1. 1 Nuclear Physics and Electron Scattering

2. 2 Four forces in nature –Gravity –Electromagnetic –Weak –Strong  Responsible for binding protons and neutrons together to make nuclei, holds together quarks that make protons and neutrons Why study the strong force? –The nucleus makes up 99.9% of the mass of the atoms around you –Nuclear reactions crucial to understanding how the universe was formed –Because it’s hard! The underlying theory is simple, but it’s difficult to understand how we get from that theory to real protons, neutrons, nuclei “Nuclear” Physics = Strong Force

3. 3 Scope of Nuclear Physics Topics that fall under the umbrella of the label “nuclear physics” depends to some degree on where you are In the United States, includes –Nuclear structure (how protons and neutrons combine to make atomic nucleus)

4. 4 Scope of Nuclear Physics Nuclear structure (how protons and neutrons combine to make atomic nucleus) Exploration of “stable” nuclei – study highly excited states to understand nuclear structure http://fribusers.org/2_INFO/2_crucial.html

5. 5 Scope of Nuclear Physics Nuclear structure (how protons and neutrons combine to make atomic nucleus) Exploration of “stable” nuclei – study highly excited states to understand nuclear structure  Expand the study to highly unstable nuclei to understand the limits of nuclear matter http://fribusers.org/2_INFO/2_crucial.html

6. 6 Scope of Nuclear Physics Topics that fall under the umbrella of the label “nuclear physics” depends to some degree on where you are In the United States, includes: –Nuclear structure (how protons and neutrons combine to make atomic nucleus) –Relativistic heavy ions – smashing together heavy nuclei at high energies to explore new states of strongly interacting matter

7. 7 Scope of Nuclear Physics Relativistic heavy ions – smashing together heavy nuclei at high energies to explore new states of strongly interacting matter Ions about to collideIon collisionQuarks gluons freed Plasma created http://www.bnl.gov/rhic/physics.asp at the beginning of the universe there were no protons and neutrons, only free quarks and gluons

8. 8 Scope of Nuclear Physics Topics that fall under the umbrella of the label “nuclear physics” depends to some degree on where you are In the United States, includes: –Nuclear structure (how protons and neutrons combine to make atomic nucleus) –Relativistic heavy ions – smashing together heavy nuclei at high energies to explore new states of strongly interacting matter –Quantum Chromodynamics  how quarks and gluons interact to form protons and neutrons and eventually nuclei –Symmetry tests  searches for physics beyond the Standard Model

9. 9 Electron Scattering and Nuclear Physics e- Electron scattering is a powerful tool for studying the physics of nuclei and nucleons  The electromagnetic interaction is very well described by Quantum electrodynamics (QED) – the probe is understood  The electromagnetic coupling is weak (  =1/137) - electrons probe the whole volume without bias Electron scattering can be used to study 1.Nuclear structure 2.Nuclei at large (local) density 3.Quantum chromodynamics Jefferson Lab was constructed to be a state of the art, electron scattering facility

10. 10 Jefferson Lab Accelerator 2 cold superconducting linacs E e up to 6 GeV Continuous polarized electron beam (P=85%) Jefferson Lab is the site of an electron scattering facility in Newport News, Virginia (USA) 3 Experimental Halls with complementary capabilities

11. 11 Experimental Hall A 2 High Resolution Spectrometers  Good for clean ID of hard to see final states

12. 12 Experimental Hall B CEBAF Large Acceptance Spectrometer (CLAS) Detects particles emitted in all directions simultaneously  Good for measurements of reactions with complicated final states

13. 13 Experimental Hall C Short Orbit SpectrometerHigh Momentum Spectrometer High accuracy measurements of absolute probabilities for processes

14. 14 A Generic Electron Scattering Experiment Target Electron beam Detector

15. 15 A Generic Electron Scattering Experiment Target Electron beam Detector

16. 16 What we measure In the “simplest” experiments, we measure the probability for an electron to scatter in a particular direction with a specific momentum In more complicated experiments, we measure the above, in combination with the probability to produce another particle –The relative (and absolute) probabilities for different processes can tell us about the structure of the nucleus (or proton/neutron) we are probing The common analogy is that it’s like trying to learn how a watch is made by throwing it against the wall and looking at the pieces!

