Neutron Scattering

Fig. 4) vertical focusing :
The gain factor P for the intensity at
the simple is givenby the ratio of
heights for source and image (hi/hz)
and the height of the deflecting crystal
hm in nuits of the height of the source
by :
_ crysFal~,~~e -_ h~ Li_±Lz
cystaln~~ L2 hl
Similarly to e .g. light, one may mirror and thus guide neutrons . On the basis of the Fermi
pseudopotential V one obtains the index of reflection for neutron by
k V I 2A 2M ' p(z) b, (r) ~ 2 = 1- E
p(r) b, (~)
b2 k2
ko
( 2m ) ' =1- 2;
where b,oh (r) denotes the average scattering length and p(r) the particle density . The losses
due to the total reflection are small even for a rather modest quality of the mirroring surface .
By suitable coating the simple beam tube may become a neutron guide and the 1/r2-law is
thus circumvented. According to eq. (9) one should use materials for such mirrors which possess
a large coherent cross section together with a large atomic density which is fulfilled for
the isotope S 8Ni with b =14 .4 -10 - ' S m . Since the limiting angle for total reflection is ex
tremely small (0, / Â z 0 .1°/10-1°m), simple homogeneous coating could be used successfully
for cold neutrons, only (the technique to produce super mirrors opened the possibility for
guiding neutrons with energies up to the thermal range) . By means of the neutron guides instruments
having still a high neutron flux can be set up at larger distances from the reactor
core . If , in addition, such a neutron guide is slightly curved one can avoid the direct view onto
the core which reduces the background . Simultaneously, one obtains an efficient ;,/2-filter by
suppressing the unwelcome faster neutrons. A marginal note might be added : in the case of extrente
cooling of neutrons one may keep and store them in "bottles" since they are totally reflected
under arbitrary angles .
10.4 Resolution for diffraction by a crystal
As we have seen already, single crystals offer the possibility to corrtrol the travelling direction
of neutrons . Thereby use is made of their coherent, elastic scattering properties which - according
to eq . (1) - allow for deflecting neutrons from an incident "white" beam under the angle
20 . This Bragg scattering becomes possible as soorr as the scattering vector corresponds
to a reciprocal lattice vector, i .e .
Q=_k-k' =G (10)
and eq. (7) satisfies the condition DE = 0, or expressed differently by :
9- 6