_D2OsubH20);
+
  DetAdiff->Write();
 
   
 
   
 +
TH1F *AsymDetA=(TH1F*)DetAdiff->Clone("AsymDetA");
 +
AsymDetB->Scale(25000); // 100 * 0.004 from the DetA sum histogram
 +
 +
[[Image:Det_A_Asym_Unpol_BackGrdSubtrctd_10-22-08.gif | 200 px]][[Image:Det_C_Asym_Unpol_BackGrdSubtrctd_10-22-08.gif | 200 px]]
 +
 +
=Solid Angle Asymmetry=
 +
 +
The "Up/Side" asymmetry is measured by positioning one detector a distance <math>D_{up}</math> vertically above the beam and another detector horizontally displaced a distance <math>D_{side}</math> away from the beam. The solid angle <math>(\Omega)</math> subtended by the PMTs used to detect neutrons is calculated in terms of the surface Area <math>(A)</math> of the PMT face divided by the PMT distance <math>(R)</math> from the target squared.
 +
 +
:<math>\Omega = \frac{A}{D^2}</math>
 +
 +
A geometrical asymmetry is induced if you position the PMTs at difference distances from the target.  Assuming that both detectors have the same surface area (A), the "Up" rate <math>(R_{up})</math> - "Side" rate <math>(R_{side})</math> asymmetry may be written as:
 +
 +
:Asymm<math> = \frac{R_{up}-R_{side}}{R_{up}+ R_{side}}</math>
 +
:<math>= \frac{\frac{A}{D^2_{up}} - \frac{A}{D^2_{side}}}{\frac{A}{D^2_{up}} + \frac{A}{D^2_{side}}}</math>
 +
: <math>= \frac{D^2_{side} - D^2_{up}}{D^2_{side} + D^2_{up}}</math>
 +
 +
For the above measurements the "Up" detector was a distance of 244.775 cm and the "Side" detector was a distance of 232.131 cm from the target.
 +
The detectors were suppose to be 231.775 cm from the target when running with polarized photons.
 +
 +
The solid angle asymmetry is
 +
 +
:Asym <math>= \frac{232.131^2 - 244.775^2}{232.131^2 + 244.775^2} = -5.3 %</math>
 +
 +
=T2E (Convert time to Neutron Energy) =
 +
Float_t T2E(Int_t UpDown, Int_t TDCval)
 +
{
 +
  Float_t Ekin,Beta,Gamma,Eneutron,Tgamma,SpeedLightcm;
 +
  Float_t Dist,polDist,UnPolTopDist,UnPolSideDist;
 +
  polDist = 231.775; //cm
 +
  UnPolTopDist = 244.775; //cm
 +
  UnPolSideDist = 232.131; //cm
 +
 +
  SpeedLightcm=30; // cm/ns
 +
 +
  Tgamma=146/0.1675;
 +
 +
  Eneutron=939.5656;
 +
 +
  if(UpDown==0)
 +
    Dist=polDist;
 +
  if(UpDown==1)
 +
    {
 +
      Dist=UnPolTopDist;
 +
      Tgamma=146/0.1675;
 +
    }
 +
  if(UpDown==2)
 +
    {
 +
      Dist=UnPolSideDist;
 +
      Tgamma=130/0.1675;
 +
    }
 +
 