17. 17 Tools of the Trade: Magnetic Spectrometers Magnets focus and bend charged particles into our detectors Dipole: acts like a prism, separates particles with different momenta Quadrupoles: act like lenses, focusing particles

18. 18 Tools of the Trade: Detectors Detectors after spectrometer magnets:  Track charged particles to determine momentum and direction  Determine particle species  Measure time of arrival of particle in spectrometer

19. 19 Jefferson Lab’s Original Mission Statement Key Mission and Principal Focus (1987): –The study of the largely unexplored transition between the nucleon-meson and the quark- gluon descriptions of nuclear matter. The Role of Quarks in Nuclear Physics We can describe nuclei, for the most part just using protons, neutrons, and other exchange particles: does there come a point at which we must describe in terms of quarks and gluons? –If not, why not?

20. 20 Related Topics Do individual nucleons change their size, shape, and quark structure in the nuclear medium? How do quarks and gluons come together to determine the structure of the proton? –What is the distribution of charge and magnetism in the nucleon? –How is the spin of the proton built up from quarks and gluons? What are the properties of the strong force (“QCD”) in the regime where quarks are confined?

21. 21 Electron Scattering Basics Cross section: Target Electron beam Detector with solid angle 

22. 22 Electron Scattering Basics Cross section: Target Electron beam Detector with solid angle  Luminosity

23. 23 Incident Electron beam  ee Scattered electron Fixed target with mass M Electron Scattering kinematics Virtual photon kinematics  m e = 0

24. 24 Z Coulomb Scattering Cross section for electron scattering from a fixed Coulomb potential  ee Mott Cross Section

25. 25 Electron Muon Scattering Cross section for electron scattering from a spin ½ particle with no structure  ee Muon

26. 26 Electron Nucleon Scattering Cross section for electron scattering from a spin ½ particle with some (quark) structure  ee Nucleon F 1 and F 2 describe the internal structure of the nucleon - commonly written, Distribution of charge and magnetization in the nucleon

27. 27 (inelastic) Electron Nucleon Scattering Cross section for electron scattering from a spin ½ particle  target does not remain intact, an inelastic reaction  ee W 1, W 2 are the inelastic structure functions At very large Q 2, they become a function of one dimensionless variable  x=Q 2 /2M F 1, F 2 related to quark distributions in nucleon/nucleus

28. 28 e e'e' xx pA–1pA–1  pq p (,q)(,q) Four-momentum transfer: Q 2  – q  q  = q 2 –  2 = 4ee' sin 2  /2 Missing momentum: p m = q – p = p A–1 = – p 0 Missing energy:  m =  –T p – T A–1 scattering plane “out-of-plane” angle reaction plane PWIA Kinematics

29. 29  Elastic Quasielastic  N*N* Deep Inelastic Nucleus  Elastic  N*N* Deep Inelastic Proton Electron Scattering at Fixed Q 2

30. 30 Plane Wave Impulse Approximation (PWIA) e e'e' q p p0p0 A A–1 A-1 spectator p0p0 q – p = p A-1 = p m = – p 0 Simple Theory Of Nucleon Knock-out

31. 31 nuclear spectral function In nonrelativistic PWIA: For bound state of recoil system: proton momentum distribution e-p cross section Spectral Function

32. 32 e e'e' q p p0p0 FSI A–1A–1 A p0'p0' Example: Final State Interactions (FSI) Reaction Mechanisms

33. 33 Distorted Wave Impulse Approximation (DWIA) “Distorted” spectral function Improve Theory

