Lecture23: (Course Summary) Nuclear Energy and Weapons

P H G N 4 2 2 : N U C L E A R P H Y S I C S PHGN 422: Nuclear Physics Lecture 23: (Course Summary) Nuclear Energy and Weapons Prof. Kyle Leach November 21, 2019 Slide 1P H G N 4 2 2 : N U C L E A R P H Y S I C S Last Class... • Nuclear fusion occurs naturally in stars through several different reactions • Fusion can release much more energy per nucleon than fission • For several reasons (including the above) this is the best choice for energy and weapons • ...but first Slide 2 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S This is our last lecture... • Well, what have we learned so far? Let’s take a recap... Slide 3 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Elementary Particles of the Standard Model Slide 4 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Structure of Nucleons u u d u d d Proton u,u,d < 10−18 m Neutron u,d,d Particle excitations: > 109 eV “Up” (u) m = 2:4 MeVc2 q = +2=3 “Down” (d) m = 4:8 MeVc2 q = −1=3 Slide 5 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Inside the Atomic Nucleus + Proton Positive Charge Mass= 938:27 MeVc2 Neutron Neutral Charge Mass= 939:56 MeVc2 Slide 6 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Protons and Neutrons In fact, protons and neutrons are so similar, they can be classified as the same object; The Nucleon Nucleons are (of course) quantum mechanical objects: • They are spin 12 Fermions • Radius: r ∼ 1 × 10−15 m, or 1 fm (fermi) • Charge: • p +e • n 0 Slide 7 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Atomic Nucleus + + + + Proton (π) Neutron (ν) ∼ 10−15 m = fm Nuclear excitations: ∼ 105108 eV Caused by transitions between nuclear states Interactions can be thought of as either microscopic or collective Slide 8 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Atom Atom is a neutral system Electrons Nucleus ∼ 10−10 m = A˚ Atomic excitations: ∼ 1105 eV Caused by transitions between electronic states Slide 9 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Terminology Nuclei are typically referred to by the number of nucleons (protons and neutrons) that they contain: A = N + Z The number of protons defines the chemical symbol, and is also referred to as the nuclear charge Slide 10 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Terminology Nuclei are typically referred to by the number of nucleons (protons and neutrons) that they contain: A = N + Z • Number of Neutrons The number of protons defines the chemical symbol, and is also referred to as the nuclear charge Slide 10 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Terminology Nuclei are typically referred to by the number of nucleons (protons and neutrons) that they contain: A = N + Z • Number of Neutrons • Number of Protons The number of protons defines the chemical symbol, and is also referred to as the nuclear charge Slide 10 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Typical Notation AZ XN • A is the number of nucleons, or the nuclear mass • X is the chemical symbol, as used in the periodic table, and is defined by the nuclear charge Z • Therefore, N and Z are often omitted, since all of the relevant information can be defined by A and X AX Slide 11 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Nuclear Chart Phil Walker, New Scientist Magazine, October 2011 Slide 12 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Navigating the Nuclear Chart • Stable Nucleus A nuclear system that does not undergo radioactive decay (ie. it is energetically unfavourable). This region of the nuclear chart is often called the Valley of Stability or Line of Stability. • Radioactive Nucleus (or unstable) A nucleus that is spontaneously able to decrease its total energy by emmitting ionizing radiation. This may result in a change in the total number of protons and neutrons. • NeutronRich Nucleus A nucleus that has an excess of neutrons relative to the stable isotope for a given Z. This is to the right of the valley of stability. • NeutronDeficient Nucleus (also: ProtonRich) A nucleus that has an excess of protons relative to the stable isotope for a given Z. This is to the left of the valley of stability. • The Driplines (proton and neutron) The limits of the nuclear chart where bound nuclei can no longer exist. On the far left is the proton dripline and the far right is the neutron dripline. Slide 13 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Isotopes, Isotones, and Isobars • Isotope: Nuclei with the same number of protons (Z), but a different number of neutrons (N) and a different mass (A) • Isotone: Nuclei with the same number of neutrons (N), but a different number of protons (Z) and a different mass (A) • Isobar: Nuclei with the same number of nucleons (mass? not really...) (A), but a different number of protons (Z) and neutrons (N) Slide 14 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Fundamental Forces As we think about limits of nuclear existence (bound nuclei), we must first discuss the nuclear force, and what holds nuclei together. • What is the nuclear force? • First...what are the fundamental forces anyway? Slide 15 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Fundamental Forces Force Theory Mediator Relative Strength Range (m) Strong QCD gluon (g) 1 ∼ 10−15 Electromagnetic QED photon (γ) α = 137 1 ≈ 10−2 1 Weak Electroweak W± and Z bosons ∼ 10−5 ∼ 10−18 Gravitational Gravity unknown ∼ 10−38 1 Slide 16 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Nuclear Force Now that we have an idea about the relative magnitude of the strong nuclear force we can investigate it in further detail: Source: http:www.cpepweb.org Slide 17 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Question: