Nuclear Physics - 2

Quantum, Atomic and Nuclear Physics, Year 2 University of Portsmouth, 2012 - 2013

Prof. Glenn Patrick

2

Last Week - RecapNotation units

Electron-nucleon scattering

Nuclear Size

Nuclear Binding Energy

Macroscopic description: Liquid Drop Model

Magic Nuclei: Z or N = 2, 8, 20, 28, 50, 82, 126

Spin, magnetic moments and NMR (MRI)

Microscopic description: Shell Model

Nuclear Structure

31

0 ARR 2)( cMNmZME A

ZnHb

XAZ

2)(qF

d

d

d

d

Mott

fmR 2.10

3

Today’s Plan16 October Nuclear Physics 2

Abundance of elements/nucleiSegre ChartZone of StabilityStable NucleiUnstable Nuclei – Mass ParabolaEnergy Valley, driplinesSuper-heavy elements, Isle of StabilityRadioactivity - Alpha, Beta, Gamma DecaysPenetrating PowerRadioactive Decay LawMultimodal Decays, Decay ChainsRadioactive Dating

Copies of Lectures: http://hepwww.rl.ac.uk/gpatrick/portsmouth/courses.htm

4

Elements- On EarthAbundance of Elements in Earth’s Crust

(atom fraction)

http://pubs.usgs.gov/fs/2002/fs087-02/

We normally make ships out of iron and jewellery

out of gold for a very good reason.

Although there are always exceptions…

5

History Supreme

History Supreme:• Gold & Platinum plated!• 100,000 kg.• Cost ~$4.5 billion.

6

Elements - In the Cosmos

Hydrogen by far the most abundant element in Universe, followed by helium:

73% Hydrogen26% Helium

1% Metals(in astronomy a “metal” is anything other than H or He)

Lodders, Palme & Gail (2009)arXiv: 0901.1149f

Present-day Solar System Composition

7

Segre Chart

Neutrons N

Pro

ton

s Z

Z=N

Stable nucleiOnly ~300 out of ~3100

nuclidesNeutron rich

Proton richor too few neutrons

Care – this can be plotted with swapped

axes in the text books!

8

Zone of Stability

Neutron/proton ratio = 2Neu

tron/p

roto

n ratio

= 1

Zone of stabilit

y

Nucleonica:Only stable isotopes plotted Pb208

82

Neutrons N

Pro

ton

s Z

Ni6228

9

Stabile NucleiAll stable nuclei lie within a definite zone of stability.

For low Z, most stable nuclei have a neutron/proton ratio of ~1.

As Z increases, the zone of stability corresponds to a gradually increasing n/p ratio.

More neutrons needed to counter Coulomb repulsion of protons.

The heaviest stable isotope was once thought to beBismuth 209, but this has been found to be slightly radioactive.

Now considered to be Lead 208, which has n/p = 1.54

Bi20983

Pb20882

is the most stable nucleus in Nature.

It has n/p=1.2, the maximum Binding Energy of 8.7946 MeV/nucleon and it’s magic!

Abundance = 3.6%

Followed by 58Fe and 56Fe. Iron makes up most of the Earth’s core due to its stability.

Ni6228

10

Unstable Nuclei – Mass Parabola

Unstable nuclei have the wrong proportion of protons and neutrons.

The wrong balance of protons & neutrons gives these nuclei too much energy.

They correct this by decaying to another nucleus with the same A and with some energy carried away by the decay products.

It is a bit like a boulder rolling down a hill.

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The Energy ValleyValley of stability

Nuclei with lowest total energyNuclei up the sides of the valley are unstable and

will decay until they reach the bottom.

In general, the higher up the valley side, the

shorter the lifetime.

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Driplines

Outside drip lines theforces are no longer

strong enough to hold nuclei together.

Unable to bind A nucleons as one nucleus

13

Artificial Elements

GSI - DarmstadtOnly facility that accelerates ions

of all chemical elements occurring on Earth.

Discovered: Bohrium (107) Hassium (108) Meitnerium (109) Darmstadtium (110) Roentgenium (111) Copernicium (112)

Fragment Separator

Elements heavier than Uranium 92 not found on Earth as decay time shorter than life of Earth. Have to be made artificially in accelerators.

