1. Nov 2006, Lecture 1 Nuclear Physics Lectures, Dr. Armin Reichold 1 Lectures 1 Introduction and Overview Nuclear sizes and isotope shifts

2. Nov 2006, Lecture 1Nuclear 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

3. Nov 2006, Lecture 1Nuclear 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 !

4. Nov 2006, Lecture 1Nuclear 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!).

5. Nov 2006, Lecture 1Nuclear 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.

6. Nov 2006, Lecture 1Nuclear 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!

7. Nov 2006, Lecture 1Nuclear 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.

8. Nov 2006, Lecture 1Nuclear Physics Lectures, Dr. Armin Reichold 8 1.2 Other Applications Radioactive Dating C 14 /C 12 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).

9. Nov 2006, Lecture 1Nuclear 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 >> m proton (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 Not on syllabus ! Boo !

10. Nov 2006, Lecture 1Nuclear 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.

11. Nov 2006, Lecture 1Nuclear Physics Lectures, Dr. Armin Reichold 11 1.4 Overview of Lectures (I) 1.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 ( , , 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

12. Nov 2006, Lecture 1Nuclear 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  -decay Selection rules and decay rates in  -decay Fermi theory of  -decay

13. Nov 2006, Lecture 1Nuclear 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)

14. Nov 2006, Lecture 1Nuclear 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 … Your answer should at least have been as good as “air”!

15. Nov 2006, Lecture 1Nuclear 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).

16. Nov 2006, Lecture 1Nuclear 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= 10 6 x e/[C] x 1 J = 1.602 x 10 -19 J Mass: MeV/c 2 (or GeV/c 2 ) 1 MeV/c 2 = 10 6 x e/[C] / c 2 x 1kg = 1.783 x 10 -30 kg Or use Atomic Mass Unit (AMU or u) defined by: mass of 12 C= 12 u 1 u = 1.661 x 10 -27 kg = 0.93 GeV/c 2 Momentum: MeV/c (or GeV/c) 1 MeV/c = 10 6 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 m 2 = 100 fm 2 Note: C = Coulomb c = speed of light

17. Nov 2006, Lecture 1Nuclear 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

18. Nov 2006, Lecture 1Nuclear 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 +  E Mass difference between X and Y+Z is  E/c 2. Absolute masses measured by mass spectrometers (next transparency). Relation between Mass and Binding energy: B = [Z M H + N M n – M atom (A,Z)]/c 2 or B’ = [Z M p + N M n – M nucleus (A,Z)]/c 2 (neglecting atomic binding energy of electrons)

19. Nov 2006, Lecture 1Nuclear Physics Lectures, Dr. Armin Reichold 19 1.6 Mass Spectrometer ion source velocity selector B E B position sensitive detector momentum selector 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 r curv r curv and v gives M x = x ( r curv )

20. Nov 2006, Lecture 1Nuclear Physics Lectures, Dr. Armin Reichold 20 1.6 Binding Energy per nucleon vs. A Typical way of representing mass measurements B increases with A up to 56 Fe and then slowly decreases. B is very small and not smooth at small A. Why? See SEMF and Shell Modell. avg. binding Energy, B per nucleon [MeV] Mass Number A Fe

21. Nov 2006, Lecture 1Nuclear 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 (  ~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

22. Nov 2006, Lecture 1Nuclear Physics Lectures, Dr. Armin Reichold 22 usual 1/r 2 factor fraction of charge inside r 1.6 Nuclear Sizes & Isotope Shifts Assume a uniform distribution of charge Ze in a spherical nucleus of radius R. Calculate potential inside nucleus V inside : E inside via Gauss’s law: V inside by integrating E inside and applying boundary conditions at r = R to match V inside to usual 1=r 2 potential: Difference between actual potential and Coulomb

23. Nov 2006, Lecture 1Nuclear Physics Lectures, Dr. Armin Reichold 23 1.6 Nuclear Sizes & Isotope Shifts Use 1 st order perturbation theory to calculate energy shift  E: result of angle integration Insert approximate Hydrogenic ground state wave function :

24. Nov 2006, Lecture 1Nuclear Physics Lectures, Dr. Armin Reichold 24 1.6 Nuclear Sizes & Isotope Shifts Note:  E is proportional to Z 4 and R 2  most noticeable effect deep inside large Z nuclei a 0 = 0.5 10 -10 m

25. Nov 2006, Lecture 1Nuclear 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(  eV) 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 m  ~ 207 m e and a 0 ~1/m.  E = O(keV) All data consistent with R=R 0 A 1/3 using R 0 =1.25fm.

26. Nov 2006, Lecture 1 26 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 10 7. (Note the even/odd structure.) Bonn et al Z Phys A 276, 203 (1976) 1.6 Isotope Shift in Optical Spectra Need to use higher n wave functions to calculate this Use Z eff ≈ Z-n expect (Z eff /Z) 4 dependence in  E Why is  E ~ A 2 / 3 ? …  E ~ R 2 (see before) and R = R 0 * A 1 / 3 A 2/3  E (  eV) 0 40 Note the invisibly small error bars 21  eV Two lines for odd and even A! See SEMF pairing term later

27. Nov 2006, Lecture 1Nuclear Physics Lectures, Dr. Armin Reichold 27 Data on the isotope shift of K X ray lines in Hg. The effect is about 1 in 10 6. Again the data show the R 2 = A 2/3 dependence and the even/odd effect. Lee et al, Phys Rev C 17, 1859 (1978) A 2/ 3  E (eV) 0.5 0 1.6 Isotope Shift in X-Ray Spectra Bigger shifts as expected Again two lines ~ A 2/3

28. Nov 2006, Lecture 1 28 Data on Isotope Shift of K Xrays from muonic atoms [in which a muon with m=207m e takes the place of the atomic electron]. The large peak is 2p 3/2 to 1s 1/2. The small peak is 2p 1/2 to 1s 1/2. The size comes from the 2j+1 statistical weight. Shera et al Phys Rev C 14, 731 (1976) 58 Fe 56 Fe 54 Fe Energy (keV) 1.6 Isotope Shift in muonic atoms See dependence on R nucl Because a 0 ~ 1/m the effect is ~0.4%, i.e. much larger than for an electron Changing R nucl by increasing A gives changes in isotope shifts of 2 keV 2keV

29. Nov 2006, Lecture 1Nuclear Physics Lectures, Dr. Armin Reichold 29 1.6 Isotope Shift Conclusions All types of isotopes shifts show ~A 2/3 as expected for an R 2 nucl dependence This holds for all types of nuclei When fitting the slopes we find the same R 0 in R nucl =R 0 *A 1/3 This tells us that the nuclear density is a universal constant