Download Announcement

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