Why Can’t We Use the Fundamental Interaction to Describe All Nuclei? (and in fact all matter in nature?) Courtesy: Witold Nazarewicz for the UNEDF collaboration Slide 18 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Force Between Nucleons Some forms of nuclear theory are able to use the residual interaction between nucleons. We’ll start by comparing what we know about the nucleonnucleon interaction to atomic physics. Electrons and Atoms • Coulomb interaction • Electrons in classical orbits that have large (relative) energy spacings • Electron distances are large (ie. small ee interaction probability) NucleonNucleon Interaction • Strong interaction • Nuclear orbits (shells) have small (relative) energy spacingsy • Due to the small nuclear size, a given nucleon will strongly interact with several nuclei Slide 19 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Nuclear Matter Radius The nucleons can also be considered spherical: Therefore: 4 3 πR3 = A · 4 3 πR3 0 =) R = R0 · A1=3 Experimentally we know that R0 ≈ 1:2 fm. So, the nuclear matter radius is R = 1:2 · A1=3 Further detailed discussion on this topic can be found in Chapter 3.1 of Krane. Slide 20 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Atomic Mass and Nuclear Binding Energy Slide 21 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Atomic Mass and Nuclear Binding Energy The mass of a given atom is not simply the sum of neutron, proton, and electron masses, ie: M(A ZXN)c2 6= Z · mpc2 + N · mnc2 − Z · mec2 − ZXi=1 Bi For a nucleus to exist (ie. be a bound system), the following constraint must be satisfied (neglecting the electrons for a moment): M(A ZXN)c2 < Z · mpc2 + N · mnc2 For the nucleons to be bound inside of the nucleus, there needs to be some energy difference. We call this the Binding Energy. Slide 22 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Nature of Nuclear Binding 1 The nuclear density is roughly constant for all nuclei 2 Nuclei are positively charged, and the nuclear charge density is also roughly constant 3 The strong force is attractive only at short range.... 4 AND is repulsive at very short range (ie. nuclear matter is highly incompressible) These observations are remarkable, and have been performed with very simple concepts so far. We are now at the level of understanding where we can begin to theoretically model the nucleus in an attempt to predict our observations. Slide 23 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S BE from the Liquid Drop Model The SemiEmpirical Mass Formula B(A; Z) = aVA − aSA2=3 − aC Z(Z − 1) A1=3 − aA (A − 2Z)2 A + aP δ A1=2 ; where, δ = 8>: +1 for eveneven nuclei 0 for evenodd or oddeven −1 for oddodd nuclei Slide 24 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Why do Nuclei Undergo Fission? Source: The Open University Slide 25 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Coulomb Barrier Source: Heyde, Fig. 4.8 Slide 26 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Quantum Tunelling and α Decay Classical Treatment Quantum Treatment Slide 27 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Mass Parabola and Stability Slide 28 — Prof. Kyle Leach — PHGN 422: Nuclear Physics Source: Krane, Fig. 3.18P H G N 4 2 2 : N U C L E A R P H Y S I C S Stable and Radioactive Nuclei Ruben Saakyan, Annu. Rev. Nucl. Part. Sci. 63, 503529 (2013) Slide 29 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S β Decay • β decay is a weak interaction process where a bound proton (neutron) is converted into a neutron (proton) inside of the nucleus • This decay process involves quarks, leptons (positrons, electrons, and neutrinos), and the weakinteraction force carriers • β decay occurs in three modes: Slide 30 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Three Types of β Decay β− Decay AZ XN A Z+1 YN−1 + e− + νe β+ Decay AZ XN A Z−1 WN+1 + e+ + νe Electron Capture (EC) AZ XN + e− A Z−1 WN+1 + νe Slide 31 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S β− Decay u d d u u d Neutron Proton W− νe e− For β− decay: AZ XN Z+A1 YN−1 + e− + νe Fermi’s golden rule: λ = 2π ~ jMfij2 dE dn Mfi: βdecay transition matrix element connecting the initial and final states Slide 32 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Deviations From the Liquid Drop Model Rather surprisingly, our simple liquiddrop model has performed quite well at describing (among other things) nuclear binding and masses. We did, however, notice that this model fails when we examine nuclear binding more closely. Source: Heyde, Pg. 255 Slide 33 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Quantum Many Body Problem Our Hamiltonian H = AXi=1 −2~m2i r2 i  + XA i>j AXj=1 vij(~ri;~rj) + AXi>j AXj>k AXk=1 vijk(~ri;~rj;~rk) 1 We can’t solve this problem exactly for anything A ≈ 2 or greater... 2 Even if we could, we don’t know the exact forms for vij(~ri;~rj) or vijk(~ri;~rj;~rk) Since we can’t solve the S.E., we need to develop a model to describe the observed data (like we did with the liquid drop) that: a) Contains the essential physics to describe observation, and b) We can solve..... Slide 34 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Mean Field Approach Since we don’t know the exact potentials, and we just showed on the board that we could make an average potential approximation...we will use a meanfield approach to describing the nucleus. =) V(~ri) ≈ AXi>j AXj=1 vij(~ri;~rj) + AXi>j AXj>k AXk=1 vijk(~ri;~rj;~rk) + : : : At this point, the manybody Hamiltonian we had before, now becomes a sum over singleparticle Hamiltonians: H = AXi=1 hi = −~2 2mi r2 i + V(~ri) This ultimately reduces to the usual particle in a potential problem from Modern Physics (see Krane Chapter 2 again...). Slide 35 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The WoodsSaxon Potential V(r) = −V0 1 + e(r−R)=d Slide 36 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Reproducing the Observed Magic Numbers Source: Krane, Fig. 5.6 Slide 37 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S γ Decay in a Nutshell • The photon emission of the nucleus essentially results from a reordering of nucleons within the shells: Source: Krane, Fig. 5.11 Slide 38 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S γ Decay • γ decay is an electromagnetic process where the nucleus decreases in excitation energy, but does not change proton or neutron numbers • This decay process only involves the emission of photons Slide 39 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S γ Decay There are only twobodies in the final state for γ decay: γ Decay AZ X∗ N A Z XN(∗) + γ Slide 40 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Radioactive Decay Law The number of nuclei that decay is proportional to the number of radioactive nuclei in the sample: − dN dt = λ · N Slide 41 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Radioactive Decay Law The number of nuclei that decay is proportional to the number of radioactive nuclei in the sample: − dN dt = λ · N • The decay constant Slide 41 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S The Radioactive Decay Law The number of nuclei that decay is proportional to the number of radioactive nuclei in the sample: − dN dt = λ · N • The decay constant • The number of radioactive nuclei Slide 41 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Exponential Radioactive Decay • Radioactivity is an exponential decay process N(t) = N0e−λt Slide 42 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Interaction of Radiation with Matter Slide 43 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Ionizing and NonIonizing Radiation • Ionizing radiation has enough energy to liberate electrons in the material it interacts with (ie. it ionizes it) • Nonionizing radiation can thermally excite matter, but does not liberate electrons Slide 44 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Interaction CrossSections of Photons with Ge 0.01 0.1 1 10 γray Energy (MeV) 0.001 0.01 0.1 1 10 100 1000 Photon CrossSection (cm2g) Total Photoelectric Compton Scattering Pair Production Slide 45 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Nuclear Reactions • Typically, a nuclear reaction occurs when two nuclei (or light particles) collide with a nonzero kinetic energy in the center of mass to produce one or more nuclides. Slide 46 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Types of Nuclear Reactions There are three primary types of nuclear reactions, which are classified in terms of the mechanism which governs each process: 1 Compound Nuclear Reactions 2 Preequilibrium Reactions 3 Direct Nuclear Reactions Projectile Target Slide 47 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Experimental Proton Scattering The difference in the reactions that can be induced depends largely on the energy imparted to the system from the projectile: Source: Fig. 1.1, Direct Nuclear Reactions, Norman K. Glendenning (2004) Slide 48 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Rutherford’s Experiment Slide 49 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Rutherford (Coulomb) Scattering CrossSection Since the α particles were undergoing Coulomb scattering, we often refer to pure electromagnetic elastic scattering as Rutherford Scattering. The crosssection for this reaction is: dσ dΩ(θ) = 4zZe π202 4T1α2 sin4(1θ=2) But of course, not all reactions are elastic scattering, or electromagnetic. How about fusion? Slide 50 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S D − T Fusion Source: Rice University Slide 51 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Stellar Fusion Slide 52 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Nuclear Energy: Fission vs. Fusion Slide 53 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Nuclear Energy: Fission vs. Fusion Fission • Little energy is required to induce and sustain reaction • Fissile nuclei are heavy, radioactive, and extremely rare • Roughly 0.5 MeV per nucleon is emitted in energy • Fragments are of intermediate mass, and typically radioactive (nasty) Fusion • Large amount of energy is required to induce reaction • Light products for fusion are abundant and stable • Up to 6 MeV per nucleon can be emitted in energy • Products are also light, and typically stable (or very short lived) Slide 54 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Where Does the Fission Energy Go? We said originally that we had roughly 200 MeV in energy that was to be released in our neutron induced fission of 235U, but 66 + 98 = 164 MeV This is only about 80% of the energy we released....where did the rest go? 1) Neutrons: For the neutron induced fission of 235U, the mean kinetic energy of the emitted neutron is ∼ 2 MeV, and there are (on average) 2.5 neutrons released per fission. Therefore the average energy carried away by neutrons is about 5 MeV. This is small....so it was ok that we neglected it in our inital assumption... Slide 55 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Where Does the Fission Energy Go? 2) Prompt gamma (γ) rays: ∼ 8 MeV These are photons which result from the fission process itself, and occur within 10−14 s. 3) Beta (β) decays from the radioactive fission fragments: ∼19 MeV In general, most of the fragments are betaunstable, and will decay back to stability by undergoing β decay. 