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TRANSCRIPT
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Introduction toNuclear and Particle Physics
Sascha VogelElena Bratkovskaya
Marcus Bleicher
Wednesday, 14:15-16:45FIAS Lecture Hall
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Elena Bratkovskaya Marcus Bleicher
[email protected]@th.physik.uni-frankfurt.de
Lecturers
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected] -
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The plan...
1) Units, scales, historical overview2) Fermi-Gas model, shell model3) Collective Nuclear Models4) Angular Momentum, Nucleon-Nucleon-Interaction
5) Hartree-Fock6) Fermion-Pairing7) Phenomenological Single Particle Models8) Klein-Gordon equation9) Covariant ED
10) 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 ZetscheParticles and Nuclei. An Introduction to the Physical Concepts
Ashok Das, Thomas FerbelIntroduction to nuclear and particle physics
Ian Simpson HughesElementary particles
Bogdan Povh, Klaus RithParticles and nuclei: an introduction to the physical concepts
Brian Robert Martin, Graham ShawParticle physics
Brian Robert MartinNuclear and particle physics
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Lecture 1
Units, scalesEarly nuclear models
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Scales
Visiblematter
10-1 m
Crystalstructures
10-9 m
Atoms10-10 m
Nucleus10-14 m
Nucleon10-15 m
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Scales in nuclear physics
10-10m
10-14m
10-15
m
typical excitation energy: ~ eV
typical excitation energy: ~ MeV
typical excitation energy: ~ 102MeV
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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 108m/s)in SI units: 1 MeV/c2= 1.783 x 10-30kg
Common prefixes: keV - 103eV
MeV - 106eV GeV - 109eV TeV - 1012eV
E=mc2
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Scales in nuclear physics
common mass scales:
photon: m!= 0 MeV
neutrino: m"~ 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+
LFor each J there are 2J+1 projections of theangular momentum
M=
J,
J+ 1, ..., J
1, J
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Quantum statistics
Assume: System of N particles
Wavefunction (r1, r2..., rN)
replace: (r2, r1..., rN) =C
(
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
= EM = e
2
40c
1
137
Important quantity:Fine structure constant
Charge is quantized as well: quanta - e
Usual choice:
0 = 1 =
e
4
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Magnetons
N =e
2mpN=
e
2me
Nuclear magneton Bohr magneton
e = 1.001159652B
p = 2.79N
n =
1.91N
2
3p
Two quantities are used to describe magneticproperties (e.g. magnetic dipole moment) ofelectrons 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 chargesuniformly distributedinside 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 #particlesIdea: Check angular distribution
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Before...
+
+
+
+
++
+
++
+
+
Prediction: #particles move through the pudding,nearly undisturbed
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But...
+
Result: some #particles got reflected at a center ofthe atom and bounced back ~180
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But...
+
Interpretation: positively charged core surroundedby negatively charges electrons
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Rutherfords 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
10-10m
10-14m
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Whats inside?
Following an idea of Rutherfordfrom 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 + e
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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 saturation
5) Nuclear forces are spin-dependent6) They do not obey a 1/r2law, 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
!0
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Yukawa potential
Mass of the virtual boson is roughly 200 MeV
Yukawa-Potential
V =g2emr
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
1
1H
197
79 Au
12
6 CExamples:
A = N+ Z
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Properties of nuclei
AZX
mass number
1
1H
197
79 Au
12
6 CExamples:
A = N+ Z
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Properties of nuclei
AZX
mass number
charge
1
1H
197
79 Au
12
6 CExamples:
A = N+ Z
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Properties of nuclei
AZX
mass number
charge
1
1H
197
79 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
17
8 O
17
7 N
17
9 F same A: isobars
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Table of Nuclides
17
8 O
17
7 N
17
9 F same A: isobars
13
6 C
12
6 C same Z: isotopes
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Table of Nuclides
17
8 O
17
7 N
17
9 F same A: isobars
13
6 C
12
6 C same Z: isotopes
13
6 C
14
7 N same N: isotones
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Table of Nuclides
17
8 O
17
7 N
17
9 F same A: isobars
13
6 C
12
6 C same Z: isotopes
13
6 C
14
7 N same N: isotones
3
1H
3
