What is the cause of the reduction in peak microscopic cross section with increasing temperature, shown here for a nuclear resonance?

Doppler Broadening of Resonance

The nuclear properties of the target material do not actually change with motion, so why does the peak reduction of the target's microscopic cross section ("effective area") suggest that they do? I understand the need to broaden with respect to relative energy of neutron-target, but not to simultaneously reduce the absolute values of the curve itself.

Taking it to an extreme like T-->infinity, I can see that if Doppler broadening were forced to be anchored to the peak, and the curve were merely expanded outward in energy, then the neutron would be considered always to be within the resonance - and, in fact, at the peak energy - which is the opposite of what is intended. Still, when considering just one neutron at a time - say, in a Monte Carlo simulation - if the target's motion is sampled independently from a temperature dependent distribution (e.g. Maxwellian) it would seem appropriate to use zero Kelvin cross sections. Is this true?

  • $\begingroup$ First time I've seen a user ask a question, then answer it an hour later. $\endgroup$ Jul 18, 2020 at 21:19
  • $\begingroup$ Couldn't sleep on it. $\endgroup$
    – jpf
    Jul 18, 2020 at 23:58

1 Answer 1


It's important to understand first that free-atom cross sections are not temperature dependent. That is, cross sections are the same for the same relative speed between a neutron and a target atom. This means that, for the case of a Monte Carlo simulation of a single particle, if the relative speed between the particle and the target is determined explicitly, then it is appropriate to sample the 0K cross sections.

This is distinct from when we perform a calculation - perhaps deterministic transport, or Monte Carlo without determining the target speed by sampling from a distribution - in the laboratory frame of reference, where the projectile (neutron) has a fixed speed, but the target has a distribution of speeds (e.g. Maxwellian). In this case, we have to average the cross section weighted by the relative speed (energy) distribution surrounding the projectile energy. This averaging reduces the peak, and it also explains why the reaction rate is preserved per neutron (area under curve).


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