Number of electron-positron pairs/sec out of Al converte

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LINAC parameters used in calculations

1) pulse width 50 ps
2) pulse current 50 A
3) repetition rate 300 Hz
4) energy 44 MeV

Number of photons/sec out of radiator

r.l.(Ti) = 3.59 cm





steps together...




Alex factor (GEANT4 calculation)

Alex factor is 6.85 %




Number of neutrons/sec

photonuclear cross section for reaction

J. T. Caldwell et all., Phys. Rev. C21, 1215 (1980):

in (10,20) MeV region the average cross section, say, is:

    130 mb


target thickness,




Let's target thickness = 1 mm:




neutrons per fission

   2.4 neutrons/fission


steps together...yeild






Worst Case Isotropic Neutrons

checking detector distance

we want:

     the time of flight of neutron >> the pulse width


take the worst case 10 MeV neutron:








take the neutron detector 1 meter away:



     23 ns >> 50 ps  <= time resolution is good


geometrical factor

taking real detector 3" x 2" => S is about 40 cm^2

1 meter away

fractional solid angle =  <= geometrical acceptance


Yield

the yield per second:





the yield per pulse:



 53.8 neutrons/sec  <= this experiment is do able

 0.18 neutrons/pulse <= good for stopping pulse


Counts Rate for U238 (25 µm Al converter)

r.l.(Al) = 8.89 cm





Calibration factor

The only difference from calculations above is:

    3.48 (for 12.5 µm Ti) / 2.81 (for 50 µm Al) = 1.24


Yield

 53.8 neutrons/sec * 1.24 = 66.7 neutrons/sec

 0.18 neutrons/pulse * 1.24 = 0.22 neutrons/pulse


Counts Rate for Deuteron (12.5 µm Ti converter)

photonuclear cross section for reaction

A. De Graeva et all., Phys. Rev. C45, 860 (1992):

in (10,20) MeV region the average cross section, say, is:

    1000 μb


target thickness,

take , liquid (20°C):






Let's target thickness = 10 cm:




angular distribution of neutron

relativistic kinematics

An Introduction to Nuclear and Subnuclear Physics. Emilio Segre (1964)




where

  asterisks are quantities referred to CM
barred quantities refer to the velocity of the CM










calculations

 20 MeV 40 MeV

geometrical factor

taking average for 20 and 40 MeV photons

 geometrical acceptance =


Calibration factor

The only differences from calculations above are:

1) cross section correction:

    1000 μb (D) / 130 mb (238U) = 1/130


2) target thickness correction:




3) neutrons per reaction correction:

   1 neutron (D) / 2.4 neutrons(238U) = 1/2.4


4) geometrical factor correction:




total calibration factor is:




Yield

saying all other factors is the same =>

the yield per second :




the yield per pulse:




Summary

 converter target neutrons/sec neutrons/pulse 0.5 mil Ti 53.8 0.18 1.0 mil Al 66.7 0.22 0.5 mil Ti 25.2 0.08