# (Neutron capture) cross section

## Main Question or Discussion Point

Cross section means the effective size of a nucleus for capturing a neutron, am I right? But what makes the cross sections for different nucleus different? I am a bit puzzled, why the cross section for Boron(for example) is so high?

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malawi_glenn
Homework Helper
in general, the more stable a nucleus can become if it captures a neutron, the higher cross section. Have you done the shell model in school yet?

The keyword "shell model" was exactly what I needed, thanks.

basically, yes. Its a measure of the probability of the nucleus capturing the neutron. Yes, it varies element to element because of the shell model (ie. its harder to capture a neutron if there the element has a "magic" number of neutrons).

But, I have a question.

The element Boron has two stable isotopes, B-10 and B-11. They differ by one neutron.
The neutron capture cross section of B-10 is 3835 barns (this means it has high probability of capturing another neutron).
The neutron capture cross section of B-11 is 0.0055 barns (low probability).

So, my question--why is there such large difference in neutron capture cross section for two stable isotopes of the same element that differ by only one neutron--how does the shell model explain this ?

malawi_glenn
Homework Helper
But, I have a question.

The element Boron has two stable isotopes, B-10 and B-11. They differ by one neutron.
The neutron capture cross section of B-10 is 3835 barns (this means it has high probability of capturing another neutron).
The neutron capture cross section of B-11 is 0.0055 barns (low probability).

So, my question--why is there such large difference in neutron capture cross section for two stable isotopes of the same element that differ by only one neutron--how does the shell model explain this ?
Boron-10 have 5 neutrons, one of them is unpaired and can easily fill the second subshell (1p_3/2). In boron-11 we already have 6 neutrons, and the (1p_3/2)sub shell is filled, hence the lower probabilty to add another neutron.

And if you want to know in more detail you should study the physics of shell model more closely or wait til someone have time to give a longer explanation, I dont have time at the moment.

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html

B-13 will have even smaller neutron cross section, since it have 8 neutrons - a magic number.

And why some radio nucleus are likewise to receive fast neutrons, and some radio nucleus slow neutrons?

malawi_glenn
Homework Helper
And why some radio nucleus are likewise to receive fast neutrons, and some radio nucleus slow neutrons?
That has to do with the pairing term (among several other things), it would take a quite long time to explain this altough;)

This is treated in Krane's textbook: Introductory Nuclear Physics

Every nuclear physicist should own a copy of it :)

Can you please give me some analogy, or with 2 sentences tell me what is the deal about...

Boron-10 have 5 neutrons, one of them is unpaired and can easily fill the second subshell (1p_3/2). In boron-11 we already have 6 neutrons, and the (1p_3/2)sub shell is filled, hence the lower probability to add another neutron
Thank you, I can see where filling the 1p_3/2 shell with 4 neutrons in boron-11 would lower the neutron cross section from 3835 barns in boron-10 to 0.0055 barns in boron-11

My next question is: "why are both boron-10 and boron-11 "stable ?". Let me attempt to answer my question and you can correct my errors. For boron-11, it appears the stability comes from the fact that the 1p_3/2 shell is complete with 4 neutrons. For boron-10 it appears the stability comes from the fact that it is an "odd-odd" (Z-N) isotope with equal number of protons and neutrons in both 1s and 1p_3/2 shells--an example of "pairing-energy". There are only three other known examples of odd-odd (Z-N) isotopes that are stable against beta-decay: deuterium, lithium-6, nitrogen-14.

But this leads to another question. Why does boron-10 convert to lithium-7 and alpha particle when it absorbs a low energy neutron ?--why does it not just convert to stable boron-11 ? Is there more energy in the added neutron than is needed to form stable boron-11 ?

B-13 will have even smaller neutron cross section, since it have 8 neutrons - a magic number.
This statement I do not understand. B-13 does not have a smaller cross section than boron-11. Boron-13 has a neutron cross section = 767 barns, boron-11 has cross section of 0.0055 barns:
http://www.site.uottawa.ca:4321/astronomy/index.html#boron13
Boron-13 is also beta unstable, with half life of 0.0174 sec. Boron-11 is beta stable.

So, the concept that magic neutron number = 8, thus isotope is more stable, does not work for element boron. Boron-13 isotope (which has a magic # = 8 neutrons) is neither more stable, nor has smaller cross section, than non-magic boron-11 isotope. Also, the concept that having completely filled first three shells with neutrons (1s, 1p_3/2, 1p_1/2) thus leads to great isotope stability is falsified with boron-13.

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malawi_glenn
Homework Helper
In reallity there are more paramters than just the magic numbers and so on, they no not work 100%. This is due to the fact that the nuclear shell model is just a model, and works best for medium sized nuclei wich are stable. {I didnt look up if B-13 was stable;-) }

I dont have the time really to look up why B-10 absorbing a thermal neutron decays into Li-7 + alpha but it should the explanation you mention. Alos you do not say what "low energy" means here.

And can I ask, how can we keep the neutrons, which want to escape, in the chain reaction? In my book says that it can be done by neutron caputre or neutron diffusion. I don't understand what they mean. PLease help! Thanks.

malawi_glenn
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In what situation? In a nuclear power plant reactor or in a nuclear bomb?

Thay said it in general, the important is to keep the coefficient constant. Is their statement correct?

In nuclear power plant.

malawi_glenn
Homework Helper
what 'constant'? Have you confused this thread with another one of yours?

Neutron capture is when you 'stop' a neutron from moving away. So you have great neutron absorbing material in the between the fuel rods.

Then you want to have slow neutrons, so you have a moderating material, which works as diffuser, it does not stop the neutrons completley.'

That is the two main parts in a reactor. Then there are nuclei that absorb a neutron, then re-emit it again - over the whole solid sphere, so they can act as 'neutron-mirrors'. This you use in an atombomb, where one does not want to loose neutrons.

And also there is thing called reflectior, which reflects the neutrons, off, right? Is reflection and scattering similar proccesses? Because when there is scattering the neutron is bouncing off the nucleus, and in reflection also the neutron is bouncing off the reflector, right? Which is that "great neutron absorbing material in the between the fuel rods"?

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malawi_glenn
Homework Helper
one often uses boron (If i remember correct) as asbsorbing material between fuel rods.

Well neutron can be back-scattered, so that is a possibility yes.

Boron after some time releases the neutron? In other words, is it neutron-mirror?

malawi_glenn
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no i just think Boron absorbs the neutron.

In nuclear power plant there isn't neutron-mirrors?

malawi_glenn
Homework Helper
I am not an expert on nuclear powerplants. Maybe you could ask the nuclear power plant related questions you have in the "Nuclear engineering" subforum (it is a bit further down this one)

In my book says. To keep the chain reaction you need to put back the neutrons which are lost, by capturing or neutron scattering...

I think control rods are acting like neutron mirrors. I don't understand how neutron capture will prevent losing neutrons...

malawi_glenn
Homework Helper
Yes you have said that quite many times now...

There are several designs for how a nuclear powerplant works. In those that I have studied, the way you "gain" neutrons to make the chain reaction speed up is to just remove some of the boron-rods, wo you loose less neutrons if you see what I mean.
If you have U-fuel, they will spontaneous decay, to make neutrons, so in those reactors you never have the problem that you have too few. It depends on the situation, if the system is intrinsic under-critical, or intrinsic over-critical. The U-fuel is intrinic over-critical, that is the reason for why you need boron rods that can take up the neutrons before U-nuclei does it.

But, again, ask the questions in the nuclear engineering forum, they know about this more than I do, and more about what other types of reactors there are available.