Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to...

Introduction to Nuclear and Particle Physics

Sascha VogelElena Bratkovskaya

Marcus Bleicher

Wednesday, 14:15-16:45FIAS Lecture Hall

Elena Bratkovskaya Marcus Bleicher

[email protected]@th.physik.uni-frankfurt.de

[email protected]

Lecturers

mailto:[email protected]






Thomas Lang Christoph Herold

[email protected]@th.physik.uni-frankfurt.de

Tutorials

Thursday, 12:00-14:00FIAS Lecture Hall





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

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”

Lecture 1

Units, scalesEarly nuclear models

Scales

Visible matter10-1 m

Crystal structures

10-9 m

Atoms 10-10 m

Nucleus10-14 m

Nucleon 10-15 m

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


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


common mass scales:

photon: mγ = 0 MeVneutrino: mν ~ 1 eVelectron: me = 0.511 MeVproton: mp = 938 MeV

Can we further simplify the unit system?


Natural units:

� = c = kB = 1

⇒ masses and lengths are the only units left and

[mass] = [energy] = [temperature] = 1 / [length]

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

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

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

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:

Historical remarks

Atomic nucleus discovered 1911 by

1882 - 19451871 - 1837 1889 - 1970

ErnestRutherford

HansGeiger

ErnestMarsden

Before...

Plum Pudding Model

Plum pudding model

++

+

+

++

+

++

+

+

positive charges uniformly distributed inside the whole atom

+electrons outside

Features: charge neutral extended in space

Rutherford experiment 1909-1911

Bombard nuclei (thin gold foil) with α particlesIdea: 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

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

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

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 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

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

Yukawa potential

Mass of the virtual boson is roughly 200 MeV

Yukawa-Potential

V = −g2e−mr

r

Also called “screened Coulomb potential”

Yukawa potential

Features: for r → ∞, V → 0 weakly attractive at low r repulsive core (blackboard)

Properties of nuclei

AZX

11H

19779 Au 12

6 CExamples:

A = N + Z


AZX

mass number

11H

19779 Au 12

6 CExamples:

A = N + Z


AZX

mass number

charge

11H

19779 Au 12

6 CExamples:

A = N + Z

Table of Nuclides

Table of Nuclides

isotone

Table of Nuclides

isotope

isotone

Table of Nuclides

Table of Nuclides

178 O

177 N 17

9 F• same A: isobars

Table of Nuclides

178 O

177 N 17


136 C12

6 C• same Z: isotopes

Table of Nuclides

178 O

177 N 17


136 C12


136 C14

7 N• same N: isotones

Table of Nuclides

178 O

177 N 17


136 C12


136 C14


31H

32He• N↔Z: mirror nuclei

Table of Nuclides

178 O

177 N 17


136 C12


136 C14


31H


18073 Ta 180m

73 Ta• same A and Z, but different excitation: nuclear isomers

Table of Nuclides

half-life of more than 1000 trillion years

178 O

177 N 17


136 C12


136 C14


31H


18073 Ta 180m

73 Ta• same A and Z, but different excitation: nuclear isomers

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)

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

too many neutrons

Nuclear fission

Nuclear fission

too much Coulomb repulsion

Nuclear fission

Decays

Derivation blackboard

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)

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.

Binding energy

Binding energy

FissionFusion

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

Binding energy

Volume Surface Coulomb

ParitySymmetry

Early Nuclear Models

Nuclear abundance

Wait...

Where do elements beyond iron come from?

FissionFusion

Universe

Where do heavy elements come from?

Some food for thought for the tutorials...

Introduction to Nuclear and Particle Physicssvogel/lecture_ws_2011_12/slides... · Introduction to...

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