nuclear physics - Why is boron so good at neutron absorption?

Why is boron so good at absorbing neutrons? Why does it have such a large target area compared to the size of its nucleus?

Answer

It's boron-10 that is the good neutron absorber. Boron-11 has a low cross section for neutron absorption.

The size of the nucleus isn't terribly relevant because neutrons are quantum objects and don't have a precise position. The incident neutron will be delocalised and some part of it will almost always overlap the nucleus. What matters is the energy of the reaction:

$$ ^{10}\text{B} + n \rightarrow ^{11}\text{B} $$

and the activation energy for the reaction.

I'm not sure we understand nuclear structure well enough to give a quantitative answer to this. However neutrons, like all fermions, like to be paired and $^{10}$B has 5 neutrons while $^{11}$B has 6 neutrons. So by adding a neutron we are pairing up the neutrons and completing a neutron shell. We would expect this to be energetically favourable.

This argument would apply to any nucleus with an odd number of neutrons, but $^{10}$B is a light nucleus so we expect the effect to be particularly big. The lightest such nucleus is $^{3}$He, with one neutron, and that has has an even bigger neutron absorption cross section. However practical considerations rule out the use of $^{3}$He as a neutron absorber. $^{6}$Li, with three neutrons, also has a reasonably high cross section, though it is less than boron and helium.