1 Geant4 to simulate Photoelectric, Compton, and Pair production Events

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1 Syed F. Naeem, hw-12, Phy Geant4 to simulate Photoelectric, Compton, and Pair production Events 1.1 Introduction An Aluminum (Al) target of 20cm was used in this simulation to see the eect of incoming photons at lower and higher energies ranging from 10eV 1GeV. A photoelectron is produced when a single electron in the metal completely absorbs a single photon. The kinetic energy with which the photoelectron is emitted from the metal is equal to the photon energy minus an energy that the electron expends in escaping the surface [1]. Geant4 simulation gives pretty good approximation if G4LowEnergyPhotoElectric function is implemented to see photo-peaks. Compton effect can be described as the scattering of incident photons on free electrons of the target material. If the incident photon energy is higher than the binding energy of electrons in the target material, the electrons can than be considered as essentially free. The cross section (σ) for Compton scattering was one of the first to be calculated using quantum electrodynamics and is known as the Klein Nishina formula [2]. If the gamma-ray energy exceeds twice the rest-mass energy of an electron, i.e, 1.02MeV, than the process of pair production is possible. However, the probability of this interaction remains very low until the gamma ray energy approaches several MeV and therefore the process is predominantly confined to high-energy gamma rays [3]. 1.2 Methods and Materials An aluminum (Al) target (15cm thick) was used in this simulation to see the effect of incoming photons both at lower and higher energies. Photoelectric effect is dominent at lower energies but Compton and Pair production effect peaks can be distinguished at higher energies as shown in Fig Conclusion Geant4 simulation gives pretty good approximation to capture photoelectric, compton, and pair production events from lower to higher energies with a given range of 10eV 1GeV. C-1

2 Eelectron:ProcessID ProcessID Eelectron Figure 1: Photoelectric effect (processid 1), Compton effect (processid 2), and Pair production (processid 3) peaks from 10eV 10GeV. C-2

3 2 Geant4 to Simulate Threshold Energies to Induce Photo-nuclear Reactions for Heavy Metals 2.1 Photon Activation Analysis (PAA) In PAA, photons are captured by the target nucleus that excites it to the higher energy level as shown in Fig. 2. The excited nucleus decays to a lower energy level (possibly the ground state) with the emission of photons, charged particles, or neutrons. The absorption of photons by the nucleus is dependant on nuclear reactions cross section and threshold energy of bremsstrahlung photons as shown in Fig. 3. Isolated energy states of the target nuclei are excited below 10 MeV however there is a broad resonance region called the Giant Dipole Resonance (GDR) between 10 30MeV in which the collective vibrational motion of nucleons is observed. The cross section (σ) of photons with spherical nuclei due to GDR absorption can be expressed as [5]. where, σ a (E) = σ m ( E =incident photon energy, E m =resonance energy, σ m =peak cross section, E 2 Γ 2 (E 2 m E2 ) 2 + E 2 Γ 2 Γ =GDR, full width half maximum (FWHM). Doubly peaked resonance curves also known as superimposed Lorentz curves are observed within GDR if the target nuclei are deformed. Equation (1) can then be modified for deformed nuclei (Segebade, Weise, & Lutz, 1987), E 2 Γ 2 1 E 2 Γ 2 2 σ a (E) = σ m1 ( ) 2 + σ m2 ( ) 2 (2) E 2 m1 E 2 + E2 Γ 2 1 E 2 m2 E 2 + E2 Γ 2 2 ) (1) While photons excite collective excitations of the target nuclei within GDR region, they are absorbed by a small number of nucleons if the incident photon energy is greater than 30MeV. This second region is called the quasi-deuteron disintegration because an interacting neutron-proton pair is disintegrated. The photon absorption cross section is lower in this region than in the region of the GDR. The final photon absorption region is called the photo-meson production region in which energy of the incident photons is C-3

4 greater than 140MeV. They produce π mesons as a result of their interaction with the target nuclei. The photon absorption cross section is higher in photon-meson production region than quasi-deuteron disintegration region but less than the GDR region. Figure 2: Energy level diagram of nuclear states [5]. Figure 3: Total cross section verses energy of incident photons [5] (γ, n), (γ, 2n), (γ, 3n) Photoneutron reactions emit one or more neutrons as a result of photon absorption. (γ, n) reactions dominate the GDR cross sections of high atomic-number nuclei. The binding energy of a nucleon is lower than the excitation energy of the nucleus, this typically results in the emission of a neutron or a charged particle. The energy threshold of the C-4

5 photoneutron reaction lies within GDR with lower E th (γ, n) energy for single neutron emission and higher E th for multiple neutron emissions per reaction shown in Fig. 4. For instance, E th = 13.38MeV is required to release a single neutron from 54 Fe nuclei and E th = 5.65MeV from 239 Pu nuclei. The total neutron production cross section in a combination of single and multiple neutron production cross sections, neutron plus charged particles production cross section [5]. σ (γ, n tot ) = σ (γ, n) + σ (γ, np) + σ (γ, 2n) + σ (γ, 2np) + σ (γ, 3n) +... (3) where, n tot =total neutrons. Figure 4: Total photon absorption cross-section of a medium atomic number nuclide[6]. Following table shows the threshold energies (E th ) required to release single neutrons from the nuclei of 238 U, 239 Pu, and 232 Th, C-5

6 Target Material E th (MeV) to induce (γ, n) reactions 238 U Pu Th 6.43 Table 1: Bremsstrahlung threshold energies (E th ) to release single neutron from heavy metals [7]. References [1] Turner, J. E., Atoms, Radiation, and Radiation Protection, New York: Wiley and Sons, Inc, 1995 [2] Leo. W. R., Techniques for Nuclear and Particle Physics Experiments, New York: Springer-Verlag, 1994 [3] Knoll. G. F., Radiation Detection and Measurements, John Wiley and Sons, Inc., 2000 [4] tforest/nucsim/day9/bindingenergytable.pdf [5] Segebade, C., Weise H. P., & Lutz G. J., Photon Activation Analysis, Berlin: Walter de Gruyter & Co., 1987 [6] Bergere, R., Beil, H., Carlos, P., Veyssiere, A., & Lepetre, A., Proceed. Intern. Conf. On Nucl. Structures Using Electron Scattering and Photoreactions, Sendai, Japan, Sept , 1972 [7] LBL/Lund ENSDF Viewer, C-6