The three photon processes trade dominance at about and in lead

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Radiation interactions, detection and dosimetry · Radiation interactions, detection and dosimetry

The Nucleus Resolved, Ch Radiation in matter, computed: Bethe, Klein-Nishina and what they leave out

Problem

The three photon processes trade dominance at about

0.5\,\mathrm{MeV}

and

5\,\mathrm{MeV}

in lead, and at about

30\,\mathrm{keV}

and

24\,\mathrm{MeV}

in water (photoelectric dominates below the first crossover, Compton scattering between the two, pair production above the second). The photoelectric cross section grows roughly as

Z^{4\text{-}5}/E^{3.5}

, the Compton cross section per atom grows only as

Z

(one factor per electron) and falls slowly with

E

, and pair production grows as

Z^2\ln E

above its

1.022\,\mathrm{MeV}

threshold. For each case below, state which process dominates, or which two compete where the energy sits at a crossover, and give a one-sentence reason from the scalings above. ((a)) A

100\,\mathrm{keV}

photon in lead. ((b)) A

100\,\mathrm{keV}

photon in water. ((c)) A

5\,\mathrm{MeV}

photon in lead, at the crossover itself. ((d)) A

5\,\mathrm{MeV}

photon in water.

Related theory

Nuclear Physics

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