Today’s Menu

1. Today’s Menu • Why study nuclear physics • Why nuclear physics is difficult • Course synopsis and textbooks • Notation & Units Nuclear Physics Lectures

2. What is the use of lectures • Definition of a lecture: a process whereby notes are transferred from the pages of a lecturer to the pages of the student without passing through the head of either. Nuclear Physics Lectures

3. The use of lectures • Lectures provide: • best introduction to the subject. • guide to the main concepts, derivations and applications. • Enough material to start to tackle problems. • During a lecture you need to: • Add your comments to the notes (the notes are very terse and are only useful if you do this). • Ask questions if you do not understand something ( if you don’t understand something, chances are that >50% of the audience also doesn’t understand). • After a lecture you need to: • go over the notes, make sure you understand them and make your own notes. • Read material from textbook(s). • Do the problem sets. Nuclear Physics Lectures

4. Why Study Nuclear Physics? • Understand origin of different nuclei • Big bang: H, He and Li • Stars: elements up to Fe • Supernova: heavy elements • We are all made of stardust • Need to know nuclear cross sections  experimental nuclear astrophysics is a hot topic. Nuclear Physics Lectures

5. Practical Applications • Nuclear fission for energy generation. • No greenhouse gasses • Safety and storage of radioactive material. • Nuclear fusion • No safety issue (not a bomb) • Less radioactive material but still some. • Nuclear transmutation of radioactive waste with neutrons. • Turn long lived isotopes  stable or short lived. • Every physicist should have an informed opinion on these important issues! Nuclear Physics Lectures

6. Medical Applications • Radiotherapy for cancer • Kill cancer cells. • Used for 100 years but can be improved by better delivery and dosimetery • Heavy ion beams can give more localised energy deposition. • Medical Imaging • MRI (Nuclear magnetic resonance) • X-rays (better detectors  lower doses) • PET • Many others…see Medical & Environmental short option. Nuclear Physics Lectures

7. 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 • Forenesic (eg date As in hair). • Biology (eg elements in blood cells) • Archaeology (eg provenance via isotope ratios). Nuclear Physics Lectures

8. Nuclear Physics Lectures

9. Why is Nuclear Physics Hard? • QCD theory of strong interactions  just solve the equations … • At short distance/large Q coupling constant small  perturbation theory ok but long distance/small Q, q  large Not on syllabus ! Nuclear Physics Lectures

10. Nuclear Physics Models • Progress with understanding nuclear physics from QCD=0  use simple, approximate, phenomenological models. • Liquid Drop Model: phenomenology + QM + EM. • Shell Model: look at quantum states of individual nucleons  understand spin/parity magnetic moments and deviations from SEMF for binding energy. Nuclear Physics Lectures

11. Corrections • To err is human … and this is a new course  lots of mistakes. • Please tell me about any mistakes you find in the notes (I will donate a bottle of wine to the person who finds the most mistakes!). Nuclear Physics Lectures

12. The Minister of Science • This is a true story honest. • Once upon a time the government science minister visited the Rutherford Lab (UK national lab) and after a days visit of the lab was discussing his visit with the lab director and he said … • I hope that you all have a slightly better grasp of the subject by the end! Nuclear Physics Lectures

13. Course Synopsis - 1 • Nuclear sizes and liquid drop model, S.E.M.F. Applications of S.E.M.F. • Williams, Nuclear & Particle Physics, OUP, chapters 4 & 5. • Krane, Introductory Nuclear Physics, Wiley, chapters 3, 8 & 9. • Cross sections and Breit Wigner Resonances • Cottingham & Greenwood, An Introduction to Nuclear Physics, CUP, chapter 8 and appendices A & D. • Radioactive decays • Alpha decay, Williams, chapter 6, Krane, chapter 8 • Beta decay, Williams, chapter 12, Krane chapter 9 Nuclear Physics Lectures

