Advanced nuclear physics (APHY 376)

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

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:

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.

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

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 LiStars: elements up to FeSupernova: 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 Nuclear fission

No greenhouse gasses but … Safety and storage of radioactive material.

Nuclear fusion Fewer safety issues (not a bomb) Less radioactive material but still some.

Nuclear transmutation of radioactive waste with neutrons. 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 Radiotherapy for cancer

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

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 Radioactive Dating

C14/C12 gives ages for dead plants/animals/people.

Rb/Sr gives age of earth as 4.5 Gyr. Element analysis

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?

We have QCD as an exact theory of strong interactions just solve the equations …

That’s fine at short distances << size of proton 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) coupling constant becomes big perturbation theory fails we don’t know how to solve the equations

1.3 Nuclear Physics (Super) Models

Progress with understanding nuclear physics from QCD=0

use simple, approximate, phenomenological models inspired by analogies to other system

Semi Empirical Mass Formula (SEMF) 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

spin, parity magnetic moments (not on syllabus) deviations from SEMF predictions for binding energy.

1.4 Notation Nuclei are labelled: e.g.

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).

ElAZ Li7

3

1.5 Units 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.

1 MeV= e/[C] x106 x 1 v = 1.602 x 10-19 M J Mass: MeV/c2 (or GeV/c2)

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:

mass of 12C= 12 u 1 u = 1.661 x 10-27 kg = 0.93 GeV/c2

Momentum: MeV/c (or GeV/c) 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) 1 barn = 10-28 m2 = 100 fm2

Note: C = Coulombc = speed of light

1.6 Nuclear Masses and Sizes Masses

Absolute values measured with mass spectrometers.

Relative values from reactions and decays. Nuclear Sizes

Measured with scattering experiments Isotope shifts in atomic spectra

1.6 Nuclear Mass Measurements

As we have studied in Special Relativity , we can Measure relative masses by energy released in decays or reactions. 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: 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

ion sourcevelocity selector

B

E

B

position se

nsitive

detector

momentumselector

Ion Source (e.g. strong laser takes out electrons) Velocity selector:

for electric and magnetic forces to be equal and opposite need

Momentum selector, circular orbit satisfies:

Measurement of x gives rcurv rcurv and v gives M

x=x(rcurv)

R

m

v

qB

R

vmBvq

2

Isomers are compounds with the same

molecular formula but different structural formulas Isomers do not necessarily share similar properties

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

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.

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.

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 Types of isotope shifts in increasing shift order:

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

A2/3

DE

(m

eV)

0

4021 meV

Two lines for odd and even A!See SEMF pairing term later

A2/3

DE

(eV

)

0.5

0

1.6 Isotope Shift in X-Ray Spectra

58Fe

56Fe

54Fe

Energy (keV)

1.6 Isotope Shift in muonic atoms

2keV

1.6 Isotope Shift Conclusions 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

This tells us that the nuclear density is a universal constant