Neutron Scattering

down power and stronger absorption for thermal neutrons (sec below) . The reason for this
seemingly paradoxical demand for stronger absorption is that the achievable neutron peak
flux is not only proportional to the proton peak current, but also depends on the storage time T
(sec below) of thermal neutrons in the moderator . We should point out here that the slowing
down time for H2O and D 20 is small compared to the storage time T. The neutron peak flux is
given by the following expression, which is the result of a convolution of a proton pulse of
duration tp with an exponential decay of the neutron field within the moderator wich storage
(decay) time T.
_ - rep -tp / r
1) th = ')th ' -(i - e )
tp
where 4) th , ~th are peak and average flux, respectively, and t,, is the time between pulses .
In the limit tp -> 0 expression (1 .3) reduces to 4 th = _~ th - trep / z, i .e . even a 8-shaped current
pulse results in a finite neutron peak flux . We see as well that in this case the peak flux is
inversely proportional to the moderator storage time . Also with finite cunrent pulses a short
storage time is important for obtaining large peak fluxes . The storage time T of a thermal neutron
is a measure of the escape probability from the moderator and is obviously determined by
both the geometry ofthe moderator vessel and the absorption cross section of the moderator
medium (sec section 1 .3) and can be written [2] :
T = ( vtn ' Y-abs + 3 D n2 / L2 ) - 1 (1 .4)
where v t1, is the average neutron velocity, E abs the macroscopic absorption cross section, D
the diffusion constant for thermal neutrons and L is a typical moderator dimension . The absorption
cross section of H2O is about 700 times bigger than that of D20 . If it were only for
this reason, an H20-moderator had to bc small (small L in (1 .4)), because we want of course
utilize the neutrons that leak from the moderator. So, a short storage time must not entirely bc
due to self-absorption . As, on the other hand, H2O possesses the langest known slowing down
density (the number of neutrons, which become thermal per cm3 and s), an H20-moderator
anyhow does not need to be big . In section 1 .3 we have already quoted that within a spherical
moderator vessel with its radius equal to the slowing down length Ls (= 18 cm for H20), 37%
of the fast neutrons emitted from a point source located in the center become thermal. In fact,
an H20-moderator must not bc essentially larger, because within a sphere with r = 23 cm already
80% ofthe neutrons are lost due to absorption .