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

Nuclear sizes and isotope shifts 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 Nuclear fission Nuclear fusion 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 Medical Imaging 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 Element analysis 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).

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 = Coulomb c = speed of light

1.6 Nuclear Masses and Sizes 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)

position sensitive detector 1.6 Mass Spectrometer 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) position sensitive detector velocity selector ion source B E B momentum selector

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 Two lines for odd and even A! See SEMF pairing term later A2/3 DE (meV) 40 21 meV

1.6 Isotope Shift in X-Ray Spectra 0.5 DE (eV) A2/3

1.6 Isotope Shift in muonic atoms 58Fe 56Fe 54Fe Energy (keV) 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