34. 34 G. van der Steenhoven, et al., Nucl. Phys. A480, 547 (1988). NIKHEF 12 C(e,e'p) 11 B DWIA calculations give correct shapes, but: Missing strength observed.  (p m ) [(MeV/c)  3 ] p m [MeV/c] 1p knockout from 12 C

35. 35 Results from (e,e’p) Measurements Independent-Particle Shell-Model is based upon the assumption that each nucleon moves independently in an average potential (mean field) induced by the surrounding nucleons The (e,e'p) data for knockout of valence and deeply bound orbits in nuclei gives spectroscopic factors that are 60 – 70% of the mean field prediction. Target Mass SPECTROSCOPIC STRENGTH

36. 36 Short-Range Correlations Nucleon s 1.7fermi 2N-SRC   5  o  o = 0.17 GeV/fermi 3

37. 37 Questions What fraction of the momentum distribution is due to 2N-SRC? What is the relative momentum between the nucleons in the pair? What is the ratio of pp to pn pairs? Are these nucleons different from free nucleons (e.g. size)? Benhar et al., Phys. Lett. B 177 (1986) 135.

38. 38 Questions What fraction of the momentum distribution is due to 2N-SRC? What is the relative momentum between the nucleons in the pair? What is the ratio of pp to pn pairs? Are these nucleons different from free nucleons (e.g. size)? Benhar et al., Phys. Lett. B 177 (1986) 135.

39. 39 Questions What fraction of the momentum distribution is due to 2N-SRC? What is the relative momentum between the nucleons in the pair? What is the ratio of pp to pn pairs? Are these nucleons different from free nucleons (e.g. size)? Benhar et al., Phys. Lett. B 177 (1986) 135. BUT Other Effects Such As A Final State Rescattering Can Mask The Signal…

40. 40 Typical energy scale of nuclear process ~ MeV Typical energy scale of DIS ~ GeV Compared to energy scale of the probe, binding energies are less for nuclear targets. So naïve assumption (at least in the intermediate xbj region) ; Nuclear quark distributions = sum of proton + neutron quark distributions 40 The EMC effect

41. 41 It turns out that the above assumption is not true! Nuclear dependence of structure functions, (F 2 A /F 2 D ), discovered over 25 years ago; “EMC Effect” Quarks in nuclei behave differently than the quarks in free nucleon 41 The EMC effect Aubert et al., Phys. Lett. B123, 275 (1983) EMC effect fundamentally challenged our understanding of nuclei and remains as an active area of interest. ( SPIRES shows 887 citations for the above publication)

42. 42 The EMC effect: models  First measurement of EMC effect on 3 He for x > 0.4  Increase in the precision of 4 He ratios.  Precision data at large x for heavy nuclei. Main goals of new Jefferson Lab experiments  Interpretation of the EMC effect requires better understanding of traditional nuclear effects (better handle at high x).  Fermi motion and binding often considered uninteresting part of EMC effect, but must be properly included in any examination of “exotic” effects.  Data are limited at large x, where one can evaluate binding models, limited at low-A, where nuclear structure uncertainties are small.

43. 43 What is the EMC Effect? EMC effect is simply the fact the ratio of DIS cross sections is not one –J.J. Aubert et al. PLB 123 (1983) 275. –Simple Parton Counting Expects One –MANY Explanations SLAC E139 –J. Gomez et al., PRD 49 (1994) 4348. –Precise large-x data –Nuclei from A=4 to 197 Conclusions from SLAC data –Q 2 -independent –Universal x-dependence (shape) –Magnitude varies with A –Average Nuclear Density Effect

44. 44 New Jefferson Lab EMC Effect Data J. Seely et al., Phys, Rev. Lett. 103 (2009) 202301. Plot shows slope of ratio σ A /σ D at EMC region. EMC effect correlated with local density not average density.

45. 45 If the EMC effect is a local density effect, then it seems reasonable to look for connections to other local density effects.