4) γ decay from the radioactive fission fragments: ∼7 MeV In general, the fragments are created in an excited nuclear state, which can then decay to the groundstate through photon emmission (γdecay). These photons come much later ∼ 10−10 s than the prompt photons. Slide 56 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Types of Reactors • Power Reactors: Designed to extract the kinetic energy of the fragments as heat, which is turned into steam, which drives a turbine. Slide 57 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Harnessing the Energy from Fission Source: Department of Chemistry, UC Davis. Slide 58 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Types of Reactors • Power Reactors: Designed to extract the kinetic energy of the fragments as heat, which is turned into steam, which drives a turbine. • Research Reactors: Designed to primarily produce a high neutron flux for a variety of physics fields Slide 59 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S A TRIGA Research Reactor Slide 60 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Types of Reactors • Power Reactors: Designed to extract the kinetic energy of the fragments as heat, which is turned into steam, which drives a turbine. • Research Reactors: Designed to primarily produce a high neutron flux for a variety of physics fields. • Converters: Designed to converte (with high efficiciency) material that is not fissile, to material that is, via thermal neutrons. • Breeding Reactors: Converter reactors that consume a fissile material, but produce one that is more fissile. Slide 61 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Breeding Reactor Slide 62 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Reactor Design Components (Concerns) • Neutron Energy: Design it for thermal or fast neutrons? • Type of Fuel: natU, 233U, 235U, 239Pu? Is Thorium a possibility? • Moderator: Prevents the reactor from being a bomb, needs to have a low (but nonzero) neutron capture crosssection • Coolant: Needs to cool the core material, or else a meltdown occurs. Typically materials with a large heat capacity. Slide 63 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Reactor Design and Components Source: Department of Chemistry, UC Davis. Slide 64 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Fusion Energy Generation • Much less information, since no working model exists currently. • Several designs are being considered, but the problem is still how to supply the energy to the system to overcome the Coulomb barrier. • Since we need ∼ 108 K for our thermonuclear fuel, most past designs consider an environment where plasmas are contained in a high magnetic field. • All types of fusion reactors are still in the ”experimental” stage, which (in this context) basically means they require more energy than they can produce. Slide 65 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Types of Fusion Reactors • For the history of magnetic confinement fusion devices, see Table 14.1 in Krane. • Tokamak: Uses a magnetic field to confine a plasma in the shape of a torus. Slide 66 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Tokamak Experimental Reactor Slide 67 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Types of Fusion Reactors • For the history of magnetic confinement fusion devices, see Table 14.1 in Krane. • Tokamak: Uses a magnetic field to confine a plasma in the shape of a torus. • Inertial confinement fusion (ICF): Uses a laser to heat and compress a small pellet with D,T in it...see last class discussion on NIF. Slide 68 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Fission vs. Fusion Weapons Slide 69 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Fission Weapons Slide 70 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S WWII Fission Bomb: ”Little Boy” Slide 71 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S WWII Fission Bomb: ”Fat Man” Slide 72 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Fusion or Thermonuclear Weapons • Warhead before firing; all suspended in polystyrene foam. • Highexplosive fires in primary, compressing plutonium and beginning a fission reaction. • Fission primary emits Xrays, irradiating the polystyrene foam. • Polystyrene foam becomes plasma and plutonium sparkplug begins to fission. • 6Li deuteride fuel produces tritium and begins the fusion reaction Slide 73 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Thermonuclear Warhead Slide 74 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Reminder: Final Presentation Information • Represents 30% of your final grade • Talks will be 10 minutes, + 2 minutes for questions • Active participation by the class is encouraged • Stick to the nuclear physics aspect of your topic • If you are making a .ppt style presentation, please export it as a .pdf • Attendance to all talks is also encouraged (mandatory) • It is not a lecture Make sure you style it as a scientific talk. Slide 75 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Reminder: Final Presentation Information • Will be graded out of 30 marks. • 1 mark Attendance and Participation • 9 marks Overall presentation (ie. organization, style, delivery, timing, preparation) • 10 marks Content and Time Management (ie. Did you highlight the proper parts of your topic...REMEMBER focus on the nuclear physics aspect of it, and make sure it has a point) • 10 marks Knowledge of subject matter (ie. is everything correct?, can you answer the questions properly?..etc.) Slide 76 — Prof. Kyle Leach — PHGN 422: Nuclear PhysicsP H G N 4 2 2 : N U C L E A R P H Y S I C S Next Week... • Thanksgiving is on Thursday (no class) • Presentations start on Tuesday • Assignment due Next Friday before 5pm Slide 77 — Prof. Kyle Leach — PHGN 422: Nuclear Physics

