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Introduction to Nuclear and Particle Physics
Sascha VogelElena Bratkovskaya
Marcus Bleicher
Wednesday, 14:15-16:45FIAS Lecture Hall
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Thomas Lang Christoph Herold
[email protected]@th.physik.uni-frankfurt.de
Tutorials
Thursday, 12:00-14:00FIAS Lecture Hall
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The plan...
1) Units, scales, historical overview2) Fermi-Gas model, shell model3) Collective Nuclear Models4) Angular Momentum, Nucleon-Nucleon-Interaction5) Hartree-Fock6) Fermion-Pairing7) Phenomenological Single Particle Models8) Klein-Gordon equation9) Covariant ED10) Dirac equation11) Quark models12) Intro to QCD13) Symmetries in QCD14) Quark-Gluon-Plasma
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Literature
•Walter Greiner, Joachim A. Maruhn, “Nuclear models”
•Bogdan Povh, Klaus Rith, Christoph Scholz, and Frank Zetsche“Particles and Nuclei. An Introduction to the Physical Concepts”
•Ashok 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”
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Lecture 1
Units, scalesEarly nuclear models
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Scales
Visible matter10-1 m
Crystal structures
10-9 m
Atoms 10-10 m
Nucleus10-14 m
Nucleon 10-15 m
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Scales in nuclear physics
10-10 m
10-14 m
10-15 m
typical excitation energy: ~ eV
typical excitation energy: ~ MeV
typical excitation energy: ~ 102 MeV
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Scales in nuclear physics
unit for length: fm (fermi, femtometer)unit for energy: eV (electron volt)unit for mass: MeV/c2 (c = 3 x 108 m/s)in SI units: 1 MeV/c2 = 1.783 x 10-30 kg
Common prefixes: keV - 103 eV MeV - 106 eV GeV - 109 eV TeV - 1012 eV
E=mc2
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Scales in nuclear physics
common mass scales:
photon: mγ = 0 MeVneutrino: mν ~ 1 eVelectron: me = 0.511 MeVproton: mp = 938 MeV
Can we further simplify the unit system?
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Scales in nuclear physics
Natural units:
� = c = kB = 1
⇒ masses and lengths are the only units left and
[mass] = [energy] = [temperature] = 1 / [length]
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Angular momentum
Spin is quantized (see atomic physics lecture)Allowed values:
S = ��s+ (s+ 1) s = 0,
1
2, 1,
3
2, 2,
5
2, ...
Orbital angular momentumAllowed values: Total angular momentum:
L = 0, 1, 2, 3... �J = �S + �L
For each J there are 2J+1 projections of the angular momentum
M = −J,−J + 1, ..., J − 1, J
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Quantum statistics
Assume: System of N particles
Wavefunction Ψ(�r1, �r2..., �rN )
replace: Ψ(�r2, �r1..., �rN ) = C ·Ψ(�r1, �r2..., �rN )
C has to be a phase factor, i.e. C2 = 1:
Bosons: C = +1Fermions: C = -1
From spin statistics theorem:Fermions have half integer spin, Bosons integer spin
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Electric charge
α = αEM =e2
4πε0�c≈ 1
137Important quantity:Fine structure constant
Charge is quantized as well: quanta - e
Usual choice:
ε0 = 1 ⇒ α =e2
4π
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Magnetons
µN =e�2mp
µN =e�2me
Nuclear magneton Bohr magneton
µe = 1.001159652µB
µp = 2.79µN
µn = − 1.91µN ≈ −2
3µp
Two quantities are used to describe magnetic properties (e.g. magnetic dipole moment) of electrons and nuclei:
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Historical remarks
Atomic nucleus discovered 1911 by
1882 - 19451871 - 1837 1889 - 1970
ErnestRutherford
HansGeiger
ErnestMarsden
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Before...
Plum Pudding Model
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Plum pudding model
++
+
+
++
+
++
+
+
positive charges uniformly distributed inside the whole atom
+electrons outside
Features: charge neutral extended in space
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Rutherford experiment 1909-1911
Bombard nuclei (thin gold foil) with α particlesIdea: Check angular distribution
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Before...
++
+
+
++
+
++
+
+
Prediction: α particles move through the “pudding”, nearly undisturbed
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But...
+
Result: some α particles got reflected at a center of the atom and bounced back ~180°
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But...
+
Interpretation: positively charged core surrounded by negatively charges electrons
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Rutherford’s model of the atom
Atom 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
10-10 m
10-14 m
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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− + ν̄e
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Nuclear forces
From Coulomb interaction alone one would expect that nuclei are not bound.
