Is there a program that can run depletion calculations in reverse?

[atomicpedals]

TL;DR Summary

Given a quantity of an isotope (e.g. U236), is there a program to calculate how much of that isotope there was n years in the past?

I was having a conversation with a coworker and this question came up: is there a program like ORIGEN (or maybe even ORIGEN) to run decay calculations in reverse?

It's a relatively easy process to start with a given quantity of an isotope (e.g. U236), run it through a program such as ORIGEN, and estimate it's decay and production of daughters in the future. Is there a program to do the reverse? Input a quantity of an isotope x today to estimate how much of that isotope there was n years in the past?

I'm quite confident that I've probably equally overthought and under-thought this question (as you can tell, this type of modeling is not something I do regularly).

 

[Philip Koeck]

If U

Summary:: Given a quantity of an isotope (e.g. U236), is there a program to calculate how much of that isotope there was n years in the past?

I was having a conversation with a coworker and this question came up: is there a program like ORIGEN (or maybe even ORIGEN) to run decay calculations in reverse?

It's a relatively easy process to start with a given quantity of an isotope (e.g. U236), run it through a program such as ORIGEN, and estimate it's decay and production of daughters in the future. Is there a program to do the reverse? Input a quantity of an isotope x today to estimate how much of that isotope there was n years in the past?

I'm quite confident that I've probably equally overthought and under-thought this question (as you can tell, this type of modeling is not something I do regularly).

If U236 is at the top of a decay chain and isn't produced from anything else then it's just a simple equation. Unfortunately I don't know so much about various decay chains.

 

[anorlunda]

Input a quantity of an isotope x today to estimate how much of that isotope there was n years in the past?

The trouble is that the heavy elements didn't exist at the time of the big bang. Our solar system was formed from a dust cloud. The dust cloud included elements created and spread by earlier events such as supernovas. Therefore, backward extrapolation is only valid as far back as the most recent element production and spreading.

 

[rpp]

I agree with this.

If you are looking at a single isotope (say U235) that is only undergoing decay, then it is fairly simple just to solve the decay equations backwards.

However, if you are looking for detailed answers about a set of isotopes, it can be impossible. For example, there may have been short-lived isotopes present that have completely decayed away, so you've lost all information about them (as well as possible sources for other isotopes). Also, if you are looking for isotopes that were created by a source (like a reactor), you will need to know the reactor conditions in the past.