Refraction - an extreme case

When multiple scattering is intense, the wave impinging on a centre of position vector r is already strongly perturbed. This wave approximately obeys the equation 

In general, the length b is positive, and in this case a neutron beam impinging on a material surface is totally reflected if the incidence angle is smaller than a limiting angle 0C defined by the condition 

The critical angles for interfaces are also small (typically = 10 1 angular degree/nm). The refraction phenomenon is used for various purposes transportation of neutrons far from their source (high-efficiency wave guide), polar- 

However, 6 is negative for hydrogen, lithium, and a few other elements. 

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