Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday, 14:15-16:45 FIS Lecture Hall
Lecturers Elena Bratkovskaya Marcus Bleicher svogel@th.physik.uni-frankfurt.de bleicher@th.physik.uni-frankfurt.de elena.bratkovskaya@th.physik.uni-frankfurt.de
Tutorials Thomas Lang Christoph Herold Thursday, 12:00-14:00 FIS Lecture Hall lang@th.physik.uni-frankfurt.de herold@th.physik.uni-frankfurt.de
The plan... 1) Units, scales, historical overview 2) Fermi-Gas model, shell model 3) Collective Nuclear Models 4) ngular Momentum, Nucleon-Nucleon-Interaction 5) Hartree-Fock 6) Fermion-Pairing 7) Phenomenological Single Particle Models 8) Klein-Gordon equation 9) Covariant ED 10) Dirac equation 11) Quark models 12) Intro to QCD 13) Symmetries in QCD 14) Quark-Gluon-Plasma
Literature Walter Greiner, Joachim. Maruhn, Nuclear models Bogdan Povh, Klaus Rith, Christoph Scholz, and Frank Zetsche Particles and Nuclei. n Introduction to the Physical Concepts shok Das, Thomas Ferbel Introduction to nuclear and particle physics Ian Simpson Hughes Elementary particles Bogdan Povh, Klaus Rith Particles and nuclei: an introduction to the physical concepts Brian Robert Martin, Graham Shaw Particle physics Brian Robert Martin Nuclear and particle physics
Lecture 1 Units, scales Early nuclear models
Scales Nucleus 10-14 m Crystal structures 10-9 m toms 10-10 m Visible matter 10-1 m Nucleon 10-15 m
Scales in nuclear physics typical excitation energy: ~ ev 10-10 m typical excitation energy: ~ MeV 10-14 m typical excitation energy: ~ 10 2 MeV 10-15 m
Scales in nuclear physics unit for length: unit for energy: unit for mass: in SI units: fm (fermi, femtometer) ev (electron volt) MeV/c 2 (c = 3 x 10 8 m/s) 1 MeV/c 2 = 1.783 x 10-30 kg E=mc 2 Common prefixes: kev - 10 3 ev MeV - 10 6 ev GeV - 10 9 ev TeV - 10 12 ev
Scales in nuclear physics common mass scales: photon: neutrino: electron: proton: mγ = 0 MeV mν ~ 1 ev me = 0.511 MeV mp = 938 MeV Can we further simplify the unit system?
Scales in nuclear physics Natural units: = c = k B =1 masses and lengths are the only units left and [mass] = [energy] = [temperature] = 1 / [length]
ngular momentum Spin is quantized (see atomic physics lecture) llowed values: S = s +(s + 1) s =0, 1 2, 1, 3 2, 2, 5 2,... Orbital angular momentum llowed values: L =0, 1, 2, 3... Total angular momentum: J = S + L For each J there are 2J+1 projections of the angular momentum M = J, J +1,...,J 1,J
Quantum statistics ssume: System of N particles Wavefunction Ψ(r 1,r 2..., r N ) replace: Ψ(r 2,r 1..., r N )=C Ψ(r 1,r 2..., r N ) C has to be a phase factor, i.e. C 2 = 1: Bosons: C = +1 Fermions: C = -1 From spin statistics theorem: Fermions have half integer spin, Bosons integer spin
Electric charge Charge is quantized as well: quanta - e Important quantity: Fine structure constant α = α EM = e2 4πε 0 c 1 137 Usual choice: ε 0 =1 α = e2 4π
Magnetons Two quantities are used to describe magnetic properties (e.g. magnetic dipole moment) of electrons and nuclei: Nuclear magneton Bohr magneton µ N = e 2m p µ N = e 2m e µ e = 1.001159652µ B µ p = 2.79µ N µ n = 1.91µ N 2 3 µ p
