Transcript LiCAS

Advanced nuclear
physics (APHY 376)
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Course Description
A study of the basic concepts for nuclear
physics, including nuclear sizes and isotope
shifts, the semi empirical mass formula, the
nuclear shell model, cross sections, particle
detectors
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Course Objectives
At the end of the course, students should
have developed a number of specific skills and
areas of knowledge that further the aims of
the course:
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To teach a variety of contemporary approaches to
Nuclear Physics and introduce the theory underlying
these approaches.
To learn some of the most interesting and important
Nuclear Physics.
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Course Items
Theoretical Aspect :
(Topics to be
Covered)
Chapter 1: Nuclear Mass and isotope
shifts
Chapter 2: The Semi Empirical Mass
Formula
Chapter 3: The nuclear shell model
Chapter 4: Cross Sections
Chapter 5: Particle Detectors
Chapter 6: Applications of Nuclear
Physics
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Learning Resources
Required Textbook(s) (maximum two).
1- W.S.C. Williams: Nuclear and Particle
Physics, Oxford Science Publications
2- W.M. Cottingham & D.A. Greenwood: An
Introduction to Nuclear Physics, Cambridge
University Press
Lectures 1
Nuclear sizes and isotope shifts
1.2 Why Study
Nuclear Physics?
1- Understand origin
of different nuclei
Big bang: H, He
and Li
Stars: elements
up to Fe
Supernova:
heavy elements
2- We are all made of stardust
3- Need to know nuclear cross sections to
understand nucleosynthesis  experimental
nuclear astrophysics is a “hot” topic.
1.2 Energy Applications
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Nuclear fission
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Nuclear fusion
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Fewer safety issues (not a bomb)
Less radioactive material but still some.
Nuclear transmutation of radioactive waste with
neutrons.
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No greenhouse gasses but …
Safety and storage of radioactive material.
Turn long lived isotopes into stable or short lived ones
Every physicist should have an informed opinion on
these important issues!
1.2 Medical Applications
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Radiotherapy for cancer
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Kill cancer cells.
Used for 100 years but can be improved by better delivery
and dosimetry
Heavy ion beams can give more localised energy
deposition.
Medical Imaging
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MRI (Magnetic Resonance Imaging) uses nuclear magnetic
resonances
X-rays (better detectors  lower doses)
PET (Positron Emission Tomography)
Many others…see Medical & Environmental short option.
1.2 Other Applications
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Radioactive Dating
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C14/C12 gives ages for dead plants/animals/people.
Rb/Sr gives age of earth as 4.5 Gyr.
Element analysis
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Forensic (e.g. date As in hair).
Biology (e.g. elements in blood cells)
Archaeology (e.g. provenance via isotope ratios).
1.3 Why is Nuclear Physics diff(eren)(icul)t?
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We have QCD as an exact theory of strong interactions  just solve
the equations …
That’s fine at short distances << size of proton
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i.e. at large momentum transfers = collisions with high CM energies >>
mproton
 coupling constant is small (asymptotic freedom)
 perturbation theory works
But it fails at large distances = (size of proton)
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coupling constant becomes big
 perturbation theory fails
 we don’t know how to solve the equations
1.3 Nuclear Physics (Super) Models
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Progress with understanding nuclear physics from QCD=0
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Semi Empirical Mass Formula (SEMF)
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 use simple, approximate, phenomenological models
inspired by analogies to other system
SEMF = Liquid Drop Model + Fermi Gas Model + phenomenology +
QM + EM.
Shell Model: look at quantum states of individual nucleons to
understand ground and low lying excited states
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spin, parity
magnetic moments (not on syllabus)
deviations from SEMF predictions for binding energy.
1.4 Notation
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Nuclei are labelled:
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e.g. 7
A
Z El
3 Li
El = chemical symbol of the element
Z = number of protons
N = number of neutrons
A = mass number = N + Z
Excited states labelled by * or m if they are
metastable (long lived).
1.5 Units
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SI units are fine for macroscopic objects like footballs
but are very inconvenient for nuclei and particles  use
appropriate units.
Energy: 1 MeV = kinetic energy gained by an electron in
being accelerated by 1MV.
