How is the Proton to Neutron Ratio Calculated After the Big Bang?

[electerr]

As I understand it, it can be calculated that 1 minute after the big bang, when protons and neutrons freeze out and are no longer being created, that for every neutron that exists there are 7 protons. Does anyone know what equation is used to calculate this and if it is not a equation that is used what is the reasoning used to get this number?

Thanks for the help!

 

[Chalnoth]

As I understand it, it can be calculated that 1 minute after the big bang, when protons and neutrons freeze out and are no longer being created, that for every neutron that exists there are 7 protons. Does anyone know what equation is used to calculate this and if it is not a equation that is used what is the reasoning used to get this number?

Thanks for the help!

Sorry, I don't remember off hand what the calculation is, but it's the sort of back-of-the-envelope calculation you can do to get a first blush estimate of big bang nucleosynthesis. Most cosmology texts should have the calculation.

 

[Chronos]

More importantly, neutrons cannot exist in a 'free' state for more than about 7 minutes. Why just 7 minutes is an interesting question.

 

[electerr]

More importantly, neutrons cannot exist in a 'free' state for more than about 7 minutes. Why just 7 minutes is an interesting question.

I thought the neutron's decay time is more like 15 minutes.

http://en.wikipedia.org/wiki/Neutron#Stability_and_beta_decay

Maybe your hinting that the decay time is slower at such high temps as there was during BBN...?

At the end of BBN, without neutron decay, I think it is calculated that the neutron/proton ratio is 1/6 but with neutron decay it becomes 1/7. I still have no idea what calculation that is used to conclude this though. I know many estimatinons concerning BBN stem from the Friedmann equation which is most likley used to calculate the energy density at BBN but how the ratio is calculated I am still not sure of... Anyone else have any info?

 

[Chalnoth]

I thought the neutron's decay time is more like 15 minutes.

http://en.wikipedia.org/wiki/Neutron#Stability_and_beta_decay

Maybe your hinting that the decay time is slower at such high temps as there was during BBN...?

At the end of BBN, without neutron decay, I think it is calculated that the neutron/proton ratio is 1/6 but with neutron decay it becomes 1/7. I still have no idea what calculation that is used to conclude this though. I know many estimatinons concerning BBN stem from the Friedmann equation which is most likley used to calculate the energy density at BBN but how the ratio is calculated I am still not sure of... Anyone else have any info?

Yeah, so, it's definitely not as simple as considering the Friedmann equation. That's only part of it. You have to consider the interplay between the weak force interaction rate (that converts protons to neutrons) and the expansion rate. I'm having difficulties finding a website, but I finally decided to look for the cosmology text I had been thinking of online. See here. It's only a preview, so you don't get the whole thing. But it looks like the essential pieces of the mathematics are there in pages 66-68. It may also be good to start with the introduction to nucleosynthesis on 62-63.

This is quite technical, of course, but it's got what you need if you really want to calculate this. Well, except perhaps for the missing pages which may produce some confusion. But it's got most of it there.

 

[elzem]

could you explain me what freeze-out means?

 

[Chalnoth]

could you explain me what freeze-out means?

Generally it means that there's not enough thermal energy around to excite that sort of activity. For example, water freezes when the rate for water molecules to accumulate in the crystal is higher than for them to be freed from it, which occurs when the amount of thermal energy available drops below a certain level. So, this would be a type of freeze-out (and is why freeze-out goes by this name).