Historical remarks tomic nucleus discovered 1911 by Ernest Rutherford Hans Geiger Ernest Marsden 1871-1837 1882-1945 1889-1970
Before... Plum Pudding Model
Plum pudding model + +electrons outside + + + + + + + + + + Features: charge neutral extended in space positive charges uniformly distributed inside the whole atom
Rutherford experiment 1909-1911 Bombard nuclei (thin gold foil) with α particles Idea: Check angular distribution
Before... + + + + + + + + + + + Prediction: α particles move through the pudding, nearly undisturbed
But... + Result: some α particles got reflected at a center of the atom and bounced back ~180
But... + Interpretation: positively charged core surrounded by negatively charges electrons
Rutherford s model of the atom tom has a small positive core and is surrounded by atoms, just like the sun by planets (also: planetary model) Important: The atom is 99.99% empty space 10-14 m 10-10 m
What s inside? Following an idea of Rutherford from 1921 Nucleus consists of protons (positive charge) neutrons (no charge) Info neutron: charge 0, spin 1/2 mass 939,56 MeV mean lifetime: 885.7s decay channel: n p + e + ν e
Nuclear forces From Coulomb interaction alone one would expect that nuclei are not bound.
Nuclear forces Nuclear force (or residual strong force) holds them together Features: 1) Nuclear force has to be short range 2) Nuclear force has to be strong 3) Nuclear force is the same for n-n, n-p and p-p (does not depend on charge) 4) Nuclear forces are next-neighbour interactions, they show saturation 5) Nuclear forces are spin-dependent 6) They do not obey a 1/r 2 law, they are not central forces, thus angular momentum is not conserved
Yukawa potential Every force is carried by a force carrier (gauge boson) Idea Yukawa: Nuclear force is carried by a virtual meson p p π 0 n n
Yukawa potential Mass of the virtual boson is roughly 200 MeV Yukawa-Potential V = g 2 e mr r lso called screened Coulomb potential
Yukawa potential Features: for r, V 0 weakly attractive at low r repulsive core (blackboard)
Properties of nuclei ZX = N + Z Examples: 1 1H 197 79 u 12 6 C
Properties of nuclei mass number ZX = N + Z Examples: 1 1H 197 79 u 12 6 C
Properties of nuclei mass number charge ZX = N + Z Examples: 1 1H 197 79 u 12 6 C
Properties of nuclei mass number charge ZX = N + Z Examples: 1 1H 197 79 u 12 6 C
Table of Nuclides
Table of Nuclides isotone
Table of Nuclides isotone isotope
Table of Nuclides
Table of Nuclides same : isobars 17 7 N 17 8 O 17 9 F
Table of Nuclides same : isobars 17 7 N 17 8 O 17 9 F same Z: isotopes 12 6 C 13 6 C
Table of Nuclides same : isobars 17 7 N 17 8 O 17 9 F same Z: isotopes same N: isotones 12 6 C 14 7 N 13 6 C 13 6 C
Table of Nuclides same : isobars 17 7 N 17 8 O 17 9 F same Z: isotopes same N: isotones N Z: mirror nuclei 12 6 C 14 7 N 3 1H 13 6 C 13 6 C 3 2He