PHGN 422: Nuclear Physics

Lecture 23: (Course Summary) Nuclear Energy and Weapons

Prof Kyle Leach

November 21, 2019

Slide 1

Last Class

reactions

for energy and weapons

• but first

This is our last lecture

Elementary Particles of the Standard Model

The Structure of Nucleons

Inside the Atomic Nucleus

+

ProtonPositive Charge

Neutral Charge

Protons and Neutrons

In fact, protons and neutrons are so similar, they can be classified as

Nucleons are (of course) quantum mechanical objects:

• p→ +e

• n→ 0

The Atomic Nucleus

++

+

+Proton (π)

Neutron (ν)

∼ 10−15m = fm

Nuclear excitations:

∼ 105-108eVCaused by transitionsbetween nuclear states

Interactions can be thought of aseither microscopic or collective

Nuclei are typically referred to by the number of nucleons (protonsand neutrons) that they contain:

A = N + Z

The number of protons defines the chemical symbol, and is alsoreferred to as the nuclear charge

Typical Notation

A

Z X N

defined by the nuclear charge Z

information can be defined by A and X

AX

The Nuclear Chart

Phil Walker, New Scientist Magazine, October 2011

Navigating the Nuclear Chart

• Stable Nucleus - A nuclear system that does not undergo

radioactive decay (ie it is energetically unfavourable) This

Line of Stability

• Radioactive Nucleus (or unstable) - A nucleus that is

spontaneously able to decrease its total energy by emmittingionizing radiation This may result in a change in the totalnumber of protons and neutrons

