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A Brief Introduction to Nuclear Physics

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A Brief Introduction to Nuclear Physics Fundamental Forces Force Relative Range Carrier Observed? Strength Gravity 10-39 Infinite Graviton No Weak 10-6 Nuclear W+ W- Z Yes (1983) Electromagnetic 10-2 Infinite Photon Yes (1923) Strong 1 Nuclear Gluon Yes (1978) (Indirect) Units and Dimensions Size: the order of magnitude is 1fm = 10-15m (a femtometer or fermi) 1/3 Radius (assuming nucleus = sphere): R = R0.A with R0 = 1.2 fm Nuclear Density: 1017 kg/m3 100 million tons per cm3 !!! density found in the core of a neutron star Enrico Fermi Nuclear matter is uncompressible (properties of the strong force) Energy: units: 1eV = 1.602 x 10-19 J energy gained by a single unit of electronic charge when accelerated through a potential of one volt Units and Dimensions Binding energy: mass of the constituents – mass of the product Atom Nucleus Force Coulomb Strong Binding Energy The hydrogen 2H: 2.2 x 106 eV atom: 13.6 eV 2.2 MeV Atoms and Nuclei emit photons. What does the binding energy imply about the photons? How might you distinguish Alpha, Beta and Gamma radiation experimentally? Example of a particle physics experiment (BNL E766) 27 GeV/c proton interactions in liquid hydrogen proton 27 GeV/c Conservation laws • Conservation of Energy • Conservation of linear momentum • Conservation of angular momentum • Conservation of electric charge •Conservation of baryon number (proton is a stable particle) • Conservation of mass number A e.g. total number of nucleons is conserved, but Z and N can change Example of a particle physics experiment (BNL E766) 27 GeV/c proton interactions in liquid hydrogen proton 27 GeV/c Radioactivity ? Emission of energy stored in the material by the mean of “mysterious” rays ~1900: The structure of the atom is not yet known... But Chemistry is ! (Mendeleiv 1834 – 1907) The radiation emitted by Radium is identified to be the element Helium 1911: Discovery of the atomic nucleus by Ernest Rutherford The first experiment with a beam of particles: The α-particles are most of the time not deflected, but sometimes they are scattered, even in the backward hemisphere. the foil is almost “transparent” to the α’s But when interaction occurs, it is on a heavy partner in the foil (the nucleus) full analysis: size of the nucleus, mass, etc… Nuclear Physics Niels Bohr: The model of the atom (1913) - Electrons in discrete orbits + Positively charged nucleus α-radiation is positively charged and too energetic to be emitted by the electron cloud α’s are emitted from the atomic nucleus. NUCLEAR PHYSICS Rutherford (1919): transmutation of one element into another by α-radiation α + N O + p Helium Nitrogen Oxygen Hydrogen The nucleus has to have exchangeable constituents Elementary Constituents of the Nucleus All the nuclei can be made with: p proton positively charge (+q) n neutron neutral (James Chadwick, 1932) Z number of protons in the nucleus N number of neutrons in the nucleus A atomic number = Z + N The atoms are neutral: Charge of the nucleus: + Z.q Electron cloud is made of Z electrons of charge (–q) The electrons determine the chemical behavior Z defines the Element Two nuclei with a same Z but different N (or A) are isotopes (of the same element) nucleons A Z X N Notations protons neutrons 1 Ex: Hydrogen 1 H 0 Isotopes of the same element 2 Deuterium 1 H 1 Other examples: 12 12 Carbon 6 C 6 C Simplified: 235 235 Uranium 92 U 143 U In practice, the Z number is redundant with the element symbol & the N number is obsolete The chart of Nuclei Stable Isotopes ~300 Unstable >2000+ Radioactive Decay Law The activity of a certain sample (e.g. source) depends on the number N of radioactive nuclei and on the probability λ for each nucleus to decay: A = λ . N [1/s] [1/s] Evolution with time: dN = -A.dt dN: number of nuclei that decayed during dt dN = -λ.N.dt, which gives: dN/dt = -λ.N Solving the differential equation: -λ.t N(t) = N0.e N(t=0) Half-life Similarly, we find that the activity of a source change with time: A(t) = A .e-λ.t 0 From λ = decay constant, one can define τ = 1/λ, the mean lifetime It is usual to define t1/2, the half-life, the time after which half of the initial nuclei have decayed: t1/2 = ln 2 / λ = τ ln 2 The half-life is characteristic to the decay of a given nucleus. This number (when known) is usually tabulated. Question • The atom and the nucleus are both composed of many components. Their structures and states can be studied through spectroscopy. • Which do you think is more complicated. – Nuclear spectroscopy or – Atomic Spectroscopy? • Why? The Nuclear (Strong) Force Short Range, only a few fm Nuclear Matter is uncompressible ; repulsive at very short range (< 1 fm) Attractive over a range of a few fm a given nucleon only interacts with its next neighbors in the nucleus Negligible at long distances Same force for protons and neutrons A (simplified) model of the nucleus U Coulomb Barrier (for the charged particles) α Unbound levels Tunnel effect (α-decay) (U>0) Distance from the center of the nucleus Bound levels Square well potential (approx.) (U<0) neutrons protons Filled levels – Quantified energy, Pauli principle (Quantum Mechanics, Shell Model) If all nucleons are in U<0, no nucleon can tunnel to the outside Stable nucleus If unbound levels are filled (U>0), tunneling is possible through the Coulomb barrier Radioactive nucleus This picture shows tracks made by alpha particles in a cloud chamber. What physics conclusions can you reach based on this picture? Two isotopes. Alpha particles from a particular decay are mono-energetic α-decay α-particle = 4He: cluster in the nucleus – α: very tightly bound system U 2 r A A-4 4 Z X N Z-2 YN -2 + 2 He 2 + Q Nuclei that emit higher energy alphas, have shorter half lives? True or False? Nuclei that emit higher energy alphas, have shorter half lives? True or False? U r U r Nuclei that emit higher energy alphas, have shorter half lives? True or False (other way around) U Shorter half life (less tunneling) Higher Kinetic Energy r β-decay Weak interaction can transform a proton into a neutron or a neutron into a proton (It’s actually happening at the quark level) β- decay: n p + e- + anti neutrino e-: electron β+ decay: p n + e+ + neutrino e+: positron β- decay Proton u d u e- W- νe Neutron u d d Beta decay of 3He Sample Electron energy spectrum of emitted electrons e- e- ν 3 + 3He+ He e- ν 3He+ ν e- Electron energy spectrum 3He+ - β decay Elementary process: n p + e- + ν A A - Decay of the nucleus: Z X N Z+1Y N -1 + e + ν + U β decay Elementary process: p n + e+ + ν (only happening inside the nucleus) A A + Decay of the nucleus: Z X N Z-1 YN+1 + e + ν neutrons protons Alternative process: electron capture (from atomic orbit) p + e- n + ν A A - Z X N + e Z-1 YN+1 + ν decay chain of 238U # of neutrons protons+ # of protons Question: For a given nuclear transition, which type(s) of emitted radiation are monoenergetic? 1: beta only 2: alpha,gamma 3: gamma,beta 4: alpha only Question: For a given nuclear transition, which type(s) of emitted radiation are monoenergetic? 1: beta only 2: alpha,gamma 3: gamma,beta 4: alpha only Beta shares energy with a neutrino that you can’t measure (in ph326) END .
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