Law 1/v | nuclear-power.com

1/v Law — For thermal neutrons (in 1/v region), absorption cross sections increases as the velocity (kinetic energy) of the neutron decreases.
Source: JANIS 4.0

For thermal neutrons (in 1/v region), the absorption cross-section increases as the neutron’s velocity (kinetic energy) decrease. Therefore the 1/v law can determine the shift in absorption cross-section if the neutron is in equilibrium with a surrounding medium. This phenomenon is because the nuclear force between the target nucleus and the neutron has a longer time to interact.

$\sigma_a \sim \frac{1}{v}}} \sim \frac{1}{\sqrt{E}}}}} \sim \frac{1}{\sqrt{T}}}}}$

This law is applicable only for absorption cross-section and only in the 1/v region.

Example of cross-sections in 1/v region:

The absorbtion cross-section for 238U at 20°C = 293K (~0.0253 eV) is:

$\sigma_a(293K) = 2.68b$ .

The absorbtion cross-section for 238U at 1000°C = 1273K is equal to:

This cross-section reduction is caused only due to the shift of temperature of surrounding medium.

See above:

Interaction of Neutrons with Matter