Introduction to Nuclear and Particle Physics

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1 Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday, 14:15-16:45 FIS Lecture Hall

2 Lecturers Elena Bratkovskaya Marcus Bleicher

3 Tutorials Thomas Lang Christoph Herold Thursday, 12:00-14:00 FIS Lecture Hall

4 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

5 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

6 Lecture 1 Units, scales Early nuclear models

7 Scales Nucleus m Crystal structures 10-9 m toms m Visible matter 10-1 m Nucleon m

8 Scales in nuclear physics typical excitation energy: ~ ev m typical excitation energy: ~ MeV m typical excitation energy: ~ 10 2 MeV m

9 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 = x kg E=mc 2 Common prefixes: kev ev MeV ev GeV ev TeV ev

10 Scales in nuclear physics common mass scales: photon: neutrino: electron: proton: mγ = 0 MeV mν ~ 1 ev me = MeV mp = 938 MeV Can we further simplify the unit system?

11 Scales in nuclear physics Natural units: = c = k B =1 masses and lengths are the only units left and [mass] = [energy] = [temperature] = 1 / [length]

12 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

13 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

14 Electric charge Charge is quantized as well: quanta - e Important quantity: Fine structure constant α = α EM = e2 4πε 0 c Usual choice: ε 0 =1 α = e2 4π

15 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 = µ B µ p = 2.79µ N µ n = 1.91µ N 2 3 µ p

16 Historical remarks tomic nucleus discovered 1911 by Ernest Rutherford Hans Geiger Ernest Marsden

17 Before... Plum Pudding Model

18 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

19 Rutherford experiment Bombard nuclei (thin gold foil) with α particles Idea: Check angular distribution

20 Before Prediction: α particles move through the pudding, nearly undisturbed

21 But... + Result: some α particles got reflected at a center of the atom and bounced back ~180

22 But... + Interpretation: positively charged core surrounded by negatively charges electrons

23 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 m m

24 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

25 Nuclear forces From Coulomb interaction alone one would expect that nuclei are not bound.

26 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

27 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

28 Yukawa potential Mass of the virtual boson is roughly 200 MeV Yukawa-Potential V = g 2 e mr r lso called screened Coulomb potential

29 Yukawa potential Features: for r, V 0 weakly attractive at low r repulsive core (blackboard)

30 Properties of nuclei ZX = N + Z Examples: 1 1H u 12 6 C

31 Properties of nuclei mass number ZX = N + Z Examples: 1 1H u 12 6 C

32 Properties of nuclei mass number charge ZX = N + Z Examples: 1 1H u 12 6 C

33 Properties of nuclei mass number charge ZX = N + Z Examples: 1 1H u 12 6 C

34 Table of Nuclides

35 Table of Nuclides isotone

36 Table of Nuclides isotone isotope

37 Table of Nuclides

38 Table of Nuclides same : isobars 17 7 N 17 8 O 17 9 F

39 Table of Nuclides same : isobars 17 7 N 17 8 O 17 9 F same Z: isotopes 12 6 C 13 6 C

40 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

41 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

42 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

43 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 half-life of more than 1000 trillion years

44 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)

45 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)

46 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)

47 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)

48 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)

49 Nuclear fission

50 Nuclear fission

51 Nuclear fission too many protons

52 Nuclear fission

53 Nuclear fission too many neutrons

54 Nuclear fission

55 Nuclear fission too much Coulomb repulsion

56 Nuclear fission

57 Nuclear fission

58 Nuclear fission too many neutrons

59 Nuclear fission

60 Nuclear fission too much Coulomb repulsion

61 Nuclear fission

62 Decays Derivation blackboard

66 (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

67 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.

68 Binding energy

69 Binding energy

70 Binding energy Fusion Fission

71 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

72 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

73 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

74 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

75 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

76 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

77 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

78 Binding energy Volume Surface Coulomb Symmetry Parity

79 Binding energy Volume Surface Coulomb Symmetry Parity

80 Binding energy Volume Surface Coulomb Symmetry Parity

81 Early Nuclear Models

82 Nuclear abundance

83 Wait... Fusion Fission Where do elements beyond iron come from?

84 Universe

85 Where do heavy elements come from? Some food for thought for the tutorials...

Introduction to Nuclear and Particle Physics Part I

WS2012/13: Introduction to Nuclear and Particle Physics Part I Lectures: Elena Bratkovskaya, Sascha Vogel, Marcus Bleicher Wednesday, 14:15-16:45 16:45 Room: FIAS Hörsaal 100 E-mail: Elena.Bratkovskaya@th.physik.uni-frankfurt.de