Neutrons 1932: Chadwick discovers the neutron 1935: Goldhaber discovers 10 B(n,α) 7 Li reaction 1936: Locher proposes boron neutron capture as a cancer therapy 1939: Nuclear fission in 235 U induced by low-energy neutrons shown to release several neutrons. Suggests that a self-sustaining chain reaction is possible. Dec. 2, 1942: E. Fermi; U. Chicago, first uranium fission reactor goes critical. Classification of neutrons by energy Thermal: E < 1 eV (0.025 eV) Epithermal: 1 eV < E < 10 keV Fast: > 10 keV Neutron sources Neutron energies Reactors neutrons in the few keV to several MeV Fusion reactions 14 MeV Large accelerators Hundreds of MeV Energy Deposition by Neutrons ? Neutrons are generated over a wide range of energies by a variety of different processes. ? Like photons, neutrons are uncharged and do not interact with orbital electrons. ? Neutrons can travel considerable distances through matter without interacting. ? Neutrons will interact with atomic nuclei through several mechanisms. o Elastic scatter o Inelastic scatter o Nonelastic scatter o Neutron capture o Spallation ? The type of interaction depends on the neutron energy 1 Sources of Neutrons Reactors: Fission Neutrons E.g., MeVQnBrLaUn 1952 1 0 87 35 147 57 235 92 1 0 =++→+ Average distribution of energy among products released by fission of 235 U (after Turner J. E. Atoms, Radiation, and Radiation Protection, 2 nd ed. New York: Wiley-Interscience, 1995. Table 9.5) Kinetic energy of charged fission fragments 162 MeV Fission neutrons 6 Fission gamma rays 6 Subsequent beta decay 5 Subsequent gamma decay 5 Neutrinos 11 Total 195 MeV Image removed. 2 Criticality When, on average, one neutron of the several neutrons released per fission reaction, causes another fission reaction. i i eff N N k )1( + = N i = # of neutrons in a “generation” critical if k eff = 1 subcritical if k eff < 1 supercritical if k eff > 1 ? Moderator: slows down the fast fission neutrons so they can react with another 235 U ? Control rods contain boron or cadmium (high cross section for thermal neutrons) 3 Accelerator neutron sources Reactions used to produce monoenergetic neutrons with accelerated protons (p) and deuterons (d) (after [Turner ], Table 9.1) Reaction Q value (MeV) 3 H(d,n) 4 He 17.6 2 H(d,n) 3 He 3.27 12 C(d,n) 13 N – 0.281 3 H(p,n) 3 He – 0.764 7 Li(p,n) 7 Be – 1.65 ? Light metals used as targets to minimize Coulomb repulsion ? Exothermic reactions require only a modest energy accelerator, few hundred keV. ? The endothermic reactions require more substantial accelerators. Examples: nHeHH 1 0 4 3 3 1 2 1 +→+ Q = 17.6 MeV neutron energy ~ 14 MeV nBeHLi 1 0 7 4 1 1 7 3 +→+ Q = - 1.64 MeV neutron energies vary Accelerated protons must supply additional energy to make this reaction proceed. 4 Isotopic Neutron Sources (a,n) Neutron Sources (after [Turner ], Table 9.2) Source Average neutron energy (MeV) Half-life 210 PoBe 4.2 138 d 210 PoB 2.5 138 d 226 RaBe 3.9 1600 y 226 RaB 3.0 1600 y 239 PuBe 4.5 24100 y Alpha source + light metal nCBeHe 1 0 12 6 9 4 4 2 +→+ Q = 5.78 MeV Light metals minimize Coulomb repulsion Neutron and recoil nucleus share Q and KE of incoming alpha particle. Neutrons have a continuous energy spectrum. E.g., emits alpha particles of ~ 5.1 MeV Pu 239 94 PuBe sources used to provide neutrons to “start” reactors. 5 Photoneutron reactions ? Photon brings enough energy to drive reaction. ? Photoneutron sources emit monoenergetic neutrons ( if a single energy photon comes in). ? Requires photons of > several MeV. (g,n) Neutron Sources (after [Turner ], Table 9.3) Source Neutron energy (MeV) Half-life 24 NaBe 0.97 15.0 h 24 NaD 2 O 0.26 15.0 h 116 InBe 0.38 54 min 124 SbBe 0.024 60 d 140 LaBe 0.75 40 h 226 RaBe 0.7 (maximum) 1600 y ? values nPbPb 1 0 205 82 206 82 +→ -23.79 → -23.77 + 8.07 neutron binding energy = 8.09 MeV ? Energy needed to remove neutron = 8.09 MeV ? If a 10 MeV photon is used to “drive” this reaction, the products share the excess energy: 1.91 MeV. ? E n = hν – binding energy ? E n = 1.90 MeV 6 Cross Sections ? Because mass attenuation coefficients have dimensions of cm 2 in the numerator, they have come to be called “cross sections”. ? Cross sections do not represent a physical area, but a probability of an interaction. ? Cross sections usually expressed in the unit, barn: (10 -24 cm 2 ) ? The atomic cross sections can be derived from the mass attenuation coefficient. Photons Attenuation coefficient, expressed at the atom level Probability of interaction per atom N A = atom density (#atoms/cm 3 ) 0 N A N A ρ = σ A = atomic cross section (cm 2 /atom) N 0 = 6.02 x 10 23 atoms/mole ρ = g/cm 3 A = g/mole AA N σμ = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? == = 0 0 0 N A A N N A A A A ρ μ σ σ ρ μ σ ρ μ 7 Neutron Cross Sections Analogous to photons ? Neutrons interact by different mechanisms depending on the neutron energy and the material of the absorber o Scattering ? elastic ? inelastic o Capture ? Each energy loss mechanism has a cross section ? Neutron cross sections expressed in barns (1 barn = 10 -24 cm 