 +
 +
  //  printf("TDCval=%g - Tgamma = %g\n",TDCval,Tgamma);
 +
 +
  Beta=(TDCval-Tgamma)*0.1676;
 +
  if(Beta<0)
 +
    return(-1.0);
 +
  Beta=1/(1+Beta*SpeedLightcm/Dist);
 +
  //  printf("Beta=%g\n",Beta);
 +
  Gamma=1/(1-Beta*Beta);
 +
  if(Gamma<0)
 +
    return(-2.0);
 +
  Gamma=sqrt(Gamma);
 +
  Ekin=(Gamma-1)*Eneutron;
 +
  return(Ekin);
 +
}
 +
 +
=Results Histogram Table=
 +
 +
{| border="3"  cellpadding="20" cellspacing="0"
 +
|
 +
Desc
 +
|colspan="2"| Det A up
 +
|colspan="2"| Det A side
 +
|colspan="2"| Det C up
 +
|colspan="2"| Det C side
 +
|-
 +
|
 +
|D2O
 +
|H2O
 +
|D2O
 +
|H2O
 +
|D2O
 +
|H2O
 +
|D2O
 +
|H2O
 +
|-
 +
|ToF
 +
|[[Image:Run229_DetAup_D20_ToF.gif | 100px]]
 +
|[[Image:Run199_DetAup_H20_ToF.gif | 100px]]
 +
|[[Image:Run234_DetAside_D20_ToF.gif | 100px]]
 +
|[[Image:Run194_DetAside_H20_ToF.gif | 100px]]
 +
|[[Image:Run234_DetCup_D20_ToF.gif | 100px]]
 +
|[[Image:Run194_DetCup_H20_ToF.gif | 100px]]
 +
|[[Image:Run229_DetCside_D20_ToF.gif | 100px]]
 +
|[[Image:Run199_DetCside_H20_ToF.gif | 100px]]
 +
|-
 +
|Energy
 +
|[[Image:Run229_DetAup_D20_E.gif | 100px]]
 +
|[[Image:Run199_DetAup_H20_E.gif | 100px]]
 +
|[[Image:Run234_DetAside_D20_E.gif | 100px]]
 +
|[[Image:Run194_DetAside_H20_E.gif | 100px]]
 +
|[[Image:Run234_DetCup_D20_E.gif | 100px]]
 +
|[[Image:Run194_DetCup_H20_E.gif | 100px]]
 +
|[[Image:Run229_DetCside_D20_E.gif | 100px]]
 +
|[[Image:Run199_DetCside_H20_E.gif | 100px]]
 +
|-
 +
|Energy Norm by NaI
 +
|[[Image:Run229_DetAup_D20_Energy.gif | 100px]]
 +
|[[Image:Run199_DetAup_H20_Energy.gif | 100px]]
 +
|[[Image:Run234_DetAside_D20_Energy.gif | 100px]]
 +
|[[Image:Run194_DetAside_H20_Energy.gif | 100px]]
 +
|[[Image:Run234_DetCup_D20_Energy.gif | 100px]]
 +
|[[Image:Run194_DetCup_H20_Energy.gif | 100px]]
 +
|[[Image:Run229_DetCside_D20_Energy.gif | 100px]]
 +
|[[Image:Run199_DetCside_H20_Energy.gif | 100px]]
 +
|-
 +
|Backgrnd Subtraction
 +
|colspan="2"|[[Image:DetAup_D20_-H20_Energy.gif | 100px]]
 +
|colspan="2"|[[Image:DetAside_D20-H20_Energy.gif | 100px]]
 +
|colspan="2"|[[Image:DetCup_D20-H20_Energy.gif | 100px]]
 +
|colspan="2"|[[Image:DetCside_D20-H20_Energy.gif | 100px]]
 +
|-
 +
|Backgrnd Subtraction
 +
|colspan="2"|[[Image:DetA_D20_-H20_Diff.gif | 100px]]
 +
|colspan="2"|[[Image:DetA_D20-H20_Sum.gif | 100px]]
 +
|colspan="2"|[[Image:DetC_D20-H20_Diff.gif | 100px]]
 +
|colspan="2"|[[Image:DetC_D20-H20_Sum.gif | 100px]]
 +
|-
 +
|Asymmetry
 +
|colspan="4"|[[Image:DetA_D20_-H20_Asym.gif | 100px]]
 +
|colspan="4"|[[Image:DetC_D20-H20_Asym.gif | 100px]]
 +
|}
 +
 +
 +
Error calculation for 4 MeV neutrons
 +
 +
 +
Cup(D2O) = 480 counts
 +
Cup(H2O) = 9 counts
 +
Cside (D2O) = 1300 Counts
 +
Cside (H2O) = 4 Counts
 +
 +
Asym <math>\equiv \frac{Diff}{Sum} = \frac{Cup(D2O) - Cup(H2O) - Cside(D2O) + Cside(H2O)}{Cup(D2O) - Cup(H2O) + Cside(D2O) - Cside(H2O)}
 +
</math>
 +
 +
<math>\left ( \frac{\delta Asym}{Asym} \right )^2 = \left ( \frac{\delta Diff}{Diff} \right )^2 + \left ( \frac{\delta Sum}{Sum} \right )^2 - 2Cov(Diff,Sum) \delta Sum \delta Diff </math>
 +
 +
<math>\delta Diff = \delta Sum = \sqrt{\frac{1}{480} +\frac{1}{9} +\frac{1}{1300} +\frac{1}{4}} =  0.6</math>
 +
 +
<math>\left ( \frac{\delta Asym}{Asym} \right )^2 = \left ( \frac{0.6}{-825} \right )^2 + \left ( \frac{0.6}{1793} \right )^2 = 1\times 10^{-6}</math>
 +
 +
<math>\frac{\delta Asym}{Asym}</math> = 0.1 %
  
