29

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

rob
  • 89,569
user43087
  • 819
  • 3
    I'm a little puzzled by the two (at the time of writing) downvotes. Why is this a bad question? It seems to me that it involves some interesting areas of physics and I'm hoping for answers from our nuclear physics experts (@dmckee). – John Rennie Oct 02 '15 at 06:34
  • I'd agree -- granted this was well-known by the Manhattan Project team early on, but it is interesting. – Carl Witthoft Oct 02 '15 at 14:38

2 Answers2

27

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.

John Rennie
  • 355,118
  • But why? What pulls them into the nucleus I understand that the probability would be higher but why is the cross-section larger? – user43087 Oct 02 '15 at 06:56
  • 3
    @user43087: The cross section is proportional to the probability of the reaction. – John Rennie Oct 02 '15 at 07:31
  • 5
    @user43087: The point John is making is that the neutron should not be considered an infinitesimal point; it is effectively delocalised (spread out) over a larger radius. The interaction is governed by the set of available energy states for the combined system, and here the nuclear forces can come into play. The 'cross section' is not a measure of how far away the neutron can be, but of the probability of the interaction taking place. As John points out, the size of different nuclei is largely unimportant. – Phil H Oct 02 '15 at 10:20
  • 11
    @user43087 "Cross section" is one of those physics terms-of-art that have their origin in classical theory, but which have lost their classical meaning. – Solomon Slow Oct 02 '15 at 10:23
  • 3
    @user43087: yes, sorry if that wasn't clear. The term cross section doesn't mean the cross sectional area of the nucleus. It's derived from a physical measurement of the scattering so it's actually a scattering probability. – John Rennie Oct 02 '15 at 10:33
  • 4
    @JohnRennie - By far the largest contributor to the total $^{10}B$ neutron cross section is the $^{10}B (n,\alpha) ^{7}Li$ reaction (see the National Nuclear Data File collection at nndc.bnl.gov). Your point remains that, like any cross section, you need an overlap of initial and final states - the more possible final states (and the more favorable the final states) the larger the cross-section. – Jon Custer Oct 02 '15 at 14:38
  • 1
    Quantum Mechanics: a particle gets bigger which makes it smaller. And people wonder why it's so hard. – corsiKa Oct 02 '15 at 17:38
  • @corsiKa It's easier without all those attempts to make it look classical. The particle doesn't really have size, per se. Those aren't little billiard balls bouncing around we're seeing. – Luaan Oct 03 '15 at 08:02
4

One thing which John Rennie hasn't mentioned is that boron gets a certain amount of "help" from the fact that neutrons are deliberately retained within a nuclear reactor.

This is the function of the moderator. Neutrons ejected from a decaying uranium travel fast (as is typical of products of nuclear reactions) and if the reactor was filled with vacuum, they would just escape through the walls. But it's filled with some low mass material like water or graphite, which slows down and scatters the neutrons (without reacting with them) until they become "thermal neutrons" (i.e with the same kinetic energy as the surrounding material at the same temperature), so that they just wander about aimlessly within the reactor. Besides the reduced velocity, they also have a much increased path length.

Once this has been done, we can to a reasonable extent ignore the loss of neutrons through the reactor wall, so there are only three other things that can happen:

  1. It can undergo beta decay, becoming an electron, proton and neutrino. The half life for this is about 10 minutes.

  2. It can collide with a fissile atom such as uranium and propagate a nuclear reaction

  3. It can be absorbed by a material like boron.

So you see, once the neutron has been slowed down, the small cross section of nuclei becomes something of a non-issue: it has an average of 10/ln(2)=15 minutes to find and interact with a nucleus, which is absolutely ages on an atomic timescale.

As to why boron in particular is good at absorbing neutrons, John already covered that.

https://en.wikipedia.org/wiki/Neutron_moderator

As an intuitive way of understanding the role of scattering, consider the effect cloud cover has on visible light. During the day, it prevents the sunlight reaching the Earth's surface and reflects it back into space, even though it does not absorb much light itself. At night, it prevents the light from buildings and streets from being released into space, and reflects it back to the Earth's surface where it is absorbed.

According to https://en.wikipedia.org/wiki/Neutron_cross_section boron-10 has an absorbtion cross section of 200 barn for thermal neutrons and 0.4 barn for fast neutrons. A barn is 1E-28m. For comparison, the van de waals radius of boron is 192E-12m https://en.wikipedia.org/wiki/Atomic_radii_of_the_elements_(data_page)

The following is a back of the envelope calculation showing the value of slowing the neutrons down.

The probability of interaction B-10 with a slow neutron is about 200E-28/pi*4/(192E-12)^2=7E-7 for a one atom thick sheet of boron atoms. For a 1mm (5208000 atom) thick sheet, the probability of the neutron surving is (1-7E-7)^5208000 = 0.026 which is pretty low. For fast neutrons a one atom thick sheet interacts with 0.4E-28/pi*4/(192E-12)^2= 1.4E-9, and the probability of surviving a 1mm thick sheet is (1-1.4E-9)^5208000 =0.9928 which is pretty high. Disclaimers: this assumes pure B-10; the Van Der Waals radius is not necessarily the best one to use, depending on the speciation of boron.

Level River St
  • 2,498
  • 3
    "it has 10 minutes" sounds like a misinterpretation of a half life. Consider rewording, maybe? – jpmc26 Oct 03 '15 at 02:36
  • I don't see the relevance of this answer to the question as formulated. Nowhere in the question does it mention the application (reactor, moderator, ...) that you are targeting. "Interesting but irrelevant". Also - while the neutron is "alive" (doesn't decay) for 10 minutes, it is the time taken to transit the absorbing material that is of interest. And even a thermal neutron has significant speed. – Floris Oct 05 '15 at 11:37
  • @Floris thank you for explaining your downvote. I've explained a bit more that the moderator slows and scatters the neutrons (longer path length) which definitely gives them more opportunity to interact. Neither a thin sheet of boron (nor a thin sheet of uranium) is going to interact much with neutrons, but force them to pass through many times and they will. For my reason for posting, please read OP's first comment on John Rennie's answer. I do think this is something that was missing from OP's understanding. And I see no harm in posting extra info - would you prefer to see just one answer? – Level River St Oct 05 '15 at 12:36
  • @jpmc26 added in factor of 1/ln(2). Yes, it's more precise that way. – Level River St Oct 05 '15 at 12:39
  • I agree that the updated answer adds some value to the over all discussion although I stand by my assertion it doesn't "answer the question". Downvote withdrawn. – Floris Oct 05 '15 at 14:23