1. Prof. Glenn Patrick Quantum, Atomic and Nuclear Physics, Year 2
This lecture…
Prof. Glenn Patrick
Quantum, Atomic and Nuclear Physics, Year 2
University of Portsmouth,

2. Last Week - Recap Notation 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

3. Today’s Plan 16 October Nuclear Physics 2 Abundance of elements/nuclei
Segre Chart
Zone of Stability
Stable Nuclei
Unstable Nuclei – Mass Parabola
Energy Valley, driplines
Super-heavy elements, Isle of Stability
Radioactivity - Alpha, Beta, Gamma Decays
Penetrating Power
Radioactive Decay Law
Multimodal Decays, Decay Chains
Radioactive Dating
Copies of Lectures:

4. Abundance of Elements in Earth’s Crust
Elements- On Earth
Abundance of Elements in Earth’s Crust
(atom fraction)
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
Present-day Solar System Composition
Lodders, Palme & Gail (2009)
arXiv: f
Hydrogen by far the most abundant element in Universe, followed by helium:
73% Hydrogen
26% Helium
1% Metals
(in astronomy a “metal” is anything other than H or He)

7. Care – this can be plotted with swapped axes in the text books!
Segre Chart
Care – this can be plotted with swapped axes in the text books!
Z=N
Proton rich
or too few neutrons
Protons Z
Stable nuclei
Only ~300 out of ~3100 nuclides
Neutron rich
Neutrons N

8. Zone of Stability Protons Z Neutrons N Neutron/proton ratio = 1
Nucleonica:
Only stable isotopes plotted
Protons Z
Neutron/proton ratio = 1
Zone of stability
Neutron/proton ratio = 2
Neutrons N

9. Stabile Nuclei
All 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 be
Bismuth 209, but this has been found to be slightly radioactive.
Now considered to be Lead 208, which has n/p = 1.54
is the most stable nucleus in Nature.
It has n/p=1.2, the maximum Binding Energy of 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.

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.

11. The Energy Valley Valley of stability Nuclei with lowest total energy
Nuclei 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.

12. Driplines Outside drip lines the
forces are no longer strong enough to hold nuclei together.
Unable to bind A nucleons as one nucleus

13. Artificial Elements
Elements heavier than Uranium 92 not found on Earth as decay time shorter than life of Earth. Have to be made artificially in accelerators.
GSI - Darmstadt
Only facility that accelerates ions of all chemical elements occurring on Earth.
Discovered: Bohrium (107)
Hassium (108)
Meitnerium (109)
Darmstadtium (110)
Roentgenium (111)
Copernicium (112)
SIS Synchrotron
Fragment Separator

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
Technetium
A=98, Z=43
Minute amounts in Nature
Predicted by Mendeleev.
Discovered by Segre & Perrier
- molybdenum in cyclotron.
Naming: 30 May 2012
flerovium (114)
livermorium (116)
Discovery: 2010
117 and 118
waiting to be named

16. Nobel Prize in Physics (1901)
First X-Rays
X-ray picture of the hand of his wife taken by Wilhelm Roentgen on 22 December 1895
The first
Nobel Prize in Physics (1901)
Roentgen’s X-ray demo using the hand of the anatomist Albert von Killiker - 23 January 1896

17. 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.

18. Alpha, Beta, Gamma Radiation
Ernest Rutherford studied radioactivity and found three different types of radiation: α, β and γ

19. (i.e. it contains 2 protons and 2 neutrons).
Alpha Decay
In 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, unstable
nucleus
Smaller, more stable
nucleus
Alpha particle
Radium example:
Energy = 4.8 MeV

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 A free neutron does decay. Mean life = 14.7 min.
But a free proton decay never been observed
to decay. Mean life > 2.1 x 1029 years!

22. Beta-Minus Decay Beta-Minus
No charge
Almost massless
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).
Really, this is all to do with the Weak Interaction and
quarks changing flavour! Particle physics….

23. Beta-plus decay usually occurs with nuclides which have N/Z too small.
Anti-particle of
the electron
Beta-Plus
No charge
Almost massless
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).

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

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

26. Gamma Decays
Many 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).

27. Gamma Rays and EM Spectrum
Electromagnetic radiation
with wavelength of ~10-12 m.

28. Penetrating Power Simple picture: 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.

29. Mean energy loss for protons
Heavy Particles
Mean energy loss for protons
Mainly ionisation and excitation of atoms.
Energy loss in single collision
Multiple collisions
with electrons & nuclei
Corrections

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

31. Photon cross-sections showing different contributions
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 N0/e
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.
Mean lifetime is inverse of decay constant
(time for nuclei to reduce by 2.718…)
N0/e
Half life is time for half
of nuclei to decay

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:
64%
36%
Solving for λ1 and λ2

34. Decay Chains 210Bi decaying
210Po increasing from 210Bi and also itself decaying.

35. Radioactive Dating

36. Cosmic rays produce 14C in the atmosphere by neutron capture:
Carbon Dating
Cosmic rays produce 14C in the atmosphere by neutron capture:
12C %
13C 1.11%
14C %
Radioactive. Half-life=5730 years
Organic matter absorbs CO2 from the atmosphere, but this stops when they die.
The 14C decays from its equilibrium ratio and measuring the proportion of 14C that remains gives the age of sample.

37. Carbon Dating
Activity is defined as number disintegrations per unit of time (e.g. dpm).
Specific activity is the amount of radioactivity per unit weight of material.
Specific activity standard for 14C is dpm/g or Bq/g (1950)
measured
known=5568y (Libby)
known
IAEA
Corrections due to assumptions
Not least the assumption of constant 14C content.

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)
If sample is large, can do simple counting, but background & time can be a problem. With low abundance/rare isotopes best to use AMS.
Strip electrons to make +ve ions
Accelerate to few MeV
Ion source converts to
-ve carbon ions
Measures 12C,13C & 14C atoms in sample.
Separated by atomic weights
Sample, burnt & CO2
converted to graphite.
In UK: Oxford University Radiocarbon Accelerator Unit
NERC Radiocarbon Laboratory, East Kilbride

40. 2.5 MV 14C Tandetron – Groningen (NL)

41. Turin Shroud 24 Mar 2012 26 September 1988 10 June 2012 Carbon Dating
Tucson 646±31 years old
Oxford 750±30 years old
Zurich 676±24 years old
MEAN 689±16 years old
(95% CL)
10 June 2012

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

43. End CONTACT Prof. G.N. Patrick Particle Physics Department
Rutherford Appleton Laboratory
Didcot, OX12 0QZ
Tel:

44. Heavy Particles Stopping power for positive muons on copper MeV/c
GeV/c
TeV/c
Stopping power for positive muons on copper
Mainly ionisation and excitation of atoms.