 +
Still need to double check the above.  This is the best possible error when assuming <math>\delta^2 Sum = \frac{1}{N}</math> it should be \frac{\sigma}{N} but I don't know what <math>\sigma</math> is yet.
  
−
http://www.iac.isu.edu/mediawiki/index.php/October_Fission_HRRL_Measurements_2008 go back
+
[http://wiki.iac.isu.edu/index.php/October_Fission_HRRL_Measurements_2008 go back]

Latest revision as of 06:30, 5 February 2009

go back


Unpolarized Measurents:

A 2x4x8" aluminum brick was placed at the HRRL export in order to destroy the photon polarization. Rate measurements were made with the descriminator and HV settings used the past week. Then the constant fraction descriminator was replaced with a threshold descriminator on two detectors but not the reference detector.

ADC =0 => Reference Detector D

ADC = 1 => NaI

ADC=2 => Detector C

ADC = 3 => Detector A

channel # * 0.1675 ns/chan => ns


Default HV and CF descriminator

Matched HV and Threshold Descriminator

2 Runs were taken with the following settings

100 ms Threshold descrimnaotr

[math]HV_{Det A}[/math] =

[math]HV_{Det_C}[/math] =

Run 168 ( 234.lst)

NaI spectrum monitoring the photon flux during run 234

Run234RefDet.gif

Run234DetAside.gif

Run234DetCup.gif


Run234RefDetNorm.gif

If I normalize using the Reference detector I see

Run234DetAsideOverRef.gif Run234DetCupOverRef.gif

If I normalize using the NaI detector I see:

Run234DetAsideNorm.gif Run234DetCupNorm.gif

The Difference and Asymmetry measurements.

Run234AsideSubCupNorm.gif Run234AsymAsideCupNorm.gif

The above is just an example of how to analyze the data. Students should take my bad example and improve upon it.


The program I used to generate the above pictures from a ROOT file is given below.

I used the "PhotoFis->MakeClass()" command within root to generate the skeleton program which has 2 files called Media:PhotoFis.h.txt and Media:PhotoFis.C.txt.

You define your histogram variables and the file you are opening to analyze in the file Media:PhotoFis.h.txt.

see the lines which look like 

  TH1F *NaiInt229, *RefDetRun229, *Aup, *Cside, *Nai229, *Unity;
  TH1F *NaiInt234, *RefDetRun234, *Aside, *Cup, *Nai234;
  TH1F *AsideOverRefDetRun234, *CupOverRefDet234, , *AupOverRefDet229, *CsideOverRefDet229;
  TH1F *AsideNormSubCupNorm, *AsideNormAddCupNorm, *AsymAsideNormCupNorm;

     TFile *f = (TFile*)gROOT->GetListOfFiles()->FindObject("DetCup_10_10_08_00234.root");
     if (!f) {
        f = new TFile("DetCup_10_10_08_00234.root");


