# 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 on target

### bremsstrahlung

in (10,20) MeV region we have about

    0.1 photons/electrons/MeV/r.l


r.l.(Ti) = 3.59 cm





### steps together...




## Alex factor (GEANT4 calculation)

Collimation factor is

    6.85 % of total # of photons


then, incident flux on target is




## 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 (1/2 mil of Ti and without detector efficiency)

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 (1/2 mil of Al converter)

r.l.(Al) = 8.89 cm





## Calibration factor

The only difference from calculations above is:

    1.41 (1/2 mil Al) / 3.48 (1/2 mil Ti) = 0.40


## Yield (1/2 mil of Al and without detector efficiency)

53.8 neutrons/sec * 0.40 = 21.5 neutrons/sec
0.18 neutrons/pulse * 0.40 = 0.07 neutrons/pulse

# Counts Rate for Deuteron (1/2 mil of 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 (1/2 mil of Ti and without detector efficiency)

saying all other factors is the same =>

the yield per second :




the yield per pulse:




# Summary (counts rate without neutron efficiency for different radiator thickness

 converter target neutrons/sec neutrons/pulse 1/2 mil Ti 53.8 0.18 1/2 mil Al 21.5 0.07 1/2 mil Ti 25.2 0.08 1/2 mil Al 10.1 0.03