# Neutron Physics

The neutron is one of the constituent nucleons of the atomic nucleus (the other is the proton). It has zero electric charge, but a magnetic moment and its mass is about 1840 times that of the electron. Outside the nucleus a free neutron will decay into a proton, electron, and antineutrino with a lifetime of about 15 minutes. The neutron can be described as a classical particle with mass m but it shows wave character too, which can be described with the deBroglie wave-length λ. Let m=1.6749 10-27 kg be the neutron mass, v its velocity and h Planck's constant. Below are the relations for neutron energy E given in meV (i.e. 10-3eV), wave-length λ in Ångstrom and velocity v in m/s.
\begin{aligned} E&=\frac {mv^2}{2}=\frac{h^2}{2m}\cdot\frac{1}{\lambda^2}\Rightarrow E[meV]=\frac{81.82}{(\lambda[\mbox{\AA}])^2}\\ \lambda[\mbox{\AA}]&=\frac{9.045}{\sqrt{E[meV]}}\\ v[m/s]&=\frac{3956}{\lambda[\mbox{\AA}]}=437\cdot\sqrt{E[meV]} \end{aligned}
Neutrons can be classified according to their kinetic energy as shown in the table below. For neutron imaging thermal and cold neutrons are preferred due to their favourable detection reactions and due to their very useful contrast behaviour.
 Neutrons Energy range Wavelength [Å] Velocity [m/s] ultra cold ≤ 300 neV ≥ 500 ≤ 8 very cold 300 neV - 0.12 meV 52.2 – 26.1 7.5 – 152 cold 0.12 meV - 12 meV 26.1 – 2.6 152 – 1515 thermal 12 meV - 100 meV 2.6 - 0.9 1515 - 4374 epithermal 100 meV - 1eV 0.9 - 0.28 4374 - 13.8 103 intermediate 1eV - 0.8MeV fast > 0.8MeV