2 ). ? These cross sections depend on the neutron energy and the absorber Moderation: slowing down of fast neutrons Fast neutrons lose energy in a series of scatter events, mostly elastic scatter. Lower energy neutrons: ? scattering continues ? probability of capture increases (capture cross sections increase at lower energies) Thermal Neutron Cross Sections Nuclide Cross section (barns) 10 B 3837 11 B 0.005 12 C 0.0035 1 H 0.33 14 N 1.70 35 Cl 43.6 23 Na 0.534 157 Gd 254,000 153 Gd 0.02 8 Cross Sections Image removed. Total cross sections for neutrons with hydrogen and carbon as a function of energy ? For hydrogen the contributors to the total cross section are elastic scatter (predominant) and neutron capture (σ = 0.33 barns at thermal neutron energy). ? For carbon, the cross section is complex due to the different nuclear states possible that may enhance or suppress elastic or inelastic scatter at particular neutron energies. Image removed. Fig. 24.3 in Hall, Eric J. Radiobiology for the Radiologist, 5 th ed. Philadephia PA: Lippincott Williams & Wilkins, 2000. Image removed. 9 Neutron Interactions Elastic scatter: The most important process for slowing down of neutrons. ? Total kinetic energy is conserved ? E lost by the neutron is transferred to the recoiling particle. ? Maximum energy transfer occurs with a head-on collision. ? Elastic scatter cross sections depend on energy and material. θ E n E n ' Q 2 max )( 4 mM mME Q n + = Maximum fraction of energy lost (Q max /E n ) by a neutron in a single elastic collision with various nuclei (from [Turner], Table 9.4) Inelastic scatter ? The neutron is absorbed and then re-emitted ? The nucleus absorbs some energy internally and is left in an excited state. 10 e.g., 14 N(n,n′) 14 N E γ = ~ 10 MeV ? De-excitation emits a gamma ray. ? In tissue, inelastic scatter reactions can occur in carbon, nitrogen and oxygen. Nonelastic scatter ? Differs from inelastic scattering in that a secondary particle that is not a neutron is emitted after the capture of the initial neutron. e.g., 12 C(n,α) 9 Be E γ = 1.75 MeV ? Energy is transferred to the tissue by the alpha particle and the de-excitation gamma ray. Neutron capture ? Same as nonelastic scatter, but by definition, neutron capture occurs only at low neutron energies (thermal energy range is < 0.025 eV). ? Capture leads to the disappearance of the neutron. ? Neutron capture accounts for a significant fraction of the energy transferred to tissue by neutrons in the low energy ranges. e.g, 14 N(n,p) 14 C Q = 0.626 MeV E p = 0.58 MeV 1 H(n,γ) 2 H Q = 2.2 MeV E γ = 2.2 MeV ? The hydrogen capture reaction is the major contributor to dose in tissue from thermal neutrons. Because the gamma is fairly energetic, the dose to tissue will depend on the volume of tissue irradiated. Spallation ? In this process, after the neutron is captured, the nucleus fragments into several parts. Only important at neutron energies in excess on 100 MeV. (cross sections are higher at 400-500 MeV). ? The dose to tissue comes from the several neutrons and de-excitation gamma rays which are emitted. 11 Threshold Reactions Q is negative, endothermic reaction. Threshold energy, E th , must be supplied. Incoming particle (M 1 ) must bring enough energy to overcome negative Q threshold and to provide enough energy to satisfy conservation of momentum requirements. M 1 Schematic of a head-on collision producing a nuclear reaction in which the identity of the particles can change. (after [Turner], Fig. 9.7) M 2 M 3 M 4 Before collision After collision ? Particle M 1 strikes M 2 (at rest). ? Identities of particles change: M 3 and M 4 are created. ? Q value is negative ? Conservation of energy: E 1 = E 3 + E 4 + Q ? Conservation of momentum: p 1 = p 3 + p 4 ? ? ? ? ? ? ? ? ?+ +?≥ 143 1 1 MMM M QE th Smallest possible E to satisfy the equation is the Threshold Energy, E th . Example: 32 S(n,p) 32 P Q = - 0.93 MeV E th = 0.957 MeV In practice, the Coulomb Barrier adds energy to E th for reaction to occur. Application: 32 S exists in human hair. 32 P activity induced by neutrons (> 3.2 MeV) can be used as a measure of the individual’s exposure following criticality accidents. 12 Neutron Activation ? Extremely useful property of neutrons. ? Neutron capture creates a new isotope (same element) ? Sensitive tool for elemental analysis Creation of a nuclide N )1( t T eNN λ σλ ? ?Φ= Activity = production – loss by decay N T = # of target atoms σ = cross section (barns: 10 -24 cm 2 ) Φ = fluence rate (n/cm 2 s) t = start of the irradiation T NσΦ = saturation activity t → ∞ lN FsN T . 0 t Buildup of induced activity lN during neutron irradiation at constant fluence rate. (after [Turner], Fig. 9.8) 13 Example: Gold activation used as a measure of thermal neutron fluence 197 Au (100% abundance) σ = 98.8 barns 197 Au + n → 198 Au t?= 2.7 days )1( t T eNN λ σλ ? ?Φ= Alternatively, neutron activation can be used to measure the amount of an element present. Gamma emission energies are element-specific and can be used to identify trace amounts Image removed. 14