klicken, um die Datei herunterzuladen

Übungen zur Vorlesung
„Einführung in die Kern- und Teilchenphysik“
II. Physikalisches Institut, Fakultät für Physik, Universität Göttingen, SS 2004
Prof. H. Hofsäss
Sheet 3
Handing out: Fr. 14.5.2004 Return: Mo 24.5.2004
Discussion: Fr 28.5.2004
Problem 7: magnetic moment of the neutron
a) Describe the experiment of Greene (Physical Review D 20 (1979) 2139 to
measure the magnetic moment of the neutron. (see also: Bethge, Kernphysik, p.
58/59)
Problem 8: magnetic moment of proton und neutron
Calculate the anomalous magnetic moments of proton an neutron und the
assumption that proton and neutron consist of three sub-particles (quarks) with
mass m ≈ 1/3 mP, spin ½ , g-factor g=2. We define an Up-Quark with charge +2/3e
and a Down-Quark with charge -1/3e.
The proton is described as a combination „up-up-down“, the neutron as combination
„up-down-down“. The spins of the three quarks couple to a total spin ½.
Für das Proton ergibt die Kopplung einen Zustand:
p = 1 18 ⋅ [2 ( u ↑ u ↑ d ↓ ) − (u ↑ d ↑ u ↓) − (d ↑ u ↑ u ↓)
− (u ↑ u ↓ d ↑) + 2(u ↑ d ↓ u ↑) − (d ↑ u ↓ u ↑)
− (u ↓ u ↑ d ↑) − (u ↓ d ↑ u ↑) + 2(d ↓ u ↑ u ↑)]
mit magnetischem Moment:
1
µ P = p | µˆ P | p = [(4 ⋅ 2µ p − 4µ down ) + µ down + µ down
18
+ µ down + (4 ⋅ 2 µ p − 4 µ down ) + µ down
+ µ down + µ down + (4 ⋅ 2µ p − 4µ down )]
1
( 4µup − µdown )
3
1
and for the neutron:
µ N = n | µˆ N | n = ( 4 µ down − µup )
3
Calculate the magnetic moments µup und µdown und the magnetic moments of proton
und neutron.
For the proton we find:
µ P = p | µˆ P | p =
Addition: Try to adjust the mass of the quarks to obtain a better agreement with the
experimentally observed values for µP and µN.
Problem 9: Landé formula
Calculate the magnetic moments of 7Li and 17O using the Landé formula. Assume
that only the unpaired nucleon contributes to the magnetic moment. For 7Li this
nucleon (proton) is in a state with angular momentum l = 1 and j = l+s = 3/2. For 17O
this nucleon (neutron) is in a state with angular momentum l = 2 and j = l+s = 5/2.