You create your histograms, loop over the ntuple entries , and perform histogram operations in the file Media:PhotoFis.C.txt

Run 164 (229.lst)

NaI spectrum monitoring the photon flux during run 229


The root commands 

root [24] TH1F *RefDetRun229=new TH1F("RefDetRun229","RefDetRun229",800,0,800);
root [25] PhotoFis->Draw("evt.ADCval*0.1675 >> RefDetRun229","evt.ADCnum==0 && evt.LastADCval>0");

Will create histogram with 800 channels and 800 bins so we have 1 bin per channel (ns).

Run229RefDet.gif Run229DetAup.gif Run229DetCside.gif


To normalize the data you need to integrate the NaI histogram. To do this a skeleton program is creates using ROOT which will loop through the ROOT ntuple using the command 

PhotoFis->MakeClass();

You will see a file called PhotoFis.C after you execute the above command within the ROOT interpreter window.


300 px 300 px 300 px

Asym

Now do Asym plots using the same detector normalize by the Reference detector in one case and the NaI detector in another.

H20 runs

Run 140 (199.lst)

Det A on top

uses file 199.lst

The spectrum below shows the Time of Flight spectrum for Detectors "A" and "C". The bottom figures represent the energy calculated from the time of flight when a neutron is assumed as the detected particle. Events beyond 15 MeV are from the photon peak (phtotons are misidentified as neutrons). In order to determine the time of flight the average ToF for a photon (140 ns) was used as the start time. Photon events above this average will appear at energies beyond 15 MeV and photon events below this average will have negative times and appear as Underflows in histogram AupNErun199. There are 7640 events in Histogram Auprun199 above 146 ns correspond to the (15050-7410=7640) events shown in AupNErun199 histogram.

Run140 RawToF.gif

Neutrons from the target should have energies below 14 MeV. The spectra below were normalized by the number of NaI events observed during the run.

Run140 NormNeutronEspectrum.gif

Run 136 (194.lst)

Det A on side

uses file 194.lst

ROOT Commands

1.)How to save histograms from several different files to a single file 


root [0] TFile *f1=new TFile("Run194Histos.root")                    
root [1] TH1F *AsideNormRun194_H=((TH1F*)f1->Get("AsideNormRun194"));
root [2] TFile* file = TFile::Open("UnpolResults.root","RECREATE");  
root [3] file->cd();                                                 
root [4] AsideNormRun194_H->Write();                                 
root [5] TFile *f2=new TFile("Run199Histos.root")                    
root [6] TH1F *AupNormRun199_H=((TH1F*)f2->Get("AupNormRun199"));    
root [7] file->cd();                                                 
root [8] AupNormRun199_H->Write();


2.) How to manipulate histograms in the saved file 

 TFile *f1=new TFile("UnpolResults.root");                    
f1->cd();
TH1F *AupNormRun199_H=((TH1F*)f1->Get("AupNormRun199"));
AupNormRun199_H->Draw();                                
TH1F *AsideNormRun194_H=((TH1F*)f1->Get("AsideNormRun194"));
AsideNormRun194_H->Draw();   
TH1F *AsideNormRun194_H=((TH1F*)f1->Get("AsideNormRun194"));
AupNormRun199_H->Sumw2();                           
AsideNormRun194_H->Sumw2();   
TH1F H2OdiffDetA= (*AupNormRun199_H - *AsideNormRun194_H);
H2OdiffDetA->Draw();                                      
TH1F H2OsumDetA= (*AupNormRun199_H + *AsideNormRun194_H); 
H2OsumDetA->Draw();