• Neutron-Rich Nucleus - A nucleus that has an excess of

neutrons relative to the stable isotope for a given Z This is to theright of the valley of stability

• Neutron-Deficient Nucleus (also: Proton-Rich) - A nucleus that

has an excess of protons relative to the stable isotope for a given

Z This is to the left of the valley of stability

• The Driplines (proton and neutron) - The limits of the nuclear

chart where bound nuclei can no longer exist On the far left isthe proton dripline and the far right is the neutron dripline

Isotopes, Isotones, and Isobars

• Isoto p e:

Nuclei with the same number ofprotons (Z), but a different number

of neutrons (N) and a different mass (A)

The Fundamental Forces

As we think about limits of nuclear existence (bound nuclei), we mustfirst discuss the nuclear force, and what holds nuclei together

The Fundamental Forces

Force Theory Mediator Relative Strength Range (m)

Electromagnetic QED photon (γ) α = 1

Weak Electroweak W±and Z bosons ∼ 10 −5 ∼ 10 −18

Gravitational Gravity unknown ∼ 10 −38 ∞

The Nuclear Force

Now that we have an idea about the relative magnitude of the strongnuclear force we can investigate it in further detail:

Source: http://www.cpepweb.org

Question: Why Can’t We Use the Fundamental Interaction toDescribe All Nuclei? (and in fact all matter in nature?)

Courtesy: Witold Nazarewicz for the UNEDF collaboration

The Force Between Nucleons

Some forms of nuclear theory are able to use the residual interactionbetween nucleons We’ll start by comparing what we know about thenucleon-nucleon interaction to atomic physics

Electrons and Atoms

that have large (relative)

energy spacings

(ie small e-e interaction

probability)

Nucleon-Nucleon Interaction

small (relative) energy

a given nucleon will stronglyinteract with several nuclei

The Nuclear Matter Radius

The nucleons can also be considered spherical:

be found in Chapter 3.1 of Krane

The Atomic Mass and Nuclear Binding Energy

The Atomic Mass and Nuclear Binding Energy

The mass of a given atom is not simply the sum of neutron, proton,and electron masses, ie:

For a nucleus to exist (ie be a bound system), the following

constraint must be satisfied (neglecting the electrons for a moment):M(AZXN)c2< Z · mpc2+ N · mnc2

For the nucleons to be bound inside of the nucleus, there needs to be

Nature of Nuclear Binding

also roughly constant

incompressible)

These observations are remarkable, and have been performedwith very simple concepts so far We are now at the level ofunderstanding where we can begin to theoretically model thenucleus in an attempt to predict our observations

BE from the Liquid Drop Model

The Semi-Empirical Mass Formula

δ =







Why do Nuclei Undergo Fission?

Source: The Open University

The Coulomb Barrier

Source: Heyde, Fig 4.8

Quantum Tunelling and α Decay

Classical Treatment Quantum Treatment

The Mass Parabola and Stability

Stable and Radioactive Nuclei

β Decay

(neutron) is converted into a neutron (proton) inside of thenucleus

electrons, and neutrinos), and the weak-interaction force carriers

Three Types of β Decay

Mfi: β-decay transition matrix

ele-ment connecting the initial and final

states

Deviations From the Liquid Drop Model

Rather surprisingly, our simple liquid-drop model has performed quitewell at describing (among other things) nuclear binding and masses

We did, however, notice that this model fails when we examinenuclear binding more closely

Source: Heyde, Pg 255

The Quantum Many Body Problem

+

The Mean Field Approach

Since we don’t know the exact potentials, and we just showed on theboard that we could make an average potential approximation we

At this point, the many-body Hamiltonian we had before, now

The Woods-Saxon Potential

1 + e(r−R)/d

Reproducing the Observed Magic Numbers

Source: Krane, Fig 5.6

γ Decay in a Nutshell

re-ordering of nucleons within the shells:

Source: Krane, Fig 5.11

γ Decay

decreases in excitation energy, but does not change proton orneutron numbers

The Radioactive Decay Law

The number of nuclei that decay is proportional to the number ofradioactive nuclei in the sample:

− dN dt = λ · N

The Radioactive Decay Law

The number of nuclei that decay is proportional to the number ofradioactive nuclei in the sample:

