18F(p,α): efficiency calculations

Revised May 14th--all-new photographic goodness.

The question: If we have one LEDA and three S2 detectors, where should we put them so as to maximize our efficiency for detecting coincidences?

Assumptions:

• The alphas are isotropic in the centre of mass
• We restrict ourselves to particles of reasonable energy: at least 300 keV deposited in the detector, to match a reasonable discriminator threshold. (This is actually a less stringent requirement than excluding all particles under 3', at least for forward angles.) (3' is the approximate scattered beam opening angle.)
• ¹⁸F beam energy 7.1 MeV (lab): no restrictions on how the reaction takes place, i.e. nothing explicit about resonances.
• ¹⁸O contaminant beam at the same energy; 50% contaminant.
  

Here's what the real energies and angles of the outgoing particles look like: assuming they hit annular detectors with thick (i.e. twice LEDA) dead layers. (Theta is the true angle of the particle, not the angle calculated by the detector.)



Here's an E vs E plot: energy of alpha vs energy of the 15O.



...and a theta vs theta plot: angle of 15O vs angle of alpha. The boxes indicate the angular ranges covered by a LEDA at 5 cm from the target and an S2 at 6 cm. This arrangement gives 50% coincidence detection efficiency; it would be even higher if we could move the detectors even closer to the target, but this is probably near the limit of convenient positions; and also past 70' the alpha energies start to get degraded by straggling through the target/deadlayer at a steep angle, and they may begin to be blocked by the target frame.



...the same thing, plotted using the program Igor to create a "binned" data set: each dot is colour-coded to represent the number of events within that particular 1'-by-1' bin. The boxes still represent the detector ranges.



Here's a plot of the summed energy (E_α + E_15O) as a function of alpha angle.


Interestingly, it may be easier to separate just the alphas from the different reactions than to separate the summed energy peaks, since the heavy ions suffer so much straggling in the target/deadlayer especially at low energies. See the following...



And here's a bonus: an image comparing E vs E for all events and for the measured coincidences.