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Introduction • Up to now have covered Quarks and Hadron Spectroscopy – Lecture III Nomenclature for baryons and their resonances QCD principles Basics of electron scattering The constituent quark model • In the next two lectures Daniel Watts Nuclear Physics Group University of Edinburgh Electron and photon beam facilities Nucleon properties Nucleon resonance properties Then hand back to Dave for the last two lectures! Types of photon Polarisation • • Both real and virtual photons can have polarisation Measuring observables based on these polarisations gives powerful additional information Transverse polarisation (Electric field vector oscillates in a plane) Circular polarisation (Electric field rotates Clockwise or anticlockwise) Virtual photon Longitudinal polarisation Virtual photons can also have a longitudinal polarisation component related to coulomb (charge) scattering EM probe facilities How do we generate intense electron beams? Microtron (MAMI, Jefferson Lab) Electron beam accelerated by rf cavities. MAMI, Mainz, Germany Tune magnetic field to ensure path through magnets multiple of Wavelength of accelerating field. - electrons arrive back in phase with the accelerating field. Hermes, DESY, Germany Postcard collection Gives “continuous” beam (high duty factor) Strecher rings Jefferson Lab, USA (SPring8, Bonn, Frascati,) Electron beams fed in from linac Then accelerated and stored in ring. Useable beam bled off slowly Many stretcher rings built for synchrotron radiation - can exploit infrastructure for multiuse (e.g. Spring8) Tend to have poorer duty factors , less stable operation and poorer beam properties than microtrons Spring 8, Japan More on Tagged Bremsstrahlung Real photon beams from electron beams • Laser back-scattering (LEGS, FRASCATI, DUKE, Spring8) Eγ smaller than beam energy Facilities up to 4 GeV • Positron annihilation in flight Only successful up to ~50 MeV Bremsstrahlung background also present e+ Bremsstrahlung cone eRadiator θe γ Radiator must be thin Don’t want each e- to produce more than one photon γ Keep radiator to target distance small to keep beamspot small • Tagged Bremsstrahlung γ Log Nγ (MAMI, Bonn, Lund, Jlab) Eγ up to ~beam energy Facilities up to 2.5 GeV (12 GeV planned at JLab ) Bremsstrahlung spectrum Collimator Tagging spectrometer should have large acceptance for scattered electron θe= (me/Ee).( Eγ/(Ee-Eγ) ) Ideally the electron detectors at focal plane of spectrometer should have: Generally collimate beam to give better defined beam spot and enhance polarisation (see later) Good timing resolution Cover wide Eγ range Highly segmented Polar angle of cone around beam direction Containing 50% of γ Reals/Randoms ~ D/Ret D = Duty factor of beam Re = mean electron rate t = resolving time e- Target Θc = me/Ee(MeV) rads e.g. MAMI – 855 MeV Θc = 0.6mrad More on Coherent bremsstrahlung Polarisation in real photon beams Bremsstrahlung facilities: Linear polarisation: Use a Linear Polarisation crystalline radiator e.g. thin diamond. Orient diamond to give polarised photons in certain photon energy ranges Circular polarisation: Use helicity polarised electrons and produce bremsstrahlung in amorphous radiator. Electrons polarised at input to the accelerator (e.g photo electrons produced from circularly polarised laser light on strained GaAs) Bremsstrahlung cone eDiamond radiator y Collimator Coh. Brem. From [022] plane Degree of Polarisation (fraction of beam Which is polarised) Laser backscattering: Circular Polarisation Linear polarisation: Use a linearly polarised laser beam to backscatter from the electron. High degrees of polarisation (~100%) achievable Detector systems used with γ beams Collimate beam to achieve linear γ polarisations up to ~90% Detector systems used with γ beams γ CLAS at Jefferson Lab ∆Eγ ~ 2 MeV 108 γ sec-1 γ TAPS 528 BaF2 crystals Crystal Ball 672 NaI crystals Crystal Ball and TAPS at MAMI Electron scattering facilities What do we use photon detectors for? Primarily used to reconstruct neutral mesons which decay to photons Eg. π0→2γ, η→2γ Require good determination of incident electron 4-vector and scattered electron 4-vector. e.g. A1 at MAMI, Mainz, Germany • Track path of