− dN dt = λ · N

The Radioactive Decay Law

The number of nuclei that decay is proportional to the number ofradioactive nuclei in the sample:

− dN dt = λ · N

nuclei

Exponential Radioactive Decay

exponential decay

process

N(t) = N0e−λt

Interaction of Radiation with Matter

Ionizing and Non-Ionizing Radiation

material it interacts with (ie it ionizes it)

liberate electrons

Interaction Cross-Sections of Photons with Ge

Nuclear Reactions

particles) collide with a non-zero kinetic energy in the center ofmass to produce one or more nuclides

Types of Nuclear Reactions

There are three primary types of nuclear reactions, which areclassified in terms of the mechanism which governs each process:

Projectile

Target

Experimental Proton Scattering

The difference in the reactions that can be induced depends largely

on the energy imparted to the system from the projectile:

Source: Fig 1.1, Direct Nuclear Reactions, Norman K Glendenning (2004)

Rutherford’s Experiment

Rutherford (Coulomb) Scattering Cross-Section

Since the α particles were undergoing Coulomb scattering, we often

Scattering The cross-section for this reaction is:

 2

1 sin 4 (θ/2)

But of course, not all reactions are elastic scattering, or

electromagnetic How about fusion?

D − T Fusion

Source: Rice University

Stellar Fusion

Nuclear Energy: Fission vs Fusion

Nuclear Energy: Fission vs Fusion

Fission

induce and sustain reaction

radioactive, and extremely

rare

is emitted in energy

intermediate mass, and

typically radioactive (nasty)

Fusion

required to induce reaction

abundant and stable

be emitted in energy

typically stable (or very shortlived)

Where Does the Fission Energy Go?

We said originally that we had roughly 200 MeV in energy that was to

This is only about 80% of the energy we released where did therest go?

1) Neutrons:

of the emitted neutron is ∼ 2 MeV, and there are (on average)2.5 neutrons released per fission Therefore the average energycarried away by neutrons is about 5 MeV

This is small so it was ok that we neglected it in our initalassumption

Where Does the Fission Energy Go?

2) Prompt gamma (γ) rays: ∼ 8 MeV

These are photons which result from the fission process itself,

3) Beta (β) decays from the radioactive fission fragments:

∼19 MeV

In general, most of the fragments are beta-unstable, and willdecay back to stability by undergoing β decay

4) γ decay from the radioactive fission fragments: ∼7 MeV

In general, the fragments are created in an excited nuclear state,which can then decay to the ground-state through photonemmission (γ-decay)

photons

Types of Reactors

fragments as heat, which is turned into steam, which drives aturbine

Harnessing the Energy from Fission

Source: Department of Chemistry, UC Davis.

Types of Reactors

fragments as heat, which is turned into steam, which drives aturbine

neutron flux for a variety of physics fields

A TRIGA Research Reactor

Types of Reactors

fragments as heat, which is turned into steam, which drives aturbine

neutron flux for a variety of physics fields

material that is not fissile, to material that is, via thermalneutrons

material, but produce one that is more fissile

Breeding Reactor

Reactor Design Components (Concerns)

have a low (but non-zero) neutron capture cross-section

occurs Typically materials with a large heat capacity

Reactor Design and Components

Source: Department of Chemistry, UC Davis.

Fusion Energy Generation

how to supply the energy to the system to overcome the

Coulomb barrier

designs consider an environment where plasmas are contained

in a high magnetic field

which (in this context) basically means they require more energythan they can produce

Types of Fusion Reactors

Table 14.1 in Krane

shape of a torus

Tokamak Experimental Reactor

Types of Fusion Reactors

Table 14.1 in Krane

shape of a torus

compress a small pellet with D,T in it see last class discussion

on NIF

Fission vs Fusion Weapons

Fission Weapons

WWII Fission Bomb: ”Little Boy”

WWII Fission Bomb: ”Fat Man”

Fusion or Thermonuclear Weapons

beginning a fission reaction

begins to fission

Thermonuclear Warhead

Reminder: Final Presentation Information

.pdf

Reminder: Final Presentation Information

timing, preparation)

the proper parts of your topic REMEMBER focus on the nuclearphysics aspect of it, and make sure it has a point!)

correct?, can you answer the questions properly? etc.)

Next Week