Table of Nuclides same : isobars 17 7 N 17 8 O 17 9 F same Z: isotopes same N: isotones N Z: mirror nuclei 12 6 C 14 7 N 3 1H 13 6 C 13 6 C 3 2He same and Z, but different excitation: nuclear isomers 180 Ta 180m Ta 73 73
Table of Nuclides same : isobars 17 7 N 17 8 O 17 9 F same Z: isotopes same N: isotones N Z: mirror nuclei 12 6 C 14 7 N 3 1H 13 6 C 13 6 C 3 2He same and Z, but different excitation: nuclear isomers 180 Ta 180m Ta 73 73 half-life of more than 1000 trillion years
Decays ZX Z+1X + e + ν e ZX Z 1X + e + + ν e ZX ZX + e Z 1X + ν e ZX 4 Z 2 X + α( 4 2He)
Decays ZX Z+1X + e + ν e ZX Z 1X + e + + ν e ZX ZX + e Z 1X + ν e ZX 4 Z 2 X + α( 4 2He)
Decays ZX Z+1X + e + ν e ZX Z 1X + e + + ν e ZX ZX + e Z 1X + ν e ZX 4 Z 2 X + α( 4 2He)
Decays ZX Z+1X + e + ν e ZX Z 1X + e + + ν e ZX ZX + e Z 1X + ν e ZX 4 Z 2 X + α( 4 2He)
Decays ZX Z+1X + e + ν e ZX Z 1X + e + + ν e ZX ZX + e Z 1X + ν e ZX 4 Z 2 X + α( 4 2He)
Nuclear fission
Nuclear fission
Nuclear fission too many protons
Nuclear fission
Nuclear fission too many neutrons
Nuclear fission
Nuclear fission too much Coulomb repulsion
Nuclear fission
Nuclear fission
Nuclear fission too many neutrons
Nuclear fission
Nuclear fission too much Coulomb repulsion
Nuclear fission
Decays Derivation blackboard
(t)/ 1 (0) Decays (t) 1 (0) 1 (t) τ 1 = 10 τ 2 τ 1 = 10τ 2 1 (t) 2 (t) 2 (t) t t/τ 2 τ 2
Binding energy M(Z, N) =N m N + Z M p + Z m e E B The binding energy is the energy set free when forming the respective nuclei.
Binding energy
Binding energy
Binding energy Fusion Fission
Binding energy E B = a V a S 2 3 ac Z2 1 3 a sym (N Z)2 δ 1 2 a sym a V a S 2 3 a C Z2 1 3 (N Z)2 δ 1 2 Volume term Surface term Coulomb term Symmetry term Pairing term
Binding energy E B = a V a S 2 3 ac Z2 1 3 a sym (N Z)2 δ 1 2 a sym a V a S 2 3 a C Z2 1 3 (N Z)2 δ 1 2 Volume term Surface term Coulomb term Symmetry term Pairing term
Binding energy E B = a V a S 2 3 ac Z2 1 3 a sym (N Z)2 δ 1 2 a sym a V a S 2 3 a C Z2 1 3 (N Z)2 δ 1 2 Volume term Surface term Coulomb term Symmetry term Pairing term
Binding energy E B = a V a S 2 3 ac Z2 1 3 a sym (N Z)2 δ 1 2 a sym a V a S 2 3 a C Z2 1 3 (N Z)2 δ 1 2 Volume term Surface term Coulomb term Symmetry term Pairing term
Binding energy E B = a V a S 2 3 ac Z2 1 3 a sym (N Z)2 δ 1 2 a sym a V a S 2 3 a C Z2 1 3 (N Z)2 δ 1 2 Volume term Surface term Coulomb term Symmetry term Pairing term
Binding energy E B = a V a S 2 3 ac Z2 1 3 a sym (N Z)2 δ 1 2 a sym a V a S 2 3 a C Z2 1 3 (N Z)2 δ 1 2 Volume term Surface term Coulomb term Symmetry term Pairing term
Binding energy E B = a V a S 2 3 ac Z2 1 3 a sym (N Z)2 δ 1 2 a sym a V a S 2 3 a C Z2 1 3 (N Z)2 δ 1 2 Volume term Surface term Coulomb term Symmetry term Pairing term
Binding energy Volume Surface Coulomb Symmetry Parity
Binding energy Volume Surface Coulomb Symmetry Parity
Binding energy Volume Surface Coulomb Symmetry Parity
Early Nuclear Models
Nuclear abundance
Wait... Fusion Fission Where do elements beyond iron come from?
Universe
Where do heavy elements come from? Some food for thought for the tutorials...