2He NZ: mirror nuclei
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Table of Nuclides
17
8 O
17
7 N
17
9 F same A: isobars
13
6 C
12
6 C same Z: isotopes
13
6 C
14
7 N same N: isotones
3
1H
3
2He NZ: mirror nuclei
180
73 T a
180m
73 T a same A and Z,
but different excitation: nuclear isomers
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Table of Nuclides
half-life of more than 1000 trillion years
17
8 O
17
7 N
17
9 F same A: isobars
13
6 C
12
6 C same Z: isotopes
13
6 C
14
7 N same N: isotones
3
1H
3
2He NZ: mirror nuclei
180
73 T a
180m
73 T a same A and Z,
but different excitation: nuclear isomers
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Decays
A
ZX
ZX Z+1X+ e
+ eA
ZX A
Z1X+ e+ + e
A
ZX+ e
A
Z1X+ eA
ZX A4
Z2X+ (42He)
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Decays
A
ZX
ZX Z+1X+ e
+ eA
ZX A
Z1X+ e+ + e
A
ZX+ e
A
Z1X+ eAZX
A4
Z2X+ (42He)
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Decays
A
ZX
ZX Z+1X+ e
+ eA
ZX A
Z1X+ e+ + e
A
ZX+ e
A
Z1X+ eAZX
A4
Z2X+ (42He)
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Decays
A
ZX
ZX Z+1X+ e
+ eA
ZX A
Z1X+ e+ + e
A
ZX+ e
A
Z1X+ eAZX
A4
Z2X+ (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
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Nuclear fission
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Nuclear fission
too much Coulombrepulsion
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Nuclear fission
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Nuclear fission
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Nuclear fission
too many neutrons
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Nuclear fission
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Nuclear fission
too much Coulombrepulsion
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Nuclear fission
D
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Decays
Derivationblackboard
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D
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Decays
A(t)/A1
(0)
t/!2
A1(t)
A2(t)
!1= 10 !2
t
2
A1(t)
1 = 102
A2(t)
A(t)
A1(0)
Bi di
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Binding energy
M(Z,N) = N mN+ Z Mp+ Z me EB
The binding energy is the energy set free when formingthe respective nuclei.
Bi di
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Binding energy
Binding energy
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Binding energy
Binding energy
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Binding energy
FissionFusion
Binding energy
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Binding energy
EB = aV AaS
A
23
aC
Z
2
A1
3asym
(N
Z)
2
A
A
1
2
aV A
SA2
3
aC Z2
A1
3
asym(N Z)2
A
A12
Volume term
Surface term
Coulomb term
Symmetry term
Pairing term
Binding energy
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Binding energy
EB = aV AaS
A
23
aC
Z
2
A1
3asym
(N
Z)
2
A
A
1
2
aV A
SA2
3
aC Z2
A1
3
asym(N Z)2
A
A1
2
Volume term
Surface term
Coulomb term
Symmetry term
Pairing term
Binding energy
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Binding energy
EB = aV AaS
A
23
aC
Z
2
A1
3asym
(N
Z)
2
A A
1
2
aV A
SA2
3
aC Z2
A1
3
asym(N Z)2
A
A1
2
Volume term
Surface term
Coulomb term
Symmetry term
Pairing term
Binding energy
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Binding energy
EB = aV AaS
A
23
aC
Z
2
A1
3asym
(N
Z)2
A A
1
2
aV A
SA2
3
aC Z2
A1
3
asym(N Z)2
A
A1
2
Volume term
Surface term
Coulomb term
Symmetry term
Pairing term
Binding energy
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Binding energy
EB = aV AaS
A
2
3
aC
Z
2
A1
3asym
(N
Z)2
A A
1
2
aV A
SA2
3
aC Z2
A1
3
asym(N Z)2
A
A1
2
Volume term
Surface term
Coulomb term
Symmetry term
Pairing term
Binding energy
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Binding energy
EB = aV AaS
A
2
3
aC
Z2
A1
3asym
(N Z
)2
A
A1
2
aV A
SA2
3
aC Z2
A1
3
asym(N Z)2
A
A1
2
Volume term
Surface term
Coulomb term
Symmetry term
Pairing term
Binding energy
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Binding energy
EB = aV AaS
A
2
3
aC
Z2
A1
3asym
(N Z
)2
A
A1
2
aV A
SA2
3
aC Z2
A1
3
asym(N Z)2
A
A1
2
Volume term
Surface term
Coulomb term
Symmetry term
Pairing term
Binding energy
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Binding energy
Volume Surface Coulomb
ParitySymmetry
Binding energy
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Binding energy
Volume Surface Coulomb
ParitySymmetry
Binding energy
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Binding energy
Volume Surface Coulomb
ParitySymmetry
Early Nuclear Models
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Early Nuclear Models
Nuclear abundance
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Nuclear abundance
Wait
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Wait...
Where do elementsbeyond iron come from?
FissionFusion
Universe
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Universe
Where do heavy elements come from?
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Where do heavy elements come from?
Some food for thought for the tutorials...