Note: C = Coulomb
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1 MeV= e/[C] x106 x 1 v = 1.602 x 10-19 M J
Mass: MeV/c2 (or GeV/c2)
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1 MeV/c2 = e/[C] x106 x 1 v / c2 = 1.78 x 10-30 kg
Or use Atomic Mass Unit (AMU or u) defined by:
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mass of 12C= 12 u
1 u = 1.661 x 10-27 kg = 0.93 GeV/c2
Momentum: MeV/c (or GeV/c)
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c = speed of light
1 MeV/c = 106 x e/[C] x 1 v / c
Length: fermi 1 fm = 10-15 m
Cross sections: barn = as big as a barn door (to a
particle physicists)
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1 barn = 10-28 m2 = 100 fm2
1.6 Nuclear Masses and Sizes
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Masses
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Absolute values measured with mass
spectrometers.
Relative values from reactions and decays.
Nuclear Sizes
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Measured with scattering experiments
Isotope shifts in atomic spectra
1.6 Nuclear Mass Measurements
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As we have studied in Special Relativity , we can
Measure relative masses by energy released in
decays or reactions.
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X  Y +Z + DE
Mass difference between X and Y+Z is DE/c2.
Absolute masses measured by mass spectrometers
(next transparency).
Relation between Mass and Binding energy:
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B = [Z MH + N Mn – Matom(A,Z)] c2 or
B’ = [Z Mp + N Mn – Mnucleus(A,Z)]c2
(neglecting atomic binding energy of electrons)
1.6 Mass Spectrometer
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Ion Source (e.g. strong laser takes out electrons)
Velocity selector:
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for electric and magnetic forces to be equal and opposite need
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Momentum selector, circular orbit satisfies:
x=x(rcurv)
2
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v
qB
m
qv  B  m
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R
v
R
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Measurement of x gives rcurv
rcurv and v gives M ion source
velocity
selector
B
E
B
momentum
selector
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Isomers
are compounds with the same molecular
formula but different structural formulas
Isomers do not necessarily share similar
properties
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Isotopomers
are isomers with isotopic atoms, having the
same number of each isotope of each element
but differing in their positions. For example,
CH3CHDCH3 and CH3CH2CH2D are are
examples of isotopic stereoisomers of ethanol
and of propene, respectively
1.6 Isotope Shifts
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Isotope shifts are the small changes in
chemical shift observed between isotopomers
of a molecule. They are useful for structural
and bonding studies as well as spectral
assignment. The most commonly studied
substitution is that of proton (1H) with
deuterium (2D) although a wide range of
substitutions may be studied.
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Factors affecting the magnitude of isotope
shifts are the fractional change in mass of the
atom (greatest for hydrogen), the chemical
shift range and the distance or number of
bonds between the exchanged and observed
nuclei.
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There are two classes of isotope shifts:
Primary – the change in chemical shift of an
atom when its isotope is changed, for
example, the 1H chemical shift versus the 2D
chemical shift.
Secondary – the change in chemical shift of
an atom when the isotope of one of the
neighboring atoms is changed, for example,
the chemical shift difference between CH3OH
and CH3OD.
1.6 Isotope Shifts
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Types of isotope shifts in increasing shift order:
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Isotope shift for optical spectra
Isotope shift for X-ray spectra (bigger effect then optical
because electrons closer to nucleus)
Isotope shift for X-ray spectra for muonic atoms. Effect
greatly enhanced because mm~ 207
All data consistent with R=R0 A1/3 using R0=1.25fm.
1.6 Isotope Shift in Optical Spectra
Two lines for odd and even A!
See SEMF pairing term later
DE (meV)
40
21 meV
0
A2/3
1.6 Isotope Shift in X-Ray Spectra
DE (eV)
0.5
0
A2/
3
1.6 Isotope Shift in muonic atoms
58Fe
2keV
56Fe
54Fe
Energy (keV)
1.6 Isotope Shift Conclusions
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All types of isotopes shifts show ~A2/3 as
expected for an R2nucl dependence
This holds for all types of nuclei
When fitting the slopes we find the same R0 in
Rnucl=R0*A1/3
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This tells us that the nuclear density is a
universal constant