18F(p,α): factors limiting resolution

The idea:

18F(p,a)15O
18F beam, energy set to populate 330 keV resonance in 19Ne,
2mm beamspot
CH2 target, 50 and 100 ug/cm2
detecting alpha and 15O forward in silicon, say S2s

What is the resolution with which we can reconstruct the centre of mass energy for the two target thicknesses and what is the dominant factor affecting the resolution?

The simulations:

• The beam energy should be near 7.116 MeV (lab) to populate the compound-nucleus state of interest.
• The residual (¹⁵O) is in its ground state. (It would be straightforward to consider other excited states; just say the word!)
  
• All reactions were done assuming an actual energy where the reaction takes place of 7.116 MeV. There is probably actually a spread of energies around the resonance that will result in the state being populated, but I'm neglecting that for now.
• Use measured energy and theta for both outgoing particles (α and ¹⁵O) to calculate the energy the beam must have had (in the lab) at the time of the reaction: calculate the standard deviation.
  
• Each simulation was done using only one limiting factor. The graph below shows the results.
  

What the graph shows:

• standard deviation of Tbeam for all events (blue bars) and for coincidence events (i.e. both particles hit a forward S2 detector: unless the detector position is noted as 500 mm, it is 100 mm downstream of the target) (red bars).
• "perfect": no limiting factors: the beam energy is calculated using the actual initial values of energy and theta for both outgoing particles: there is no energy loss in the target or the dead layer, and the detector does not introduce any error in energy or theta.
• "ples in 50 ug tgt": the particles' energy straggling (not loss--we're assuming we can reconstruct the energy loss perfectly) in a 50 μg/cm² target is taken into account. The reaction position is randomly chosen to be anywhere in the target. This is an overestimate: the reaction may actually take place in a narrow range of positions near the centre of the target. Update: I did a simulation of the beam's energy loss to see over what range of positions the reactions were likely to take place: turns out it's like a gaussian with a fwhm of 2 ug/cm2 at the centre of the target for 50 ug/cm2 target. Putting that position distribution into the particle energy loss simulation doesn't change the results that much, actually: 1 keV for both "all" and "coincidence" cases, for 50 ug.
  
• "ples in 100 ug tgt": same as above, only assuming a 100 μg/cm² target. Like with the thinner target, the position range over which the reaction takes place isn't very important: the results using a realistic distribution (near the centre; gaussian with fwhm=5 ug/cm2) are 3-4 keV different from the results using a flat distribution over the whole target.
  
• "deadlayer": the particles' energy straggling in the deadlayer is calculated.
  
• "Erez": the detector is assumed to have an energy resolution of 50 keV for both particles: the measured energy of a particle is then its true energy plus a random number that has a Gaussian probability distribution with a fwhm of 50 keV.
  
• "det granularity 500 mm": Theta is calculated using the particle's hit position on the detector (if it starts on axis at the target) given the downstream detector distance of 500 mm, and a strip width of 0.5 mm: theta is the effective theta of the strip the particle hits.
  
• "det granularity 100 mm": same as above, only for a detector distance of 100 mm downstream.
  
• "beamspot 500 mm sigma=2mm": the detector is 500 mm downstream; the beamspot has a Gaussian probability distribution with a sigma of 2 mm; the effective theta of the particle is calculated from its hit position on the detector given that it starts off axis at the target.
  
• "beamspot 100 mm sigma=2mm": same as above, but the detector is closer.
  
• "beamspot 100 mm fwhm=2mm": same as above, but the Gaussian distribution has a fwhm (not sigma) of 2 mm.
  

(Click for a larger image)

What these results seem to show is that the dominant source of error is the detector itself: the loss in the detector dead layer, and its energy resolution. The resolution won't get dramatically worse using the thick target. I do tend to distrust the simulation results for energy losses of low-energy heavy particles in the dead layer though. I could do a Srimulation to check those numbers.

It's important to note that the alphas at backwards angles will have such low energies that they will stop either in the target itself or in the dead layer: above 90', all the alphas have an initial energy of less than 1 MeV. So it will be impossible to detect coincidences for the highest-cross-section ejectiles: we'll be restricted to detecting the lowest-cross-section part of the solution where both particles are going forward.