Topic 5 - Dose Units

Neutrons

Neutron Production

• Nuclear Reactors
  • Fission neutrons from U or Pu
• Accelerators
  • Many different reactions
• Combined sources
  • Radium & Be
  • Polonium & Be

Neutron Classification

• Thermal
  • In thermal equilibrium with their environment
  • Distributed according to Maxwell Boltzman distribution
  • Most probable energy ~ 0.025 eV at 20 C
• Higher energies: 0.01 or 0.1 MeV
  • Slow, or intermediate or resonance
• Fast neutrons have energies up to ~10-20 MeV
• Relativistic neutrons have still higher energies

Interaction with Matter

• Uncharged like photons
• Travel appreciable distances without interacting
• Attenuated exponentially under good geometry
• Don’t interact appreciably with electrons
• Collide with atomic nuclei in elastic and inelastic collisions
• Elastic collisions:
  • Total energy is conserved
  • Energy lost by neutron is equal to total  energy of recoil nucleus
• Inelastic collisions
  • Nucleus absorbs some of the energy and is left in an excited state
• Fast neutrons
  • Series of mostly elastic scattering reactions
  • Slowing down process is called moderation
  • As energy decreases, scattering continues but probability of capture by another nucleus increases.
  • If neutron reaches thermal energies it will randomly move around until absorbed by a nucleus.

Important Neutron Reactions

• ¹H(n,g )²H
  • Example of radiative capture
  • Neutron absorption followed by immediate emission of gamma photon. 
  • Explicitly:
    
  • The photon has an energy of 2.22 MeV
  • Of significance when tissue exposed to thermal neutrons
• ¹⁴N(n,p)¹⁴C
  • Cross section is 1.78 barns for thermal neutrons
  • Q value is 0.626 MeV
  • Significant contributor to dose when tissue is irradiated by neutrons
  • Since p and recoil nucleus have limited range, energy deposited locally.
• Neutron Activation
  • Production of radioactive isotope by absorption of neutron.
  • Equation dictating creation of radioactive isotope:
    
  • Where
    • f is the flux, neutrons per cm² per s
    • s is the activation cross section, cm²
    • l is the decay constant of the produced isotope (s^-1)
    • N is the number of produced atoms
    • n is the number of target atoms.

Absorbed Dose from Neutrons

• Concerned primarily with
  • Neutron interaction with tissue elements  H, C, O, N
  • Resultant dose
• Neutrons interactions
  • produce HCPs
  • short range
  • CPE occurs
  • Therefore, dose = kerma (for E_n <= 20 MeV)

Fast Neutrons

• f(E) flux, n cm^-2s^-1
• E, neutron energy in Joules
• N_i, atoms per kg of the i^th element
• s_I, scattering cross section, barns*10^-24 cm²
• f = fractional energy transferred from neutrons

• Isotropic scattering
• Average fraction of neutron energy transferred in elastic collision
• Nucleus of atomic mass number M

Thermal Neutrons

• Two reactions:
  • ¹⁴N(n,p)¹⁴C
  • ¹H(n,g)²H – uniformly distributed g isotope

Thermal Neutrons

• ¹H(n,g)²H  dose rate
  
• Absorbed fraction, j
• Emission fraction (energy, abundance, conversion factor), D

Neutrons Dose Summary

• Divide into two types of dose calculations
  • Fast neutrons with multiple energy groups
  • Thermal or slow neutrons