nuclear physics - 2 quantum, atomic and nuclear physics, year 2 university of portsmouth, 2012 -...
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Nuclear Physics - 2
Quantum, Atomic and Nuclear Physics, Year 2 University of Portsmouth, 2012 - 2013
Prof. Glenn Patrick
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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
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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
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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…
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History Supreme
History Supreme:• Gold & Platinum plated!• 100,000 kg.• Cost ~$4.5 billion.
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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
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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!
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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
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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
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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?
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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.
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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
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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.
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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
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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 )(
35
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.
39
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
40
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: [email protected]
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