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Lectures 1

Lectures 1. Introduction and Overview Nuclear sizes and isotope shifts. 1.0 Overview. 1.1 User guide to these lectures 1.2 Why study nuclear physics 1.3 Why nuclear physics is diff(eren)  (icul)t 1.4 Course synopsis 1.5 Notation & Units 1.6 Nuclear Masses and Sizes Mass measurements

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Lectures 1

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  1. Lectures 1 Introduction and Overview Nuclear sizes and isotope shifts Nuclear Physics Lectures, Dr. Armin Reichold

  2. 1.0 Overview • 1.1 User guide to these lectures • 1.2 Why study nuclear physics • 1.3 Why nuclear physics is diff(eren)(icul)t • 1.4 Course synopsis • 1.5 Notation & Units • 1.6 Nuclear Masses and Sizes • Mass measurements • Isotope Shifts Nuclear Physics Lectures, Dr. Armin Reichold

  3. 1.1 How to use these lectures • Definition of a classical lecture: • A lecture is 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. • Disadvantages: • obvious … • Conclusion: to make lectures useful YOU have to participate • annotate the notes: • notes are not a replacement for text book(s!). • Without your comments writtend during and after the lectures they are of very little use to all but the lecturer • take your own notes “As if you were never given these pages” • exception: might be good to write your notes onto the sides of these • ask questions: • If you don’t understand something the chances are >50% of the audience doesn’t either, so don’t be shy ! Nuclear Physics Lectures, Dr. Armin Reichold

  4. 1.1 Corrections • To err is human … and I am giving half of this course for the first time  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, Dr. Armin Reichold

  5. 1.2 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 to understand nucleosynthesis  experimental nuclear astrophysics is a “hot” topic. Nuclear Physics Lectures, Dr. Armin Reichold

  6. 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! Nuclear Physics Lectures, Dr. Armin Reichold

  7. 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. Nuclear Physics Lectures, Dr. Armin Reichold

  8. 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 (eg date As in hair). • Biology (eg elements in blood cells) • Archaeology (eg provenance via isotope ratios). Nuclear Physics Lectures, Dr. Armin Reichold

  9. 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 (HEP) •  coupling constant is small (asymptotic freedom) •  perturbation theory works • But it fails at large distances = O(size of proton) • coupling constant becomes big •  perturbation theory fails •  we don’t know how to solve the equations Boo ! Not on syllabus ! Nuclear Physics Lectures, Dr. Armin Reichold

  10. 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. Nuclear Physics Lectures, Dr. Armin Reichold

  11. 1.4 Overview of Lectures (I) • Introduction Fri. Week 1, Lindemann (L) • Why do we study Nuclear Physics • What will this course cover • Shape and density of the nuclei 2. The Semi Empirical Mass Formula (SEMF) Thu. Week 2, Martin Wood (MW) • The liquid drop model • The Fermi Gas Model • Experimental verification 3./4./5. Using the SEMF and transition to Shell Model Fri. (L) Week 2 & Thu. (MW), Fri (L) Week 3 • The valley of nuclear stability • Nuclear decays (a, b, fission, others) • Natural radioactivity • The end of SEMF: Evidence of magic numbers • The Shell Model Note: lectures in the Martin Wood lecture theatre starting 12:05 lectures in the Lindemann lecture theatre starting 14:05 Nuclear Physics Lectures, Dr. Armin Reichold

  12. 1.4 Overview of Lectures (II) 6./7. Crossections Thu. (MW), Frid (L) Week 4, • Experiments, natural units, conventions and definitions • Fermi’s Golden Rule • Rutherford Scattering • Breit-Wigner resonances and partial decay widths Note: No nuclear physics lectures in week 5 ! 8./9. Theory of Decays Thu. & Fri. Week 6, (MW) • Tunnelling model of a-decay • Selection rules and decay rates in g-decay • Fermi theory of b-decay Nuclear Physics Lectures, Dr. Armin Reichold

  13. 1.4 Overview of Lectures (III) 10./11. Particle Interactions with Matter Thu. & Fri. Week 7, (MW) • dE/dx by ionisation and the Bethe-Bloch formula (9) • Photoeffect, Compton Scattering, Bremsstrahlung, Pair Production • Cherenkov radiation 12./13. Applications of Nuclear Physics Thy. & Fri. Week 8, (MW) • Particle Detectors • Fission Reactors • Bombs • Fusion reactors • Radioactive dating (notes only) Nuclear Physics Lectures, Dr. Armin Reichold

  14. The Minister of Science • This is a true story honest. • Once upon a time the UK science minister visited the Rutherford Lab (UK national lab. near Didcot) and after a days visit of the lab was discussing his visit with the lab director and he said …<censored> • Your answer should at least have been as good as “air”! Nuclear Physics Lectures, Dr. Armin Reichold

  15. 1.5 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). Nuclear Physics Lectures, Dr. Armin Reichold

  16. 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 eV= 106 x e/[C] x 1J = 1.602 x 10-19 J • Mass: MeV/c2 (or GeV/c2) • 1 MeV/c2 = 106 xe/[C] / c2 x 1kg = 1.783 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] / c x kg • 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 Nuclear Physics Lectures, Dr. Armin Reichold

  17. 1.6 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 in atomic spectra Nuclear Physics Lectures, Dr. Armin Reichold

  18. 1.6 Nuclear Mass Measurements • Lets collect all the experimental facts first ! • 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) Nuclear Physics Lectures, Dr. Armin Reichold

  19. 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 Nuclear Physics Lectures, Dr. Armin Reichold

  20. Fe avg. binding Energy, B per nucleon [MeV] Mass Number A 1.6 Binding Energy per nucleon vs. A • Typical way of representing mass measurements • B increases with A up to 56Fe and then slowly decreases. • B is very small and not smooth at small A. • Why? • See SEMF and Shell Modell. Nuclear Physics Lectures, Dr. Armin Reichold

  21. 1.6 Nuclear Sizes and Isotope Shifts • Measure size of nucleus by the effect of its charge distribution on the energy levels of atomic electrons • Simple point like Coulomb field will be modified by finite size of nucleus. • This should be felt most by electrons close to the nucleus i.e. k-shell & L=0 • And should be negligible for electrons with minimal overlap with the nucleus, i.e. L>0 (Y~r L) •  study this assuming Hydrogenic ground state wave functions for the electrons • that’s justified even for large Z atoms since k-shell electron does not see much of “outer” electrons Nuclear Physics Lectures, Dr. Armin Reichold

  22. fraction of charge inside r usual 1/r2 factor 1.6 Nuclear Sizes & Isotope Shifts • Assume a uniform distribution of charge Ze in a spherical nucleus of radius R. • Calculate potential inside nucleus Vinside: • Einside via Gauss’s law: • Vinside by integrating Einside and applying boundary conditions at r=R to match Vinside to usual 1=r2 potential: • Difference between actual potential and Coulomb Nuclear Physics Lectures, Dr. Armin Reichold

  23. result of angle integration 1.6 Nuclear Sizes & Isotope Shifts • Use 1st order perturbation theory to calculate energy shift E: • Insert approximate Hydrogenic ground state wave function: Nuclear Physics Lectures, Dr. Armin Reichold

  24. 1.6 Nuclear Sizes & Isotope Shifts • Note: E is proportional to Z4 and R2 most noticeable effect deep inside large Z nuclei • a0 = 0.5 10-10 m Nuclear Physics Lectures, Dr. Armin Reichold

  25. 1.6 Isotope Shifts • Look at transitions from l=1 (no isotope shift) to l=0 (large isotope shift) • Preferably look for transitions at low n. • Types of isotope shifts in increasing shift order: • Isotope shift for optical spectra: E = O(meV) • Isotope shift for X-ray spectra (bigger effect then optical because electrons closer to nucleus): E = O(0.1 eV) • Isotope shift for X-ray spectra for muonic atoms. Effect greatly enhanced because mm~ 207 me and a0~1/m. E = O(keV) • All data consistent with R=R0 A1/3 using R0=1.25fm. Nuclear Physics Lectures, Dr. Armin Reichold

  26. Two lines for odd and even A! See SEMF pairing term later Note the invisibly small error bars 40 21 meV DE (meV) 0 A2/3 1.6 Isotope Shift in Optical Spectra • Need to use higher n wave functions to calculate this • Use Zeff≈ Z-n • expect (Zeff/Z)4 dependence in E • Why is E~A2/3 ? • … E~ R2 (see before) • and R=R0*A1/3 Energy shift of an optical transition in Hg at =253.7nm for different A relative to A=198. Data obtained by Doppler free laser spectroscopy. The effect is about 1 in 107. (Note the even/odd structure.) Bonn et al Z Phys A 276, 203 (1976)

  27. 1.6 Isotope Shift in X-Ray Spectra • Bigger shifts as expected • Again two lines ~ A2/3 0.5 DE (eV) 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) 0 A2/3 Nuclear Physics Lectures, Dr. Armin Reichold

  28. 58Fe 2keV 56Fe 54Fe Energy (keV) 1.6 Isotope Shift in muonic atoms • See dependence on Rnucl • Because a0 ~ 1/m the effect is ~0.4%, i.e. much larger than for an electron • Changing Rnucl by increasing A gives changes in isotope shifts of 2 keV Data on Isotope Shift of K Xrays from muonic atoms [in which a muon with m=207metakes the place of the atomic 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)

  29. 1.6 Isotope Shift Conclusions • All types of isotopes shifts show ~A2/3 as expected for an R2nucldependence • 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 Nuclear Physics Lectures, Dr. Armin Reichold

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