Neutron Scattering

Therefore, for any scattering event we may perform a separation into partial waves and
consider only thé isotropie S-wave scattering . These scattering processes may bc described by
one parameter thé scattering length b = bi + i - b2. Thereby bl describes scattering, while b2 is
thé absorption part. For thermal neutrons thé scattering potential of a single nucleus becomes
(Ferrai pseudo potential)
V (r) = 2z b z bS (L-R) (2 .22)
Mn
The scattering lengths b have been measured as a fonction of neutron energy . For thermal and
lower energies thé réal parts of these scattering lengths are constant and depend in an nonsystematic
way on thé number ofnucléons (sec Fig .2 .7).
We realize, that there are positive as well as negative scattering lengths . Following a
convention most of thé scattering lengths are positive . In this case, we have potential
scattering with a phase shift of 180° between thé incoming and scattered wave . Negative
values result from résonance scattering where thé neutrons penetrate thé nuclei and create a
compound nucleus . The emitted neutrons do not undergo a phase shift. We also realize strong
différences in thé scattering lengths for some isotopes . In particular important is thé différence
in scattering length between hydrogen and deuterium (by, = -0 .374, bd =+0.667) . This
significant différence in scattering length is thé basis of all contrast variation experiments in
sort condensed matter research as well as in biology (sec later lectures) . We also note, that thé
scattering lengths may dépend on thé relative orientation of thé neutron spin with respect to
thé spin of thé scattering nucleus . Again a veiy prominent example is thé hydrogen. There thé
scattering length for thé triplet state, neutron and hydrogen spins are parallel, amounts to
bl,ipiet = 1 .04 - 10 -12cm while thé scattering length for thé singlet situation, neutron and
hydrogen spins are antiparallel, is b,ingret = -0.474 - 10-12cm .