Gadolinium-157 has the highest thermal-neutron capture cross-section among any stable nuclide. Based on my layman's understanding of neutron capture – particularly the fact that (I assume) neutrons don't much care about electron shells – I would have guessed that neutron capture cross-section would be proportional to either:

  1. Size of the nucleus. I.e., strictly increasing with (N+Z).
  2. Density of the solid.

Gadolinium is middling with respect to both properties. So what is it about the phenomenon of neutron capture that results in the cross-sectional peak for promethium through gadolinium?

Neutron Cross Section of elements by atomic number


2 Answers 2


Welcome to the world of nuclear physics, where the answer is "It's a little more complicated than that."

  1. Density of the solid

You can rule this out: cross sections are tabulated per target atom.

  1. Size of the nucleus, i.e., strictly increasing with (N+Z).

This is a good guess, but you miss an important feature of thermal neutron physics: the relevant size parameter isn't the diameter of the nucleus, but the size of the neutron's wavepacket --- whose scale parameter is something like the neutron's wavelength. Thermal neutrons have wavelengths of a few angstroms ($1\text{ Å} = 10^{-10}\,\rm m$), many orders of magnitude larger than the physical size of a nucleus.

The actual result has more to do with nuclear structure: in order for there to be a capture reaction, there has to be a final state available to receive the neutron with the correct energy and quantum numbers. If you look at a table of isotopes (see also), you'll find that gadolinium and its lanthanide neighbors are pretty far from any nuclear magic numbers. That means that they have a very high density of nuclear states and are easy to excite --- and it increases the probability that there's a resonance in the nucleus $\rm^{158}Gd^*$ whose energy and quantum numbers overlap with a ground-state $\rm^{157}Gd$ and a milli-eV neutron.

The nuclear structure data file for $\rm^{158}Gd$ cites this 1978 paper in a description of the structure of the resonance. That reference (which I can't access) apparently refers to a resonant state in $\rm^{157}Gd$ with an energy of about thirty milli-eV, which is approximately the energy of a room-temperature neutron. That statement doesn't make sense to me right away, but there is an inflection in the cross-section curve at a thermal-ish energy.

If you look at neutron capture cross sections on a table of isotopes (this link should work)

table of isotopes: neutron cross sections

you can see your promethium-to-gadolinium cluster of high-$\sigma$ isotopes just to the right of the $N=82$ magic number. Midway between the $N=50$ and $N=82$ magic numbers is another very strong absorber, cadmium. You can also see that the elements in the uranium-ish island of stability are also eager neutron absorbers.

There are also pairing effects happening in gadolinium. Nucleons don't like to be alone, so nuclei with odd $N$ or odd $Z$ (or both) are less stable than their even neighbors. Gadolinium, like many heavy even-$Z$ elements, has a whole pile of stable isotopes, but the even-$N$ isotopes are more tightly bound than the odd-$N$ isotopes. If you look at the neutron cross sections for all of the gadolinium isotopes, you can see how desperately the odd-$N$ species want to collect an extra neutron:

isotope   σ (barn)
-------   --------
Gd-152       735
Gd-153     22310
Gd-154        85
Gd-155     60740
Gd-156         1.8
Gd-157    253700
Gd-158         2.2
Gd-159    (unstable)
Gd-160         1.4

Your original speculation about electron shells was, as you surmised, not applicable to nuclei, but it turns out that nuclei have shells too, called 'magic numbers'. So give yourself credit for thinking along a parallel line.


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