SIS Synchrotron

14

Isle of Stability“Expedition” to find a predicted “island” of super-heavy elements:

a region of increasingly stable nuclei around Z~114 amongst short-lived artificial elements.

Due to shell effects : new magic number of Z = 114? 120? 126?…Long lifetimes of minutes or days or years?

15

Periodic Table (June 2012)

International Union of Pure and Applied Chemistry

Naming: 30 May 2012flerovium (114)

livermorium (116)

Discovery: 2010117 and 118

waiting to be named

TechnetiumA=98, Z=43

Minute amounts in NaturePredicted by Mendeleev.

Discovered by Segre & Perrier- molybdenum in cyclotron.

16

First X-Rays

Roentgen’s X-ray demo using the hand of the anatomist Albert von Killiker - 23 January 1896

X-ray picture of the hand of his wife taken by Wilhelm Roentgen on 22 December 1895

The first Nobel Prize in

Physics (1901)

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Followed by Discovery of Radioactivity

Henri Becquerel was studying the properties of X-rays using

uranium salts.

He found that nearby photographic plates became “fogged”. This radiation was

bent by a magnetic field, so not due to X-rays.

After processing tons of uranium ore, Marie & Pierre Curie

discovered Radium & Polonium.

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Alpha, Beta, Gamma RadiationErnest Rutherford studied radioactivity and found three

different types of radiation: α, β and γ

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Alpha DecayIn the early 20th century, Rutherford et al proved that the alpha particle is the positively charged nucleus of 4He

(i.e. it contains 2 protons and 2 neutrons).

Large, unstablenucleus

Smaller, more stablenucleus

Alpha particle

HeRaRa 42

22286

22688 Radium example:

Energy = 4.8 MeV

)2,2,4(),,( NZANZA

20

Alpha Decay - Quantum Tunnelling decay of radioactive nuclei such as uranium is an example of tunnelling.

First proposed by George Gamow in 1928.

The particle is held inside the nucleus by strong short-range nuclear forces. Outside of the nucleus, the repulsive EM force dominates.

21

Beta Decay

epn

enp A free neutron does decay. Mean life = 14.7 min.

But a free proton decay never been observedto decay. Mean life > 2.1 x 1029 years!

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Beta-Minus Decay

Beta-Minus

eNC e01

147

146

No chargeAlmost massless

e

Really, this is all to do with the Weak Interaction andquarks changing flavour! Particle physics….

Beta-minus decay usually occurs with nuclides which have N/Z too large.

In the decay, N decreases by 1 and Z increases by 1 (A does not change).

133.1 Z

N

Z

NeeNZANZA )1,1,(),,(

epn

23

Beta-Plus Decay

eBC e01

105

106

No chargeAlmost massless

Anti-particle of the electron

eBeta-Plus

Beta-plus decay usually occurs with nuclides which have N/Z too small.

In the decay, N increases by 1 and Z decreases by 1 (A does not change).

167.0 Z

N

Z

NeeNZANZA )1,1,(),,(

enp

24

Beta Decay – 3 Body Process

Electron (or positron) has a distribution of energies

Means it is a 3 body process rather than 2-body.

Evidence for existence of the neutrino

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Electron Captureβ+ decay not always energetically possible (after all a proton weighs less than a neutron) . Orbital electron (usually from K shell) can provide necessary energy.

enp

Electron Capture

eBeC 115

01

116

eNZAeNZA )1,1,(),,( 2.183.0 Z

N

Z

N

26

Gamma DecaysMany alpha and beta decays leave daughter nucleus in an excited state.

Often decay to ground state by gamma emission

High energy photon(s) emitted (keV – MeV).

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Gamma Rays and EM Spectrum

Electromagnetic radiation with wavelength of ~10-12 m.

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Penetrating Power

Paper Aluminium Lead

The different penetrating powers are due to the different processes by which heavy particles (like alphas), electrons and photons lose energy.

This is a field in itself and the following three slides are just for illustration – just to give you an idea.

Simple picture:

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Heavy ParticlesMean energy loss for

protons

Mainly ionisation and excitation of atoms.

22

22

22

22

0

2

)1ln(2

ln4

4

I

cm

A

ZN

cm

ze

dx

dE eA

e

Energy loss in single collision

Multiple collisionswith electrons & nuclei

Corrections

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Electrons/Positrons

Fractional energy loss in lead as a function of electron energy.Messel & Crawford, 1970

31

Photons

Photon cross-sections showing different contributions (Atomic Photoelectric Effect, Rayleigh Scattering, Compton Scattering, Pair

Production off nuclear and electron fields and Photonuclear Reactions).

