Varying dE/dx model: part II

So my hunch was correct:  the parameter $A \log (\Lambda)$ that I varied yesterday was not actually impacting the RIF spectrum (other than through the yield / peak burn time) because in fact it corresponds to a parameter in the $\alpha$ particle deposition model in the Garnier-Cherfils paper, and has nothing whatever to do with Jerry's RIF calculation.  That's why yesterday's plots were so unexciting.

Just to remind myself later, what is this $A$?  Well, if we have

$\frac{dE}{dx} \propto \frac{1}{E} G(y) \ln (\Lambda(y))$

where

$y=\frac{E}{\Theta} \frac{m_e}{m_{\rm particle}}$

and

$G(y) = \frac{A y^{3/2}}{1 + A y^{3/2}}$

Then the parameter $A$ affects the normalization, and it affects the energy at which the function $\frac{dE}{dx}$ rolls over.

Yesterday I got Jerry to expose the $A$ parameter, so I could make the plot I was intending to make in the first place. I have to say, the results are somewhat unexciting (although totally what Jerry predicted off the cuff):

What we see, not surprisingly, is that changing the parameter $A$ changes the normalization.  What I had hoped is that, since changing $A$ affects the energy at which $\frac{dE}{dx}$ rolls over, that the measured SHAPE of the RIF spectra would change noticeably as we monkeyed with this parameter (this might give us some hope of constraining in in an observation of the RIF spectrum).  Sadly, it looks as if the shape of the measured RIFS is probably just dominated by the shape of the underlying 14s, and  the dependence on $A$ is weak at best. Jerry: Incidentally, I tried to run the Zimmerman model for $\frac{dE}{dx}$, to compare its normalization and shape to these, however I am getting NANs or INFs, so that seems to be broken for the time being.

Indeed, the shape is almost TOO insensitive for me to believe, so I made a plot where I re-normalized all the curves to the $A=0.5$ curve, and my hunch was correct, there seems to be NO dependence on the shape... this seems odd to me...

Could this be good news?  It's probably just wrong of course, but it might also be an indication that we can argue that differences in the shape of the RIF spectrum come from mix, and are not affected by uncertainties in the model of $\frac{dE}{dx}$ in the strongly coupled limit....

Before we decide this is right though, I'd really like to see the shape of $\frac{dE}{dx}$ as we shift $A$.  Maybe Jerry's "test_stopping" functions would print this out?  I should see what it does...


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Addendum:  Here are plots of $\frac{dE}{dx}$ for the various values of $A$.  The roll over is moving slightly, but not as much as I was expecting given Anna's chalkboard drawings.  Still, seems to be doing the right thing.  I was surprised that Zimmerman seems to agree with A=0.5 much better than A=1...

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Addendum 2:  Jerry found a bug that affects all RIF plots made before this date.  Here is an updated version of the first plot in this post.

This does more what we'd expect: the asymptotic behavior is the same in each case.  The zimmerman curve (not shown here) has the same asymptotic behavior, but more rif neutrons around 14.6 than any of these models.