14. Course Synopsis - 2 • Interactions of particles with matter • Textbook ??? • Applications of Nuclear Physics • Particle detectors, textbook ? • Fission reactors and bombs, Krane chapter 13 • Fusion reactors, Krane, chapter 14. • Radioactive dating, Krane, chapter 6. Nuclear Physics Lectures

15. Notation • Nuclei are labelled where El is the chemical symbol of the element, mass number A = number of neutrons N + number of protons Z. eg • Excited states labelled by * or m if they are metastable (long lived). Nuclear Physics Lectures

16. Units • SI units are fine for macroscopic objects like footballs but are very inconvenient for nuclei and particles  use natural units. • Energy: 1 eV = energy gained by electron in being accelerated by 1V. • 1 eV= e J. • Mass: MeV/c2 (or GeV/c2) • 1 eV/c2 = e/c2 kg. • Or use AMU defined by mass of 12C= 12 u • Momentum: MeV/c (or GeV/c) • 1 eV/c = e/c kg m s-1 • Cross sections: (as big as a barn door) • 1 barn =10-28 m2 • Length: fermi 1 fm = 10-15 m. Nuclear Physics Lectures

17. Nuclear Masses and Sizes • Masses and binding energies • Absolute values measured with mass spectrometers. • Relative values from reactions and decays. • Nuclear Sizes • Measured with scattering experiments (leave discussion until after we have looked at Rutherford scattering). • Isotope shifts Nuclear Physics Lectures

18. Nuclear Mass Measurements • 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 mass by mass spectrometers (next transparency). • Mass and Binding energy: • B = [Z MH + N Mn – M(A,Z)]/c2 Nuclear Physics Lectures

19. Mass Spectrometer • Ion Source • Velocity selector  electric and magnetic forces equal and opposite • qE=qvB  v=E/B • Momentum selector, circular orbit satisfies: • Mv=qBr • Measurement r gives M. Detector Velocity selector Ion Source Nuclear Physics Lectures

20. Binding Energy vs A • B increases with A up to 56Fe and then slowly decreases. Why? • Lower values and not smooth at small A. Nuclear Physics Lectures

21. Nuclear Sizes & Isotope Shift • Coulomb field modified by finite size of nucleus. • Assume a uniform charge distribution in the nucleus. Gauss’s law  integrate and apply boundary conditions • Difference between actual potential and Coulomb • Use 1st order perturbation theory Nuclear Physics Lectures

22. Isotope Shifts Nuclear Physics Lectures

23. Isotope Shifts • Isotope shift for optical spectra • Isotope shift for X-ray spectra (bigger effect because electrons closer to nucleus) • Isotope shift for X-ray spectra for muonic atoms. Effect greatly enhanced because mm~ 207 me and a0~1/m. • All data consistent with R=R0 A1/3 with R0=1.25fm. Nuclear Physics Lectures

24. Isotope Shift in Optical Spectra Frequency shift of an optical transition in Hg at =253.7nm for different A relative to A=198. Data obtained by laser spectroscopy. The effect is about 1 in 107. (Note the even/odd structure.) Bonn et al Z Phys A 276, 203 (1976) DE/h (GHz) A2/3 Nuclear Physics Lectures

25. Data on the isotope shift of K X ray lines in Hg. The effect is about 1 in 106. Again the data show the R2 = A2/3dependence and the even/odd effect. Lee et al, Phys Rev C 17, 1859 (1978) Nuclear Physics Lectures

26. 58Fe Data on Isotope Shift of K Xrays from muonic atoms [in which a muon with m=207metakes the place of the atomic electron]. Because a0 ~ 1/m the effect is ~0.4%, much larger than for an electron. The large peak is 2p3/2 to 1s1/2. The small peak is 2p1/2 to 1s1/2. The size comes from the 2j+1 statistical weight. Shera et al Phys Rev C 14, 731 (1976) 56Fe 54Fe Energy (keV) Nuclear Physics Lectures

27. SEMF • Aim: phenomenological understanding of nuclear binding energies as function of A & Z. • Nuclear density constant (see lecture 1). • Model effect of short range attraction due to strong interaction by liquid drop model. • Coulomb corrections. • Fermi gas model  asymmetry term. • QM pairing term. • Compare with experiment: success & failure! Nuclear Physics Lectures

28. Liquid Drop Model Nucleus • Phenomenological model to understand binding energies. • Consider a liquid drop • Ignore gravity and assume no rotation • Intermolecular force repulsive at short distances, attractive at intermediate distances and negligible at large distances  constant density. E=-an + 4pR2T B=an-bn2/3 • Analogy with nucleus • Nucleus has constant density • From nucleon nucleon scattering experiments: Nuclear force has short range repulsion and attractive at intermediate distances. • Assume charge independence of nuclear force, neutrons and protons have same strong interactions check with experiment! Nuclear Physics Lectures

29. Mirror Nuclei • Compare binding energies of mirror nuclei (nuclei n p). Eg 73Li and 74Be. • Mass difference due to n/p mass and Coulomb energy. Nuclear Physics Lectures

30. nn and pp interaction same (apart from Coulomb) “Charge symmetry” Nuclear Physics Lectures

31. Charge Symmetry and Charge Independence • Mirror nuclei showed that strong interaction is the same for nn and pp. • What about np ? • Compare energy levels in “triplets” with same A, different number of n and p. e.g. • Same energy levels for the same spin states  SI same for np as nn and pp. Nuclear Physics Lectures

32. Charge Independence 2311Na 2312 Mg • Is np force is same as nn and pp? • Compare energy levels in nuclei with same A. • Same spin/parity states have same energy. • np=nn=pp 2212Mg 2210Ne 2211Na Nuclear Physics Lectures

33. Charge Independence of Strong Interaction • If we correct for n/p mass difference and Coulomb interaction, then energy levels same under n p. • Conclusion: strong interaction same for pp, pn and nn if nucleons are in the same quantum state. • Beware of Pauli exclusion principle! eg why do we have bound state of pn but not pp or nn? Nuclear Physics Lectures

34. IllustrationNeutron and proton states with same spacing .Crosses represent initially occupied states in ground state.If three protons were turned into neutrons the extra energy required would be 3×3 .In general if there are Z-N excess protons over neutrons the extra energy is ((Z-N)/2)2 . relative to Z=N. AsymmetryTerm • Neutrons and protons are spin ½ fermions  obey Pauli exclusion principle. • If other factors were equal  ground state would have equal numbers of n & p. Nuclear Physics Lectures

35. Asymmetry Term • From stat. mech. density of states in 6d phase space = 1/h3 • Integrate to get total number of protons Z, & Fermi Energy (all states filled up to this energy level). • Change variables p  E Nuclear Physics Lectures

36. Asymmetry Term • Binomial expansion keep lowest term in y/A • Correct functional form but too small by factor of 2. Why? Nuclear Physics Lectures

37. Pairing Term • Nuclei with even number of n or even number of p more tightly bound fig. • Only 4 stable o-o nuclei cf 153 e-e. • p and n have different energy levels  small overlap of wave functions. Two p(n) in same level with opposite values of jz have AS spin state  sym spatial w.f. maximum overlap maximum binding energy because of short range attraction. Neutron separation energy in Ba Neutron number Nuclear Physics Lectures

38. Pairing Term • Phenomenological fit to A dependence • Effect smaller for larger A Nuclear Physics Lectures

39. Semi Empirical Mass Formula • Put everything together: • Fit to measured binding energy. • Fit not too bad (good to <1%). • Deviations are interesting  shell effects. • Coulomb term agrees with calculation. • Asymmetry term larger ? • Explain valley of stability. • Explains energetics of radioactive decays, fission and fusion. Nuclear Physics Lectures

40. The Binding Energy per nucleon of beta-stable (odd A) nuclei. Fit values in MeV 9.0 B/A (MeV) 7.5 Nuclear Physics Lectures A

41. Valley of Stability • SEMF allows us to understand valley of stability. • Low Z, asymmetry term  Z=N • Higher Z, Coulomb term  N>Z. Nuclear Physics Lectures