Physics and Engineering of Radiation Detection

11.2. Quantities Related to Dosimetry 625

J.1 InternalDosefromChargedParticles

Bothαandβparticles can inflict damage to tissues. There is a large number of
naturally occurring and man made radionuclides that emit these particles. If one
knows the activity concentration of the radionuclide in the tissue and the energy of
the particles, the dose can be calculated from

D=AmE t, (11.2.46)

whereAmis the activity per unit mass of the tissue,Eis the average particle energy,
and tis the exposure time (or the time for which the integrated dose is to be
calculated). UsuallyAgis given in the units ofBq/gandEinMeV/disintegration.
If tis in seconds, the above equation with these units can be written as

D[Gy]=1. 6 × 10 −^10 AmE t (11.2.47)

J.2 InternalDosefromThermalNeutrons

Thermal neutrons are known to be extremely hazardous due to their ability to
penetrate deep into the atom and get captured by the nucleus. Recall that a thermal
neutron has an energy in the vicinity of 0.025eV. A tissue is mostly composed
of light elements: hydrogen, carbon, oxygen, and nitrogen. The cross sections of
thermal neutrons for these elements, specially hydrogen and nitrogen, are fairly
high. For example, a thermal neutron reacts with hydrogen according to

1

1 H+n→

2

1 H+γ(2.^224 MeV), (11.2.48)

with a cross section of 0.33 barns. The 2.2MeV γ-rays thus emitted may deposit
all of their energy in the tissue. Same is true for other elements in the tissue. The
cross section for nitrogen (1.7 barns) is even higher than that for hydrogen and in
this case a proton is emitted. The proton, being a charged particle, quickly looses
its energy along its track. In such a case the probability that the released energy
gets deposited within the tissue under consideration is much higher than in case of
capture by hydrogen. Therefore even though nitrogen density is more than an order
of magnitude lower than that of hydrogen in a typical tissue, its effect is significant
and can not be ignored.
The dose due to neutron capture by a single element can be estimated from

D=

Φ

ρm

σcEρa, (11.2.49)

where Φ is the incident photon flux,ρmis the mass density of the tissue,σcis the
capture cross section for thermal neutrons in the tissue,Eis the energy released,
andρais the atom density of the element in the tissue.
The above formula is valid for one element in the tissue. The total dose can be
obtained by simply summing the contributions from all elements, that is

D=

Φ

ρm

∑

i

(σc,iEiρa,i), (11.2.50)

where now the subscriptirefers to theithelement in the tissue. The atom densities
and capture cross sections of different elements in a typical soft tissue are listed in