Having problems finding an equation for radioisotope production yield

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Discussion Overview

The discussion revolves around finding an equation for calculating the yield of radioisotope production, specifically focusing on parameters such as target mass, irradiation time, and beam flux. Participants are seeking to derive a formula that can provide mass results based on given activity yields and other constants.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses difficulty in finding a suitable equation for radioisotope production yield and requests assistance in deriving a formula based on specific parameters.
  • Another participant suggests that most parameters are constants except for time, mass, and beam flux, and emphasizes the need for a realistic irradiation time given the long half-life of the radionuclide.
  • A participant indicates a desire for optimal mass results for a specific activity yield and questions the validity of existing equations, seeking clarification on how to relate beam current to beam flux.
  • There is a suggestion to simplify the equation by dividing it by flux and time, which one participant describes as basic algebra that should be familiar to those working in the field.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the appropriate equations or methods for calculating the desired results, and multiple competing views on how to approach the problem remain evident.

Contextual Notes

Participants express uncertainty regarding the availability of beam flux and the applicability of certain equations, indicating a reliance on specific assumptions and the need for further clarification on the relationships between parameters.

Who May Find This Useful

This discussion may be of interest to individuals involved in nuclear physics, radioisotope production, or those seeking to understand the calculations related to activity yields and irradiation parameters.

fissile_uranium
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TL;DR
I'm trying to find the required target mass for a specific nuclear reaction with a fixed yield and cross-section.
I am trying to get a plot, or a result for target like this:
ToS7w.png


I've found some equations for my requested results, but they are from the same person's articles and I couldn't find another source. I've searched for EOB and TTY calculations but couldn't really do something. Could you give me an easy equation to apply? Also there are equations from this link:
https://www.degruyter.com/document/doi/10.1515/ract-2013-2234/html

DRdl2.png


64FqF.png


Could you help me with the wanted results? What equation should I use?

Properties:

29.4 TBq
0.05 barns
45 (target molar mass)
59.1 years (produced radionuclide half-life).
 
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All parameters in your equation are constants or given except the time, the mass and the beam flux (calculate the decay constant from the half life). The flux you have to find somewhere. For the best rate (minimal target mass) you would assume "infinite irradiation time" (##t\gg\lambda##). That is not realistic with a half life of 59 years, so choose some realistic irradiation time.
 
@mfb I do not have the flux. And I want to get mass results for 29.4TBq/μA.h, just like the graph on top. But I do not have the equation. Are those real equations that give me mass or should I use another TTY equation?

I actually want something optimal, an optimal mass with an optimal time but to get there I think at first I need the mass information for 1 hour irradiation at 1 μA for the required activity yield. Also is there some way to transform beam current to the beam flux?

Sorry I am very new at these calculations.
 
fissile_uranium said:
And I want to get mass results for 29.4TBq/μA.h, just like the graph on top.
Then divide the equation by the flux and the time.
This is elementary algebra, things you should have mastered 10+ years before working on formulas for radioisotope production.
 
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