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If neutrons are stopped by a dense material, they are shedding their energy somehow. Does this mean the lead is becoming a heavier isotope (neutron capture), does the neutron embed itself into the material and turn to hydrogen? Is there a probabalistic distribution of reactions?

I would like to know for lead, tungesten, and water. I don't know what to look up but surely for water there are outcomes like deuterium, tritium, hydrogen gas in the water? If there are tables of these reactions, that would be a great resource.

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  • $\begingroup$ The place for data is the Evaluated Nuclear Data Files site at Brookhaven National Lab. Some will get absorbed in to nuclei, many will not and will decay away. $\endgroup$ – Jon Custer Mar 16 '17 at 12:38
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A neutron in a block of material can do 3 things each time it passes near a nucleus:

  1. Nothing
  2. Elastic scattering - transfers some of its kinetic energy to the nucleus
  3. Inelastic scattering - the nucleus+neutron turn into several particles, usually liberating several neutrons (fission)
  4. Absorption - transmutes the nucleus into a heavier isotope

Variants 3 and 4 are similar, so I just call them "nuclear reaction".

The outcome for every encounter is random. Combining a great number of encounters, these are the possible outcomes:

  1. Nothing (if the sheet of material is too thin) - the neutron flies onward
  2. Some scattering (if the probability of absorption is low) - the neutron flies out with less kinetic energy and different direction; the material is heated a little
  3. Endless scattering (if the probability of absorption is very low, and the block of material is very big) - the neutron's kinetic energy becomes comparable with thermal energy; it wanders among the atoms until it beta-decays
  4. Nuclear reaction (if the probability of absorption is significant)

Note that option 3 leads to a proton (positively-charged ion of hydrogen) and a beta particle (an electron with much kinetic energy, which immediately flies away).

If a nuclear reaction occurs, the result has many possibilities:

  • A stable heavier nucleus (the case for hydrogen and oxygen, as well as heavier elements)
  • A radioactive heavier nucleus (the usual case for heavy elements)
  • Several smaller nuclei and/or neutrons (the usual case for uranium-235)

It may be possible to estimate the probability for various outcomes using measured data for neutron cross-sections (see e.g. here): if the absorption cross-section is big when compared to scattering cross-section, the probable outcome is absorption. However, this is complicated by dependence of the cross-section on the neutron's energy.

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