Kern- und Teilchenphysik I — SS 2006 — Prof. G. Dissertori — Serie 4
Abgabe: 4.Mai 2006
1. Wirkungsquerschnitt
Ein Protonenstrahl trifft auf ein Target aus fl¨ussigem Wasserstoff, wodurch es zu Proton- Proton Wechselwirkungen kommt. Der Wirkungsquerschnitt betrage 40 mb. Berechnen Sie nun, wieviel Prozent der einfallenden Protonen gestreut werden. (Die L¨ange des Targets be- tr¨agt 0.45 m und seine Dichte 70 kg/m3.)
2. Abweichung von der Rutherford- und Mott-Streuung
Ein Elektronenstrahl mit einer Energie von 137 MeV wird an Goldkernen gestreut.
a) Berechnen Sie den R¨uckstoss der Kerne. Kann man ihn vernachl¨assigen?
b) Berechnen sie die Abweichung von der Rutherford-Formel beim Streuwinkel Θ = 900, wenn der Spin des Elektrons ber¨ucksichtigt wird.
c) Warum ist die berechnete Abweichung viel kleiner als die gemessene Abweichung?
3. Formfaktoren
Elektronen werden elastisch an Protonen gestreut. In der Abbildung ist der Quotient aus dem experimentell bestimmten Wirkungsquerschnitt und dem Mott-Wirkungsquerschnitt als Funktion von tan2 θ2
dargestellt. Der Viererimpuls¨ubertrag betr¨agt: Q2 = 2.92 GeV2/c2. Sch¨atzen Sie die elektrischen und magnetischen Formfaktoren GE und GM ab.
dΩdσ dσ dΩ
0.01 0.02 0.03
0.00
0.2 0.4 0.6 0.8 1.0
0.0 tan2
( )
Θ2( )
Mott*
*
4. The discovery of the proton structure
In the sixties, it was not obvious at all that the proton was composed of partons and many different theories were competing to explain its structure. The article given here describes an experiment made at SLAC-MIT studying the proton structure by scattering electrons from an hydrogen target and detecting the outgoing electrons in a large magnetic spectrometer set at angles θ = 6◦ and θ = 10◦, which measured the scattered electron momenta.
Look in the paper for the description of the different models that were trying to explain the observed proton structure.
Let us give in the following some explanations to help in the understanding of this paper(The notations used here are the same than in the lecture notes).
As expected, the data showed peaks when the mass W of the produced hadronic system corre- sponded to the mass of the one of the bound quarks resonances (likeN∗ or ∆). Each resonance showed the expected behavior as a function ofQ2, i.e. the production fell with increasing mo- mentum transfer. What was surprising was that for W values beyond the resonances, the cross section did not fall with increasing Q2.
The differential cross section for such a process can be written like dσ
dΩdE0 = α2 4E2
cos2(12θ) sin4(12θ)
W2+ 2W1tan2(1 2θ)
This is analogous to the Rosenbluth formula, which describes an elastic collision. Here however W1andW2are functions of two variablesν =E−E0 andQ2. In contrast, for elastic scattering, the two variables are related with Q2 = 2M ν.
To determine W1 and W2 separately it is necessary to measure the differential cross section at two values of E0 and θ that correspond to the same values of ν and Q2. This is possible by varying the incident energy, E. At small values of θ, W2 dominates, so it is most convenient to focus on this quantity.
The most important result from the experiment at SLAC was the discovery that νW2 did not fall with increasingQ2but tended to a value that depended on the single variablex= 2M ν/Q2. This behavior, named scaling, was proposed first by Bjorken, who imagined the proton to be composed of point-like quarks !
(adapted from ’The experimental foundations of particle physics’, Cahn and Goldhaber)
