18F(p,α): update

Don Tomas el Sabio wrote:

The detector energy resolution for alpha particles and oxygen ions
is ~10keV and ~80keV FWHM respectively plus (in quadrature) the dead
layer energy straggling.

If we consider 1H(18F,4He) at E_lab=6.5MeV (say) the beam energy
loss in a 50ug (CH2)n target is ~0.8MeV or E_CM = 0.300 - 0.345MeV.
Can you allow the beam to interact at random depths within the 50ug
and 100ug (CH2)n targets at the energy appropriate to that depth
(E_beam - dE) and, including the various effects on resolution, plot
the beam's actual interaction energy versus the sum of the 15O+alpha
energies (for given angles)?

Here's an update. This simulation is done using energy straggling parameters derived from SRIM, so more accurate (though at least for the alphas not much different) than what I had before. The interaction position is randomly chosen within the target (flat probability distribution). The beam loss/straggling is calculated up to that point. From then on, only straggling of the outgoing particles is taken into account--that is, I assume we can somehow correct for the average energy loss. There is also angular straggling included, which for the ¹⁵O is fairly large. The detector is an S2 at 100 or 500 mm downstream. The beam energy at the time of the reaction is reconstructed using the measured particle energy and angle (θ).
The simulations were done for two CH₂ target thicknesses (50 and 100 μg/cm^/2) with beam energies chosen to get 6.27 MeV in the centre of the target (6.7 and 7.1 MeV respectively).
Here's a plot of how the standard deviation of the reconstructed beam energy changes with different degrading factors (click for a larger version):

What this implies is that the (corrected, particle-dependent) energy resolution of the detector is by far the dominant factor in the resolution of the final measurement, if you're using a 50 μg/cm² target. The beam straggling through the thicker target can have an additional degrading effect, but everything else gets washed out.

Revised Update: try plotting the actual beam interaction energy as a function of the sum of E_α + E_15O, for a narrow range of alpha angles (choose 19-20'). (I tried making a similar plot for 5-7' and it was virtually identical.)



Same thing, 16-18', thick target: