1 / 29
Télécharger la présentation

Exploring Nuclear Physics: Overview and Applications

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 Thu. Week 1, Martin Wood (MW) • Why do we study Nuclear Physics • What will this course cover • Shape and density of the nuclei 2. The Semi Empirical Mass Formula (SEMF) Fri. Week 1, Lindemann (L) • The liquid drop model • The Fermi Gas Model • Experimental verification 3./4./5. Using the SEMF and transition to Shell Model Thu. (MW) & Fri. (L) Week 2 & Thu. Week 3, (MW) • 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 Fri. Week 3, (L) & Thu. Week 4, (MW) • 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 1V. • 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 lower 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 angel integration 1.6 Nuclear Sizes & Isotope Shifts • Use 1st order perturbation theory to calculate energy shift E: • Insert 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

More Related