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**Summary:**Problem: nuclear physics, neutron capture

In the problem one should calculate time dependence of number of nuclei.

**Problem statement:**

Neutron beam radiates sample A with initial number of atoms N

_{0}. With neutron capture nuclei (cores) of A are transitioning to nuclei B (they are just one neutron richer isotope).

A + n → B + ϒ

Expected time for neutron capture on core is equal to τ

_{N}. With an assumption that neutrons do not affect the sample B, calculate time dependence number of nuclei B if:

1. cores B are stable

2. cores B are unstable with average lifetime of τ

_{0}and they decay to the nuclei (cores) different then A

3. cores B are unstable with average lifetime τ

_{0}and they decay back to the nuclei (cores) A.

There are also two hints in helping problem to solve:

Hint 1:

Parameter τ

_{N}considers that contribution to the destroying of nuclei A with neutron captures is described as:

##(\dfrac{dN_A}{dt})_{capture} = \dfrac{-N_A}{\tau_N}##

Hint 2:

Sometimes it is useful to assume solution in advance, but sometimes it is easier to switch to the new set of variables like:

##\Sigma = N_A+N_B## and ##\Delta = N_A-N_B##

So, this is the problem. It is hard for me to actually attack it anyhow, because problem is generalized and what bothers me the most are conditions for 1, 2 an 3. On the other side, kind of confused with hint 2.

How should I treat here stable and unstable nuclei B. To just assume N/Z ratio, like even - even nuclei or similar. But the also to assume the same for nuclei A.

For any advice and help, thanks in advance!

**[Moderator's note: Moved from a technical forum and thus no template.]**

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