Coupled nuclear decay rate equations

[jmz34]

If we have the following partial decay chain:

N1 -> N2 -> N3 where N1 is the number of nuclei of species 1, etc.

and N1 -> N2, not via a decay but by the reaction such as N1 + neutron -> N2 + photon
and we know this rate of formation of N2, say 'a'.

I then get the following rate equation:

dN2(t)/dt=at-R2N2(t)=at-R2N2(0)exp(-R2t) where R2 is the decay rate from N2->N3

This would be simple to solve if the RHS wasn't coupled. By this I mean in a certain time, dt, there will be an increase in N2, dN2, which will couple into the N2(0) term and subsequently decay.

How would I go about solving this? Thanks.

 

[Astronuc]

If one knows the neutron flux, then the reaction rate is just ΣΦ = N(t)σΦ, where Φ is the neutron flux and σ is the microscopic cross-section of the reaction yielding the nuclide of interest. Then, one can take λ = σΦ for the reaction involving neutron absorption, and treat is the same as a decay constant for the reactant.