scattered electron in a magnetic field • Determine momenta from path in the magnetic field (wire chambers and focal plane detectors) • Electrons have high energies → large path length in magnet and intense B field Hall A at Jefferson Lab Recap • New generation of intense electron beam facilities give high quality polarised beams of electrons and photons • Have large scale detector systems to detect scattered electron as well as charged and uncharged reaction products (p, n , π, η, ω, ρ ...) Hermes at DESY • For the rest of lecture will look at experimental work carried out at these facilities start with: elastic electron scattering W =M Q2 ⇒ω = 2M Elastic electron scattering and nuclear form factors Nuclear Shapes Cos2 term only difference From Rutherford formula Arises from Dirac theory For spin ½ particle ρ (r ) = 1 sin (qr / = ) F (q ) 4πr 2 dr (qr / = ) 2π ∫ Elastic electron scattering - discussion Rosenbluth separation If we keep Q2 fixed and vary ε we can disentangle the magnetic and electric form factors • Information on the charge distribution of nuclei arises from coulomb scattering BUT what about magnetic scattering – does that not also contribute?? ( ) ( ) Q 2 2 2 2 θ ⎫⎪ dσ ⎛ dσ ⎞ ⎧⎪ GE Q + 4 M 2 GM Q Q2 2 2 + GM Q tan 2 ⎬ =⎜ ⎟ ⎨ 2 2 Q dΩ ⎝ dΩ ⎠ Mott ⎪ 2M 2⎪ 1 + 4M 2 ⎩ ⎭ 2 ( ) • Nuclei with total angular momentum 0 do not have a magnetic moment (e.g. 12C, 16O, 208Pb) – therefore contribution from magnetic scattering negligible • Nuclei that are not spin 0 will have contributions from charge and magnetic scattering (as will protons & neutrons!!) • How can we separate effects from charge and magnetic contributions in the scattering process? Major drawback - Gm weighted with Q2 Q2 < ~1 GeV2 both form factors make measurable contributions Q2 > ~1 GeV2 contributions from electric form factor become very small – large systematic errors in extraction Polarisation observables in form factor measurements Nuclear magnetic form factors • Need polarisation observables to get more accurate information on nucleon form factors – particularly the electric form factors at high Q2 • Only have suitable experimental facilities available in recent years • Longitudinally polarised electron will transfer it’s polarisation to the recoiling proton • Charge and magnetic form factors are accessible from the nucleon polarisation components. Give information on distribution of magnetization in the nucleus GE P E + Ee ' ⎛θ ⎞ =− t e tan ⎜ e ⎟ ⎝ 2⎠ GM Pl 2M Aside: How do we measure the polarisation of a nucleon ?? Nucleon Scattering and polarisation n(θ,φ) =no(θ){1+A(θ)[Pycos(φ)–Pxsin(φ)] Number of nucleons scattered In the direction θ, φ Polar angle distribution for unpolarised nucleons x and y (transverse) components of nucleon polarisation Analysing power of scatterer Proton form factors - the Shape of the Proton GE/GM gives the ratio of the electric charge and magnetisation distributions in the proton A surprising effect was noted in the recent experiment. Ratio of magnetic and electric form factors change with Q2 ?! The recent polarisation data question the results using Rosenbluth separation – latest thinking is that double photon exchanges cause the discrepancy between the 2 methods θ Imply proton’s charge distribution not the same as it’s magnetization!! Neutron Form Factor GEn • Neutron is very interesting object to study no net charge but has charged quark components. How are they distributed? • Good quality data only obtained in recent years. Double polarisation technique e-Beam+target polarised: e-Beam+recoil nucleon: Simultaneous fit to all 4 Form factors – recently conjectured that we see evidence of a pion cloud from new accurate data Bump at Q2~0.3 ? Pion Cloud? P E + Ee ' GE ⎛θ ⎞ =− t e tan ⎜ e ⎟ ⎝ 2⎠ GM Pl 2M To access z component of nucleon polarisation need to precess spin in a magnet before the nucleon Polarimeter δ – precession angle r2ρ(r) Aside p π- Evidence for negative pion cloud? neutron dissociates to p & π- ~7-20% of time Friedrich and Walcher, hep-ph-0303054 • RMS radii related to slope of form factor at Q2=0 < (rpE)2>1/2 0.895±0.018 fm < (rpM)2>1/2 < (rnE)2>1/2 < (rnM)2>1/2 0.855±0.035 fm -0.119±0.003 fm2 0.87±0.01 fm Excellent agreement With QED calculation of Lamb Shift !