Does anyone have a link or pointer to preferably freely available software with which I can calculate the energy spectrum of the electrons or positrons liberated in regular beta or beta+ - decay for a given isotope? My background is not in physics (chemical engineering, rather), and although I found the description of the theory of beta decay on HyperPhysics very useful, it doesn't tell me what C and F(Z', KE_e) are, or how to calculate them. Introductory texts on the quantummechanical theory of beta decay quickly went over my head, so these two unknowns remain a mystery to me. I'd be very grateful for any leads and/or help. (I know the spectra have in most cases been carefully measured and tabulated in thick data books, but for that I need to go to a library which is about 100 km away from me .)
There's roundabout way of doing this (I'm sure there are better ways). 1) from the loss in energy as the product decays, and using conservation laws (energy and momentum), you should be able to calculate the maximum and minimum energies of the electron/anti-neutrino pair (or positron/neutrino). As for the shape of the spectrum, I haven't gotten that far yet in my studies.
There is a general formula for the distribution of beta energy in beta decay. It looks something like - http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/beta.html#c5 I'll see if I can find a formula.
After hard searching, I came up with a text which writes out the equations in full. It did require a bit of Real World data to 'drive' the function, and then reminded me what a pain it is to work with density functions which must be normalised (and what an even bigger pain it is if you want to draw samples from that density function), but I got the job done. I have to say beta decay theory is a beautiful example of lots of approximations still yielding a very workable and useful result.