Background subtracted Det A

TFile *f1=new TFile("Run194Histos.root"); // H2O Aside
TFile *f2=new TFile("Run199Histos.root"); // H2O Aup
TFile *f3=new TFile("Run229Histos.root"); // D2O Aup
TFile *f4=new TFile("Run234Histos.root"); // D2O A side
f1->cd();
TH1F *AsideNormRun194=((TH1F*)f1->Get("AsideNormRun194"));
f2->cd();
TH1F *AupNormRun199=((TH1F*)f2->Get("AupNormRun199"));
f3->cd();
TH1F *AupNormRun229=((TH1F*)f3->Get("AupNormRun229"));
f4->cd();
TH1F *AsideNormRun234=((TH1F*)f4->Get("AsideNormRun234"));
TFile* file = TFile::Open("UnpolResultsDetA.root","RECREATE");  
file->cd();
AsideNormRun194->Write();
AupNormRun199->Write();
AupNormRun229->Write();
AsideNormRun234->Write();
AsideNormRun194->Sumw2();
AupNormRun199->Sumw2();
AupNormRun229->Sumw2();
AsideNormRun234->Sumw2();

TH1F DetAdiffH20= ( *AupNormRun199 - *AsideNormRun194);
DetAdiffH20->SetName("DetAdiffH20");

TH1F DetAup_D2OsubH20= ( *AupNormRun229 - *AupNormRun199);
DetAup_D2OsubH20->SetName("DetAup_D2OsubH20");
TH1F DetAside_D2OsubH20= ( *AsideNormRun234 - *AsideNormRun194);

DetAside_D2OsubH20->SetName("DetAside_D2OsubH20"); 

TH1F DetAdiff= (DetAup_D2OsubH20 - DetAside_D2OsubH20);
 DetAdiff->SetName("DetAdiff");
DetAdiffH20->Write();

TH1F DetAsum= (DetAup_D2OsubH20 + DetAside_D2OsubH20); 

 DetAsum->SetName("DetAsum");
DetAsumH20->Write();

DetAup_D2OsubH20->Write();
DetAside_D2OsubH20->Write();
DetAdiff->Write();

TH1F *AsymDetA=(TH1F*)DetAdiff->Clone("AsymDetA"); 

AsymDetB->Scale(25000); // 100 * 0.004 from the DetA sum histogram

Det A Asym Unpol BackGrdSubtrctd 10-22-08.gifDet C Asym Unpol BackGrdSubtrctd 10-22-08.gif

Solid Angle Asymmetry

The "Up/Side" asymmetry is measured by positioning one detector a distance [math]D_{up}[/math] vertically above the beam and another detector horizontally displaced a distance [math]D_{side}[/math] away from the beam. The solid angle [math](\Omega)[/math] subtended by the PMTs used to detect neutrons is calculated in terms of the surface Area [math](A)[/math] of the PMT face divided by the PMT distance [math](R)[/math] from the target squared.

[math]\Omega = \frac{A}{D^2}[/math]

A geometrical asymmetry is induced if you position the PMTs at difference distances from the target. Assuming that both detectors have the same surface area (A), the "Up" rate [math](R_{up})[/math] - "Side" rate [math](R_{side})[/math] asymmetry may be written as:

Asymm[math] = \frac{R_{up}-R_{side}}{R_{up}+ R_{side}}[/math]
[math]= \frac{\frac{A}{D^2_{up}} - \frac{A}{D^2_{side}}}{\frac{A}{D^2_{up}} + \frac{A}{D^2_{side}}}[/math]
[math]= \frac{D^2_{side} - D^2_{up}}{D^2_{side} + D^2_{up}}[/math]

For the above measurements the "Up" detector was a distance of 244.775 cm and the "Side" detector was a distance of 232.131 cm from the target. The detectors were suppose to be 231.775 cm from the target when running with polarized photons.

