Neutron Scattering

number of neutron sources is described in the Appendix, in particular with respect to the
achievable intensities . There are, of course, other criteria (e.g . cost or technical limitations),
but for the neutron scattering experiment the highest possible signal (intensity) at the detector
is decisive . The quality of an experiment strongly depends on the counting statistics,
which in turn govems the resolution capability of a neutron diffractometer or spectrometer .
This criterion excludes most of the sources described in the Appendix for modem neutron
scattering instruments, although electron accelerators for (y,n)-reactions were successfully
utilized for a certain time . For other applications like medical or in nuclear and plasma
physics those sources were and still are of importance .
In the following we will explain in greater detail the two most important sources for neutron
scattering experiments : the nuclear reactor and the spallation source .
1 .3 The nuclear reactor as a neutron source
Fission of a single 235U nucleus with one thermal neutron releases on average 2 .5 fast neutrons
with energies around 1 MeV . So, this is more than needed to sustain a chain reaction .
Therefore we can withdraw typically 1 neutron per fission for puiposes like neutron scattering
experiments without disturbing the chain reaction. The source strengths Q(n/s), i .e. neutrons
emitted per second, achievable with these surplus neutrons are limited in particular by problems
ofremoving the energy released, which is about 200 MeV per fission. Using the relation
1 eV = 1.6x10 -19 Ws we get Q - 3x10 16 n/s per MW reactor power to be removed . As mentioned
in the introduction the fast neutrons have to be slowed down to thermal energies to be
useful for neutron scattering .
The stochastic nature ofthe slowing down of neutrons by collisions with light nuclei ofthe
moderator medium (e .g . protons in water) leads to the notion of a neutron flux ~D as a quality
criterion for thermal neutron sources . This flux is defined as the number of (thermal) neutrons
per second isotropically penetrating a unit area . In order to calculate the flux d)(r) for a given
source distribution Q(r) (the fuel elements of a reactor core submersed in a moderator medium)
we had to solve the general transport (Boltzmann) equation . But there are no analytical
solutions possible for realistic geometries of reactor cores [1] . An estimate, however, will be
given for simple model : a point source located in the center ofa spherical moderator vessel. If
the radius of the vessel is equal to the so called slowing down length Ls [2], then 37% of the
source neutrons become thermal . Using the deflnition (Dt, = v ,l, - n (average neutron velocity
Pu,), where the stationaiy neutron density n is given by a balance equation, viz . n = q ' ti (balance
= production rate - life time) with q as the so called slowing down density, we have