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I would note that Mn54 has a 300 day half life, and also emits at 834keV - you are likely seeing activation of material from the past neutron activity (Mn is a fairly standard alloying addition in steels and aluminum alloys).


What method should I use to find the best fit curve that satisfies the model constraints (quadratic at low x, linear at large x, anything goes for intermediate x) and fits the data as best as possible? It depends on what your goal exactly is, whether you want to find $\alpha,\beta$ as accurately as possible or whether you want "good fit" in the sense ...


Well the first step would be to plot $f(x)/x$. From this you should be able to identify two regions of linearity to which you can apply linear regression to find the $\alpha$ and $\beta$ constants: Without knowing the relevant physics or seeing the data, it's difficult to say what the best approach for handling the 'intermediate' region would be. If the ...

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