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Announcement next Tuesday (5.6.2012), the time slot of the lecture is exceptionally shifted: 14:00h - 15:15h – gr. Hörsaal, Philosophenweg 12 Electron-proton scattering Probing the structure of extended/composite objects p' p resolution depends on wavelength of exchanged photon 10 MeV2 1 GeV2 100 GeV2 thus introduce: 2 fm 0.2 fm 0.02 fm Electron-proton scattering Rutherford scattering : kinetic energy of incoming electron [ ×z2Z2] for charge z of incoming particle and charge Z of target valid for < 50 keV, low momentum limit, no recoil of proton neither spin of electron nor proton taken into account, proton regarded as pointlike particle Mott scattering h=-1 back scatter suppressed due to non-conservation of “electron helicity” Note: same formular can be derived descriping proton as static coulomb potential proton h=+1 high energetic limit for electron: chirality eigenstates = helicity eigenstates no recoil of proton, proton regarded as pointlike spinless particle Electron-proton scattering Take into account extended size of proton → form factor normalized charge density of proton Idea of form factor similar to diffraction of plane wave in optics: Finite size of scattering center introduces a phase difference between plane waves “scattered from different points in space”. If wavelength is long compared to size all waves in phase: → maximum constructive interference, all other interference reduce the cross-section Elastic electron-nucleon scattering R. Hofstadter, Ann. Rev. Nucl. Sci. 7 ,231 (1957) To conclude on charge distribution of nucleus, need model assumption. For uniform sphere: 1st minimum at consistent with Scattering from extended charge distributions Form factors is an interference effect, coherent scattering from charges all over the source. Form factors always reduce the corresponding point-source cross-section. represents nucleous with low atomic number represents nucleous with high atomic number Electron-proton scattering: recoil of proton y high relativistic treatment of z start from full expression of QED matrix element (no high or low energy limit) (e.g. Halzen & Martin 6.5) Exploit energy and momentum conservation to get rid of [1] [2] in CMS system: however in this example we work not in CMS (derivation see backup) Rutherford → electron helicity (Mott) recoil of proton magnetic contribution due to spin-spin IA: spin-flip compare to Mott (spin ½ in fixed electro-magnetic potential) Sideremark: 1) still consider proton as point-like particle 2) up to now elastic scattering, thus cross section depend on initial electron energy and only one more parameter e.g. Dirac Scattering scattering of point-like spin ½ electron with point-like spin ½ proton backward scatter forward scatter before after angular momentum and helicity conserved angular momentum and helicity not simultaneously conserved Contribution from spin flip: magnetic moment of Dirac particle: Spin-Spin IA ~ Integrated B field at position of proton due to moving charge of electron: Electron proton scattering Measurement of and o Rosenbluth formula: SLAC Experiment: 1969 θ Magnetic form factor of proton dipole form for Form factor fits data best exponential distribution of magnetic moments RMS radius of spherical (charge) distribution Electric and magnetic form factor of proton and neutron charge and magnetic moment have the same size in proton proton and neutron have same size Electric form factor of the neutron Problem: There are no targets of free neutrons Study of neutrons bound in nucleus suffer from additional nuclear forces, which need to be corrected Idea: Scatter of low momentum neutrons from a nuclear reactor on loosely bound electrons of the outermost shell of atoms Both electrical charge and magnetic moment contribute to electric form factor, no lorentz-invariant computation of both contributions separately possible. Size of the Proton Alternative measurements exploit hydrogen spectroscopy 10.3 eV 0.2 meV 35μeV 6 μeV fine structure Lamb-Shift: higher order corrections precisely computed in QED 5 neV Published in July 2010 Muonic Hydrogen muon orbit significantly closer to proton, thus more sensitive to its size! Corresponding energy difference in “normal” hydrogen about 10-4 smaller Inelastic scattering elastic scattering Inelastic scattering Produce excited states e.g. Δ+ (1232) Deep inelastic scattering (DIS) proton splits up in many final state particles