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Nuclear forces
Nuclear force (or residual strong force) holds them together
Features:1) Nuclear force has to be short range2) Nuclear force has to be strong3) 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 saturation5) Nuclear forces are spin-dependent6) They do not obey a 1/r2 law, they are not central
forces, thus angular momentum is not conserved
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Yukawa potential
Every force is carried by a force carrier (gauge boson)
Idea Yukawa: Nuclear force is carried by a virtual meson
pp
nn
π0
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Yukawa potential
Mass of the virtual boson is roughly 200 MeV
Yukawa-Potential
V = −g2e−mr
r
Also called “screened Coulomb potential”
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Yukawa potential
Features: for r → ∞, V → 0 weakly attractive at low r repulsive core (blackboard)
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Properties of nuclei
AZX
11H
19779 Au 12
6 CExamples:
A = N + Z
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Properties of nuclei
AZX
mass number
11H
19779 Au 12
6 CExamples:
A = N + Z
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Properties of nuclei
AZX
mass number
charge
11H
19779 Au 12
6 CExamples:
A = N + Z
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Properties of nuclei
AZX
mass number
charge
11H
19779 Au 12
6 CExamples:
A = N + Z
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Table of Nuclides
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Table of Nuclides
isotone
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Table of Nuclides
isotope
isotone
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Table of Nuclides
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Table of Nuclides
178 O
177 N 17
9 F• same A: isobars
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Table of Nuclides
178 O
177 N 17
9 F• same A: isobars
136 C12
6 C• same Z: isotopes
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Table of Nuclides
178 O
177 N 17
9 F• same A: isobars
136 C12
6 C• same Z: isotopes
136 C14
7 N• same N: isotones
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Table of Nuclides
178 O
177 N 17
9 F• same A: isobars
136 C12
6 C• same Z: isotopes
136 C14
7 N• same N: isotones
31H
32He• N↔Z: mirror nuclei
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Table of Nuclides
178 O
177 N 17
9 F• same A: isobars
136 C12
6 C• same Z: isotopes
136 C14
7 N• same N: isotones
31H
32He• N↔Z: mirror nuclei
18073 Ta 180m
73 Ta• same A and Z, but different excitation: nuclear isomers
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Table of Nuclides
half-life of more than 1000 trillion years
178 O
177 N 17
9 F• same A: isobars
136 C12
6 C• same Z: isotopes
136 C14
7 N• same N: isotones
31H
32He• N↔Z: mirror nuclei
18073 Ta 180m
73 Ta• same A and Z, but different excitation: nuclear isomers
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Decays
AZX
AZX → A
Z+1X + e− + ν̄e
AZX → A
Z−1X + e+ + νe
AZX + e
− → AZ−1X + νe
AZX → A−4
Z−2X + α( 42He)
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Decays
AZX
AZX → A
Z+1X + e− + ν̄e
AZX → A
Z−1X + e+ + νe
AZX + e
− → AZ−1X + νe
AZX → A−4
Z−2X + α( 42He)
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Decays
AZX
AZX → A
Z+1X + e− + ν̄e
AZX → A
Z−1X + e+ + νe
AZX + e
− → AZ−1X + νe
AZX → A−4
Z−2X + α( 42He)
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Decays
AZX
AZX → A
Z+1X + e− + ν̄e
AZX → A
Z−1X + e+ + νe
AZX + e
− → AZ−1X + νe
AZX → A−4
Z−2X + α( 42He)
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Decays
AZX
AZX → A
Z+1X + e− + ν̄e
AZX → A
Z−1X + e+ + νe
AZX + e
− → AZ−1X + νe
AZX → A−4
Z−2X + α( 42He)
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Nuclear fission
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Nuclear fission
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Nuclear fission
too many protons
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Nuclear fission
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Nuclear fission
too many neutrons
![Page 54: Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday,](https://reader031.vdocuments.us/reader031/viewer/2022022420/5a7abdcb7f8b9a66798b7f2d/html5/thumbnails/54.jpg)
Nuclear fission
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Nuclear fission
too much Coulomb repulsion
![Page 56: Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday,](https://reader031.vdocuments.us/reader031/viewer/2022022420/5a7abdcb7f8b9a66798b7f2d/html5/thumbnails/56.jpg)
Nuclear fission
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Nuclear fission
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Nuclear fission
too many neutrons
![Page 59: Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday,](https://reader031.vdocuments.us/reader031/viewer/2022022420/5a7abdcb7f8b9a66798b7f2d/html5/thumbnails/59.jpg)
Nuclear fission
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Nuclear fission
too much Coulomb repulsion
![Page 61: Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday,](https://reader031.vdocuments.us/reader031/viewer/2022022420/5a7abdcb7f8b9a66798b7f2d/html5/thumbnails/61.jpg)
Nuclear fission
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Decays
Derivation blackboard
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Decays
A(t)
/A1(
0)
t/τ2
A1(t)
A2(t)
τ1 = 10 τ2
t
τ2
A1(t)
τ1 = 10τ2
A2(t)
A(t)
A1(0)
![Page 67: Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday,](https://reader031.vdocuments.us/reader031/viewer/2022022420/5a7abdcb7f8b9a66798b7f2d/html5/thumbnails/67.jpg)
Binding energy
M(Z,N) = N ·mN + Z ·Mp + Z ·me − EB
The binding energy is the energy set free when forming the respective nuclei.
