2012AnnihCountrRateEstimate

Rate Estimates

Previous experiment at the IAC

IAC apparatus for positron production experiment	Counts observed when the dipole is tuned to direct positrons onto the Ta target	Counts from electrons on Ta target

HpGe observed about 1 annihilation photon per 10 microCoulombs of electrons on the upstream Tungsten target

Ratio of annihilation photons observed when using positrons to electrons 120 to 10

Bend 2 Dipole Spot size at 2nd Dipole D2 Spot size at Phosphorous Target

Condition	Grade Calculation
Electron Beam Energy	10 MeV
Peak current	40 mA
Pulse width	100 ns
Rep Rate	300 Hz

NaI rate Ratio of positron to electron beam

Assumed Geometry

Assume a 2 mm thick Tungsten target that is 1" square

The target is located at -80 < Z < -80.2

The NaI crystal is 2.32" or 56.49 mm in diameter

The NaI crystal is 8" from the target then the opening angle is atan(2.32/8/2) = 8.25 degrees

Solid Angle

[math]\Omega = \frac{\pi (2.34)^2}{(8)^2} = 0.27 strad[/math]

Chromox target

Chromox target is 0.011" thick = 0.279 mm

File:Chromox datasheet CERN.pdf

G4 Chromox description

G4Element* Cr =
    new G4Element("Chromium", "Cr",z=24., a= 51.9961*g/mole);

  G4Element* Al =
    new G4Element("Aluminum","Al", z=13., a= 26.98154*g/mole);


  //                                                                                                                                        
  // typically the viewers are 99.5% Al_2 O_3 and 0.5% Cr_2 O_3                                                                             
  //                                                                                                                                        
  // I will construct a material that is 99.5% made of  2 Al and 3 O  Atoms/nuclei                                                          
  //             and 0.5% made of  2 Cr and 3 O  Atoms/nuclei                                                                               
  //                                                                                                                                        
  //   Al = 99.5 * 2/5 = 39.8 %                                                                                                             
  //  O = 99.5 * 3/5 = 59.7 %                                                                                                               
  //  O = 0.5 * 3/5 = 0.3 %                                                                                                                 
  //  Cr = 0.5 * 2/5 = 0.2%                                                                                                                 
  //                                                                                                                                        
  // Jlab PePPo Chromox viewer is 0.011" thick = 0.279 mm                                                                                   
  //                                                                                                                                        
  //                                                                                                                                        

  G4Material* ChroMox = new G4Material("ChroMox", density= 3.85*g/cm3, nel=3);
  ChroMox->AddElement(Al, 30.8*perCent);
  ChroMox->AddElement(O, 60*perCent);
  ChroMox->AddElement(Cr, 0.2*perCent);

Rates using GEANT4

Assume 3 MeV electron and positron beam.

2 mm Thick Tungsten annihilation target

Integrating between 0.3 and 0.7 MeV (511 peak unclear)

[math]\frac{\mbox{Positrons}}{\mbox{electron}} = \frac{6768}{1367} = \frac{5}{1}[/math]

Integrating between 0.5 and 0.53 MeV

[math]\frac{\mbox{Positrons}}{\mbox{electron}} = \frac{2685}{120} = \frac{22}{1}[/math]

Experiment at IAC had [math]\frac{12}{1}[/math]

Chromox

The photon rates predicted by GEANT4 when electrons and positrons interact with the ChroMox target and enter one of the NaI detectors having a solid angle of (0.27 strad)

Integrating between 0.5 and 0.53 MeV

[math]\frac{\mbox{Positrons}}{\mbox{electron}} = \frac{1094}{8.4} = \frac{130}{1}[/math]

PePPO_2012Run