Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Nuclear Reactions Reactions A + a → B + b A (a,b) B (p,p)12C Inelastic scattering: 12C (p,p´)12C* Rearrangement reaction: 54Fe (32S,28Si)58Ni Capture reaction: 12C (p,γ)13N Others: 2H(n,2n)1H Elastic scattering: 12C 1 Terminology Channels (Entrance and Exit) p – proton d – deuteron (deuterium): 2H t – triton (tritium): 3H α – alpha (Helium-4): 4He Photodisintegration – reaction with γ in entrance channel Capture – nucleon absorbed and γ in exit channel Q-value in Reactions The Q-value in reactions is the difference between the mass energies of the entrance channel particles and the exit channel particles. Q = [ M (Entrance)! M (Exit )]c 2 The Q-value is the energy release in the reaction. For elastic collisions Q = 0 in inelastic collisions Q < 0. 2 Q-value and Kinetic energy The Q-value can also be expressed in terms of the incoming and outgoing kinetic energies. Q = Kb + K B ! K A ! K a For fixed target experiments KA = 0. For exothermic reactions Q > 0 some of the mass energy is converted to kinetic energy. For endothermic reactions Q < 0 some of the incoming particle’s kinetic energy is converted to mass. Threshold Kinetic Energy In endothermic reactions the kinetic energy of the incoming particle must be sufficient to supply the needed mass and conserve momentum. The minimum kinetic energy of the incoming particle needed to initiate the reaction is called the threshold energy. & M + MA # !! K th = 'Q$$ a M % " A 3 A Typical Experiment Detector Faraday Cup Incoming particle beam Target What do we measure? Detector might measure the outgoing particle’s: Type of particle Energy Momentum (direction and magnitude) Number of particles (of each type) 4 Number of particles The number of particles detected depends on a variety of factors: Beam flux Number of “targets” – target thickness Detector placement, size and efficiency Physical properties of the reaction Cross-section != number of outgoing particles emitted (number of particles incident/unit area)(number of target nuclei within beam spot) The cross-section is related to the probability that a certain reaction will take place. Independent of other factors such as beam flux or target size. σ has units of area: barn (b) = 10-28 cm 5 Cross-section as Effective Area One way to visualize crosssection is to think of it as the effective area of the target (assuming the incident particle is point-like.) Cross-section of a Reaction Cross-section is a measure of the reaction probability. Collision of two classical spheres. R2 b R1 b R 1 + R2 6 Calculating Cross-section from Experimental Parameters Y = yield = number of reactions/unit time n = particle density = number of target particles/unit volume t = thickness of target A = area of beam spot Φi = incident flux = beam particles/[(unit time)(unit area)] Experimental Cross-section The yield is Y = ΦinAtσ so the total cross-section is Y "= ! i nAt 7 Differential Cross-section An actual experiment does not measure the total yield but the yield of particles that scatter into the detector. The detector is placed at a position (r,θ,φ) and has an active area facing the target. In general the cross-section is not isotropic – it depends on (θ,φ) . Nuclear Reactions Mechanisms 8 Direct reactions Reaction energy ~ 20 MeV or greater Dominated by strong interaction Examples: Knockout Pickup Stripping Compound Nucleus Mechanism Low energy (< 20 MeV) A composite nucleus is formed. Time scale on order of 10-15 s. p + 15N d + 14N 3He + 13C 4He + 12C 6Li + 10B 16O γ + 16O t + 13N n + 15O p + 15N d + 14N 3He + 13C 4He + 12C 6Li + 10B 9 Energy Level of Compound Nucleus Resonances "# ! h 2 Fission and Fusion 10 Fission Nucleus splits into two roughly equal sized fission fragments ( and a few stray nucleons in some cases.) Moves lower on the binding energy curve. Spontaneous fission: Z2/A >48, A > 220 Spontaneous fission has low rates compared to alpha decay. Induced fission Neutron is absorbed producing a compound nucleus that quickly fissions. 11 Prompt and Delayed Neutrons Neutrons released with the fragments are called prompt neutrons. These have high kinetic energies and a low cross section for absorption. The neutron-rich fission fragments may also emit neutrons during the their beta decay back to the line of stability. These have low kinetic energies and high absorption cross sections. Fission fragments usually have unequal masses. Chain Reactions Emitted neutrons can be used to create secondary fission reactions and so on. 12 Controlled Chain Reactions Moderating material is used to slow fast neutrons. (water, graphite) Control rods absorb neutrons (cadmium). Nuclear Reactors 13 Fusion Two light nuclei combine to form a heavier nucleus. Fusion vs. Fission 14 Stellar Fusion The p-p chain Stellar Nucleosynthesis All elements with the exception of H, He and Li were made in stars. Nuclear processes that provide the energy of a star make heavier nuclei out of the H and He. Some nuclei are made during the normal lifetime of a star. The nuclei above 56Fe on the binding energy curve are made only during supernovae explosions. 15 25 0 The r-process 20 0 r-a bu nd an ce s Known mass Known half-life r process waiting point (ETFSI-Q) 100 98 96 So lar 94 92 90 88 86 84 186 188 190 82 80 15 0 78 76 164 166 168 170 172 174 74 158 68 66 64 140 142 144 146 148 62 58 128 130 132 134 136 150 152 154 156 138 46 44 116 118 10 -3 10 0 10 -1 56 54 52 10 -2 10 1 180 182 160 60 10 0 178 162 72 70 50 48 42 92 94 40 38 36 34 74 76 32 30 28 26 28 176 184 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 78 80 82 84 86 96 98 100 102 104 106 108 110 120 122 124 126 112 114 88 90 72 Fusion Power – Magnetic confinement http://ippex.pppl.gov/ 16 Fusion Power – Magnetic Confinement National Spherical Torus Experiment Fusion Power – Inertial Confinement NOVA Laser test chamber 17 Fusion Power – Inertial Confinement National Ignition Facility 18