A5 - neutron radiation

EM radiation:

E = \frac{h c}{λ}

but for neutrons:

E = \frac{h^{2}}{2 m λ} = \frac{1}{2} m v^{2}

a neutron with $λ = 0.1 nm$ has $E = 5.83 \times 10^{- 21} J = 36.4 meV$ (cf. x-rays with the same $λ$ has $E \sim 8.2 keV$ )
bond energy between two carbons: $E \sim 4 eV$
therefore, neutrons have an advantage over x-rays for the study of sensitive samples
light and x-rays are scattered by the electrons, but neutrons are scattered by the nuclei
the scattering cross-section of an atom ( $σ$ ) for light and x-rays increases with the atomic number
the neutron-nucleus interaction strength varies irregularly with atomic number
therefore, even isotopes of the same element have different $σ$
hydrogen: $σ_{c o h} = 1.75 \times 10^{- 24} {cm}^{2}$ (barns) but deuterium: $σ_{c o h} = 5.6 barns$
therefore, neutrons can see and differentiate between hydrogen isotopes
atomic nuclei are $10^{4} - 10^{6}$ times smaller than typical neutron wavelengths
therefore they effectively act as point scatterers
scattering remains constant as the angle increases
scattering patterns can be collected over the full range from forward to backward angles
it is spherically symmetric
neutron-matter interaction is weak and its absorption by most materials is negligible, making it very penetrating
neutrons have a small magnetic moment that can interact with the spin and the orbital magnetic moments in a sample with unpaired electrons, leading to more scattering mechanisms
neutrons may be polarized, so it can have its plane of polarization rotated by a material giving rise to refraction
the refractive index of a neutron:

n = 1 - \frac{N b_{c o h} λ^{2}}{2 π}

where, $N$ is the atomic number density

it is typically slightly less than one, cf. optical refractive indices, which are usually greater than one
this allows neutrons to be totally externally reflected - neutron reflectometry

drawbacks

neutron sources are very large and expensive
also weaker compared to x-ray sources
difficult t focus neutrons

neutron sources

nuclear reactor

fission of uranium-235
2-3 per fisssion

spallation sources

use particle accelerators and synchrotrons
given enough kinetic energy, protons can overcome the long-range electrostatic and short-range nuclear forces and blast the target nuclei apart
spallation refers to 'chipping away'
used by ISIS