The solid angle asymmetry is

Asym [math]= \frac{232.131^2 - 244.775^2}{232.131^2 + 244.775^2} = -5.3 %[/math]

T2E (Convert time to Neutron Energy)

Float_t T2E(Int_t UpDown, Int_t TDCval)
{
 Float_t Ekin,Beta,Gamma,Eneutron,Tgamma,SpeedLightcm;
 Float_t Dist,polDist,UnPolTopDist,UnPolSideDist;
 polDist = 231.775; //cm
 UnPolTopDist = 244.775; //cm
 UnPolSideDist = 232.131; //cm

 SpeedLightcm=30; // cm/ns

 Tgamma=146/0.1675;

 Eneutron=939.5656;

 if(UpDown==0)
   Dist=polDist;
 if(UpDown==1)
   {
     Dist=UnPolTopDist;
     Tgamma=146/0.1675;
   }
 if(UpDown==2)
   {
     Dist=UnPolSideDist;
     Tgamma=130/0.1675;
   }
 

 //  printf("TDCval=%g - Tgamma = %g\n",TDCval,Tgamma);

 Beta=(TDCval-Tgamma)*0.1676;
 if(Beta<0)
   return(-1.0);
 Beta=1/(1+Beta*SpeedLightcm/Dist);
 //  printf("Beta=%g\n",Beta);
 Gamma=1/(1-Beta*Beta);
 if(Gamma<0)
   return(-2.0);
 Gamma=sqrt(Gamma);
 Ekin=(Gamma-1)*Eneutron;
 return(Ekin);
}

Results Histogram Table

Desc

Det A up Det A side Det C up Det C side
D2O H2O D2O H2O D2O H2O D2O H2O
ToF Run229 DetAup D20 ToF.gif Run199 DetAup H20 ToF.gif Run234 DetAside D20 ToF.gif Run194 DetAside H20 ToF.gif Run234 DetCup D20 ToF.gif Run194 DetCup H20 ToF.gif Run229 DetCside D20 ToF.gif Run199 DetCside H20 ToF.gif
Energy Run229 DetAup D20 E.gif Run199 DetAup H20 E.gif Run234 DetAside D20 E.gif Run194 DetAside H20 E.gif Run234 DetCup D20 E.gif Run194 DetCup H20 E.gif Run229 DetCside D20 E.gif Run199 DetCside H20 E.gif
Energy Norm by NaI Run229 DetAup D20 Energy.gif Run199 DetAup H20 Energy.gif Run234 DetAside D20 Energy.gif Run194 DetAside H20 Energy.gif Run234 DetCup D20 Energy.gif Run194 DetCup H20 Energy.gif Run229 DetCside D20 Energy.gif Run199 DetCside H20 Energy.gif
Backgrnd Subtraction 100px 100px DetCup D20-H20 Energy.gif DetCside D20-H20 Energy.gif
Backgrnd Subtraction 100px 100px DetC D20-H20 Diff.gif DetC D20-H20 Sum.gif
Asymmetry 100px DetC D20-H20 Asym.gif


Error calculation for 4 MeV neutrons


Cup(D2O) = 480 counts Cup(H2O) = 9 counts Cside (D2O) = 1300 Counts Cside (H2O) = 4 Counts

Asym [math]\equiv \frac{Diff}{Sum} = \frac{Cup(D2O) - Cup(H2O) - Cside(D2O) + Cside(H2O)}{Cup(D2O) - Cup(H2O) + Cside(D2O) - Cside(H2O)} [/math]

[math]\left ( \frac{\delta Asym}{Asym} \right )^2 = \left ( \frac{\delta Diff}{Diff} \right )^2 + \left ( \frac{\delta Sum}{Sum} \right )^2 - 2Cov(Diff,Sum) \delta Sum \delta Diff [/math]

[math]\delta Diff = \delta Sum = \sqrt{\frac{1}{480} +\frac{1}{9} +\frac{1}{1300} +\frac{1}{4}} = 0.6[/math]

[math]\left ( \frac{\delta Asym}{Asym} \right )^2 = \left ( \frac{0.6}{-825} \right )^2 + \left ( \frac{0.6}{1793} \right )^2 = 1\times 10^{-6}[/math]

[math]\frac{\delta Asym}{Asym}[/math] = 0.1 %

Still need to double check the above. This is the best possible error when assuming [math]\delta^2 Sum = \frac{1}{N}[/math] it should be \frac{\sigma}{N} but I don't know what [math]\sigma[/math] is yet.

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