I work in applied mathematics and have no background in atomic physics. I need to have a good understanding of the principle and application of Gamma spectroscopy. I am ok to spend the needed time but would like not to spend too much time on avoidable subjects. I fell a bit lost into this subject and do not know what to begin with. If somebody can provide me a learning map (with online resources if possible) I will greatly appreciate.
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I am not aware of any specialized physics course being run for (and totally devoted to) Gamma-Ray spectroscopy in any university (I would love to stand corrected regarding this issue.) If that was the case, the nicest thing would be to post a link to the relevant webpage, and be done with it.
So, here is the map, I think, should work:
Arthur Beiser - ``Perspectives of Modern Physics'' -> Use this book only to grasp the basics of atomic structure and spectra. It also contains a lot of information regarding relativity etc. and lots of other great things - don't dive into that yet. (You will most probably never need to take into account relativistic effects on atomic spectra you would need in your field!) [Don't get me wrong! It is a great book to learn the rudiments of physics from, but you wanted an optimization of sorts, didn't you? You can read the rest of it in your leisure time.]
Now, advance to Gordon Gilmore - ``Practical Gamma-Ray Spectroscopy'' (This is the second edition of a book originally co-authored by another guy.) A limited preview can be found at Google Books. This is a pretty compact account of what one is basically doing with the technique. The first five chapters provide a pretty comprehensive coverage, though the later works have too much of instrumentation, which you may not need.
Actually, the reason for recommending 1. before 2. was that, 2. is not exactly tailored for a person who doesn't know the basics already. It is not too introductory.
Happy Learning :)
Based on your profile it looks like you're active in statistical verification. I'm guessing you're going to be working on data analysis so you might like a more lab or hardware oriented introduction.
This paper from Ian Rittersdorf briefly covers an introduction to the mechanisms, equipment, calibration and verification of experimental results.
Here is another tutorial focused on HPGe detectors that might be helpful and is more lab oriented.
Manufacturers often offer training courses (on-line and workshops) or consultation on their equipment. Depending on what equipment you are working on and how big of a customer your lab is, you might even be able to arrange personal assistance.