![Page 68: Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday,](https://reader031.vdocuments.us/reader031/viewer/2022022420/5a7abdcb7f8b9a66798b7f2d/html5/thumbnails/68.jpg)
Binding energy
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Binding energy
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Binding energy
FissionFusion
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Binding energy
EB = aV ·A− aS ·A 23 − aC · Z
2
A13
− asym · (N − Z)2
A− δ
A12
aV ·A
aS ·A 23
aC · Z2
A13
asym · (N − Z)2
A
δ
A12
Volume term
Surface term
Coulomb term
Symmetry term
Pairing term
![Page 72: Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday,](https://reader031.vdocuments.us/reader031/viewer/2022022420/5a7abdcb7f8b9a66798b7f2d/html5/thumbnails/72.jpg)
Binding energy
EB = aV ·A− aS ·A 23 − aC · Z
2
A13
− asym · (N − Z)2
A− δ
A12
aV ·A
aS ·A 23
aC · Z2
A13
asym · (N − Z)2
A
δ
A12
Volume term
Surface term
Coulomb term
Symmetry term
Pairing term
![Page 73: Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday,](https://reader031.vdocuments.us/reader031/viewer/2022022420/5a7abdcb7f8b9a66798b7f2d/html5/thumbnails/73.jpg)
Binding energy
EB = aV ·A− aS ·A 23 − aC · Z
2
A13
− asym · (N − Z)2
A− δ
A12
aV ·A
aS ·A 23
aC · Z2
A13
asym · (N − Z)2
A
δ
A12
Volume term
Surface term
Coulomb term
Symmetry term
Pairing term
![Page 74: Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday,](https://reader031.vdocuments.us/reader031/viewer/2022022420/5a7abdcb7f8b9a66798b7f2d/html5/thumbnails/74.jpg)
Binding energy
EB = aV ·A− aS ·A 23 − aC · Z
2
A13
− asym · (N − Z)2
A− δ
A12
aV ·A
aS ·A 23
aC · Z2
A13
asym · (N − Z)2
A
δ
A12
Volume term
Surface term
Coulomb term
Symmetry term
Pairing term
![Page 75: Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday,](https://reader031.vdocuments.us/reader031/viewer/2022022420/5a7abdcb7f8b9a66798b7f2d/html5/thumbnails/75.jpg)
Binding energy
EB = aV ·A− aS ·A 23 − aC · Z
2
A13
− asym · (N − Z)2
A− δ
A12
aV ·A
aS ·A 23
aC · Z2
A13
asym · (N − Z)2
A
δ
A12
Volume term
Surface term
Coulomb term
Symmetry term
Pairing term
![Page 76: Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday,](https://reader031.vdocuments.us/reader031/viewer/2022022420/5a7abdcb7f8b9a66798b7f2d/html5/thumbnails/76.jpg)
Binding energy
EB = aV ·A− aS ·A 23 − aC · Z
2
A13
− asym · (N − Z)2
A− δ
A12
aV ·A
aS ·A 23
aC · Z2
A13
asym · (N − Z)2
A
δ
A12
Volume term
Surface term
Coulomb term
Symmetry term
Pairing term
![Page 77: Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday,](https://reader031.vdocuments.us/reader031/viewer/2022022420/5a7abdcb7f8b9a66798b7f2d/html5/thumbnails/77.jpg)
Binding energy
EB = aV ·A− aS ·A 23 − aC · Z
2
A13
− asym · (N − Z)2
A− δ
A12
aV ·A
aS ·A 23
aC · Z2
A13
asym · (N − Z)2
A
δ
A12
Volume term
Surface term
Coulomb term
Symmetry term
Pairing term
![Page 78: Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday,](https://reader031.vdocuments.us/reader031/viewer/2022022420/5a7abdcb7f8b9a66798b7f2d/html5/thumbnails/78.jpg)
Binding energy
Volume Surface Coulomb
ParitySymmetry
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Binding energy
Volume Surface Coulomb
ParitySymmetry
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Binding energy
Volume Surface Coulomb
ParitySymmetry
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Early Nuclear Models
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Nuclear abundance
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Wait...
Where do elements beyond iron come from?
FissionFusion
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Universe
![Page 85: Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to Nuclear and Particle Physics Sascha Vogel Elena Bratkovskaya Marcus Bleicher Wednesday,](https://reader031.vdocuments.us/reader031/viewer/2022022420/5a7abdcb7f8b9a66798b7f2d/html5/thumbnails/85.jpg)
Where do heavy elements come from?
Some food for thought for the tutorials...