32

Radioactive Decay Law

NdtdN

Decays are statistical – cannot predict when any particular nucleon will decay.

For N nuclei present at time t, the number dN decaying in time dt is proportional to N.

NdtdN dtN

dN

tN

N

dtN

dNt

00

tN

N t

0

ln teNtN 0)(

1

Mean lifetime is inverse of decay constant(time for nuclei to reduce by 2.718…)

2ln

2/1 tHalf life is time for half of nuclei to decay

6932.0

2/1 t

N0/e

33

Multimodal Decays• Unstable nuclei can often decay via more than one mode (i.e. separate

alpha and beta decays).

• Each decay mode is random and independent of the other decay modes.

• Each mode has it’s own transition probability (i.e. own λ).

For example, Bismuth 212 can decay to both Polonium(Po) and Titanium(Ti) with a total mean lifetime of 536 secs:

eePoBi 21284

21283 64%

TiBi 20881

21283 36%

dtdtN

dN21

teNtN )(0

21)(

21 constant decay Total 1-321 10 x 1.87536

11 s

36

64

2

1

sec10 x 6.72 -42

sec10 x 19.1 -31 Solving for λ1 and λ2

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Decay Chains5days τhas Bi: 1 Nucleus 1/2

21083

days 138 τhas Po: 2 Nucleus 1/2210

84

dtNdN 111 210Bi decaying

dtNdtNdN 22112 210Po increasing from 210Bi and also itself decaying.

PbNo 00

PoNo 00

BiPure )0(

2063

2102

21001

)(tN

)(tN

NtN

tt eeNtN 21

12

102 )(

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Radioactive Dating

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Carbon Dating

pCnN 1414

Cosmic rays produce 14C in the atmosphere by neutron capture:

Organic matter absorbs CO2 from the atmosphere, but this stops when they die.

12C 98.89%13C 1.11%14C 0.0000000001%

Radioactive. Half-life=5730 years

eNC e01

147

146

The 14C decays from its equilibrium ratio and measuring the proportion of 14C that

remains gives the age of sample.

37

Carbon Dating

Specific activity is the amount of radioactivity per unit weight of material.Specific activity standard for 14C is 13.56 dpm/g or 0.226 Bq/g (1950)

λNdt

dN -A Activity

Activity is defined as number disintegrations per unit of time (e.g. dpm).

teAtA 0)(

IAEA

0

2/1 ln2ln

death since TimeA

AtT

known=5568y (Libby) measured

known

Corrections due to assumptions

Not least the assumption of constant 14C content.

refsample AAT ln8033

38

Origin and Distribution of 14C

Complications:Addition to the air of CO2 by fossil fuels (without 14C)

Production of 14C by neutrons released by fission/fusion.

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Accelerator Mass Spectrometry (AMS)

In UK: Oxford University Radiocarbon Accelerator Unit NERC Radiocarbon Laboratory, East Kilbride

If sample is large, can do simple counting, but background & time can be a problem. With low abundance/rare isotopes best to use AMS.

Sample, burnt & CO2

converted to graphite.

Measures 12C,13C & 14C atoms in sample.

Separated by atomic weights

Ion source converts to -ve carbon

ions

Accelerate to few MeV

Strip electrons to make +ve

ions

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2.5 MV 14C Tandetron – Groningen (NL)

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Turin Shroud24 Mar 2012

10 June 2012 26 September 1988Carbon Dating

Tucson 646±31 years oldOxford 750±30 years oldZurich 676±24 years oldMEAN 689±16 years old

1262-1384 (95% CL)

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You should now be able to do your Lab Classes even better!

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CONTACTProf. G.N. PatrickParticle Physics DepartmentRutherford Appleton LaboratoryDidcot, OX12 0QZTel: 01235 445343

email: glenn.patrick@stfc.ac.uk

End

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Heavy Particles

MeV/c GeV/c TeV/c

Stopping power for positive muons on copperMainly ionisation and excitation of atoms.

22

22

22

22

0

2

)1ln(2

ln4

4

I

cm

A

ZN

cm

ze

dx

dE eA

e