Slides Vogel 1

8/13/2019 Slides Vogel 1

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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

[email protected]

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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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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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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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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AZX

mass number

1

1H

197

79 Au

12

6 CExamples:

A = N+ Z


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AZX

mass number

charge

1

1H

197

79 Au

12

6 CExamples:

A = N+ Z


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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


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


13

6 C

14


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


13

6 C

14


3

1H

3


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


13

6 C

14


3

1H

3


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


ParitySymmetry

Binding energy


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Binding energy


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...

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