I Problem calculating Li-7 neutron - induced nuclear reaction

[CMTacoTophat]

TL;DR Summary

I'm having issues determining the exact details/mechanisms of the reaction, and online resources appear scarce.

Hello All,

Firstly, I'd like to apologize if any of this comes across as wrong or off-putting, as I am a completely new user. However, this question has been troubling me for months.

I'm trying to work out an experiment involving the reaction where Li-7 absorbs an incoming neutron, transforms into Be-8, and subsequently splitting into 2 alpha particles. However, working with it has been difficult, as I am not sure of several things witht he reaction:

1. Does the reaction go to Be-8 first, or essentially straight to the 2 alpha particles? I had read that Beryllium-8 is an "unbound" nucleus, which I believe means something to the order of it's inability to exist as a meaningful intermediate step in the reaction

2. For researching, how is it refferred to as? Continuing the above, would it simply be Li-7(n, a)a? or would it be something like Li-7(n, a)He-4, or even as the two separate Li-7(n, B-)Be-8 and Be-8 --> 2a?

3. Although I may be able to figure this out given the first two, if the answer is more complicated than Beryllium-8 existing as a complete intermediate or not at all (e. g., somewhere in the middle as one that impacts the following), how would I be able to calculate the energies of the resultant alpha particles?

Again, I am still relatively new to this deep of a level of nuclear/particle physics, so any additional info is welcome and appreciated.

Also, if it is worth anything, I can try simulating this using EMPIRE, which I downloaded for something like this. Unfortunately, I am not too well versed in using that software, so if the solutions to the posted questions have to be answered analytically, I can try doing that, but it may be somewhat of a struggle, so it's not really the preferential option for me.

Thanks in advance for any answers you all might have!

 

[Astronuc]

TL;DR Summary: I'm having issues determining the exact details/mechanisms of the reaction, and online resources appear scarce.

Li-7(n, a)a? or would it be something like Li-7(n, a)He-4

I've seen it different ways, including ⁷Li(n,2α). Both alphas would capture two electrons each and form ⁴He. ⁸Be is very unstable, such that it essentially doesn't have a half-life, not in the conventional sense. It's half-life is expressed as an energy, or differential energy, 5.57 eV (NNDC, BNL), which one can find in the Chart of the Nuclides. It disintegrates essentially instantaneously.

KAERI's data base shows half life of 6.8 eV - https://atom.kaeri.re.kr/cgi-bin/nuclide?nuc=Be8

One temporal estimate - 8.19×10⁻¹⁷ seconds
https://www.osti.gov/servlets/purl/1773479

 

[CMTacoTophat]

Thank you very much! I will look into this more when i get home

 

[CMTacoTophat]

I do see what you're saying. Beryllium-8 is so unstable it essentially doesn't exist as an intermediate step. Would you therefore be able to treat the Li-7(n, 2a) reaction as a single step in terms of physics (e. g., in calculating the outgoing energies of the alpha particles)? I assume then that you would calculate the Q-value with the initial mass being Lithium-7 and a neutron, and the final mass being 2 alpha particles.

Thanks again for the helpful response, and please correct me if I'm wrong.

 

[mfb]

It's short-living on human timescales but still long-living on nuclear timescales. Not that it matters: You get two alphas in opposite directions in the center of mass frame either way. There shouldn't be any spin shenanigans either.

 

[Ammaniya]

I do see what you're saying. Beryllium-8 is so unstable it essentially doesn't exist as an intermediate step. Would you therefore be able to treat the Li-7(n, 2a) reaction as a single step in terms of physics (e. g., in calculating the outgoing energies of the alpha particles)? I assume then that you would calculate the Q-value with the initial mass being Lithium-7 and a neutron, and the final mass being 2 alpha particles.

Thanks again for the helpful response, and please correct me if I'm wrong.

Yeah, that's pretty much the right idea. Beryllium-8 essentially collapses too fast to act as a stable step. So, treating it as a one-step reaction works for the Q-value calculation. Just make sure to double-check your mass values for accuracy. But honestly, it can get complicated, so I hope it all makes sense when you calculate it.

 

[CMTacoTophat]

Thank you all very much, your insight is invaluable, and I believe I can use this to move forward. One final question, however (and sorry if I'm asking too many of them), but I can assume that most of the energy released is split between the two alpha articles, right (given the small mass of the beta particle in going from lithium-8 to beryllium-8)?

 

[Astronuc]

NNDC shows ⁸Li has a half-life of 838.79 ms 35.
https://www.nndc.bnl.gov/nudat3/
8.19×10⁻¹⁷ seconds is much shorter than the half-life of ⁸Li
https://pripyat.mit.edu/KAERI/cgi-bin/nuclide?nuc=Li8
https://pripyat.mit.edu/KAERI/cgi-bin/nuclide?nuc=Be8
https://atom.kaeri.re.kr/cgi-bin/nuclide?nuc=Li8
https://atom.kaeri.re.kr/cgi-bin/nuclide?nuc=Be8
https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=3&isotype=all
https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=4&isotype=all
Compare with a muon half-life of ~ 1.56 microseconds, or mean lifetime of ~2.2 microseconds.
http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muonex.html
http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/lepton.html#c3
Or, the half-life of a neutron pion, 8.5×10⁻¹⁷ s
https://en.wikipedia.org/wiki/Pion
http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/hadron.html#c1

Some homework is required.

Edit/upate - I forgot the following attachment.

 

[CMTacoTophat]

Thanks for the help. I believe I have the correct alpha (kinetic) energy now pegged at around 10 MeV, taking it as a single-step, nonrelativistic scenario. Thank you all for your help!

 

[Astronuc]

I just thought of a related physical process - photoneutron production from ⁹Be(γ,n)2α, in which a gamma of ~1.667 MeV causes ⁹Be to eject a neutron leaving ⁸Be, which essentially promptly fissions into 2 alpha particles. The reaction is the basis of secondary (neutron) startup sources in nuclear reactors (LWRs).

 

[CMTacoTophat]

Thats fairly interesting, Ill have to look into that. Maybe ot can also provide additional insight