Orsay data: still looking for coincidences

The data: Run 105 (80 MeV 14C on nat C)
The sort routine: require exactly one good event (i.e. both ends of strip have good signal) in det 1 (downstream), and exactly one good event (i.e. both ends of strip have good signal, and the complementary strip in det 3 does NOT have a signal) in det 4 (downstream quad).

Strip number of hit in det 1


Strip number of hit in det 4


det 4 strip number vs det 1 strip number


I find that last plot quite encouraging: it looks just like this one (the simulation of the same thing), just with strip numbers reversed for det 1.
I don't think that necessarily means that most of what we're seeing is elastic scattering (although it strongly suggests that that's true), but it makes it highly improbable that it's noise at any rate.

Orsay data: looking for coincidences

The data: Run 105 (80 MeV 14C on nat C)
The sort routine: require exactly one good event (i.e. both ends of strip have good signal) in det 1 (downstream), and exactly one good event (i.e. both ends of strip have good signal, and the complementary strip in det 3 does NOT have a signal) in det 4 (downstream quad).

Trying to track which events in one detector match events in another detector.

First gate on a single strip in det 1 and see where corresponding events go in det 4. Here's the strip in det 1...


...and here are the corresponding events in det 4.


Now gate only on a selected bit of that strip in det 1: try to select the most intense part of the locus that I think looks like elastic scattering. Here it is...


...and here are the corresponding events in det 4. The fact that they are show up more in one side of the detector than the other is encouraging. There also do seem to be loci, although I'm not yet sure what to make of them.

Orsay: Simulations of coincidences

Reaction:

• Of alpha-alpha coincidences, where both particles are detected with good energies in both ends of the strips, 99% involve both particles hitting a single detector
• 4% of those events involve both alphas hitting the same strip

• the "upstream" detectors, 2 and 3, each have just over 40% of the two-alpha events, with the remainder being in the downstream detectors.
• Assuming that we can reconstruct the initial energies of the alphas from the energy they deposit, in some sort of sensible way, it should be possible to calculate a Q-value for the reaction from the two alpha energies and angles, with a fwhm of ~5oo keV

Elastic scattering:

• Strip vs strip, E vs E, and theta vs theta for the reaction products from 80 MeV ¹⁴C on ¹²C:
  

Distribution of theta hits for elastic scattering coincidences between dets 1 and 4:

--> we expect real ES events to occur mostly between 15-20' in det 1 and 69-75' in det 4; also 18' in det 1 corresponds to ~69' in det 4.

Alphas (just to check geometry)

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.

Orsay: attempting to gainmatch det 1

The above image compares data for the same strip of detector 1 for four different data sets: 80 MeV ¹⁴C beam on carbon target; 40 MeV beam on carbon; 40 MeV beam on gold; 80 MeV beam on gold. There are some features that clearly scale by approximately a factor of 2 as the beam energy increases, but it's not clear what those features are! Also there is a feature that seems to be in approximately the same location in all runs. I was initially trying to identify it as one of the expected elastic scattering loci, but now I'm wondering whether it isn't just an artefact of the ... amplifiers? pre-amps? since det 1 wasn't using the splitter boards, we can't blame those.
(The other thing that's obvious is the odd shapes of the loci: things that should be straight lines are either graceful curves or squiggles. No theories on that yet.)
Test: select two groups in det 1 and see where the corresponding events are in the quad. --> need to use run 105 for this test, because the 40 MeV C runs may have v. low energy coincidences in the quad, and the gold runs will have no coincidences at all.
Hypothesis: The upper group (the one that looks about the same in all runs) will correspond to noise or bad events in the quad, and the lower group will correspond to good coincidences.
...is there a way to eliminate bad quad events entirely? Could do a quick comparison: the current results (with the requirement that "good strips in det 1" greater than 0 and "good strips in quad" greater than 0), vs. the same data sorted requiring exactly one good strip in det 1 and exactly 1 in the quad. That way would miss some good events that also had noise, but *should* eliminate the bad events. Let's see. ...actually the opposite seems to happen: run 105 sorting with quad greater than 0 has more coincidences than sorting with quad = 1.


The figure compares the same data (strip 5 of det 1) with two different conditions: at least one hit in the quad vs exactly one hit in the quad. The colour scale is the same for both trials. The locus labelled "good" is what I think might be the real elastic scattering events. weird.

Try a different way of making the coincidence requirement: require exactly one good event in det 1 (both ends of strip fire), and exactly one very-good event in det 4, since it will get half of the real coincidences and most of the identifiable ones (both ends of strip fire and the complementary channel in det 3 doesn't fire).
The results are astonishing.
det 1 80 MeV carbon (run 105)

det 4 80 MeV carbon (run 105)

det 1 40 MeV carbon (run 106)

det 4 40 MeV carbon (run 106)


--What I was tentatively identifying as the "good" events have no real coincidences, while the "bad" events mostly do have coincidences. weird.

So now. Trying again to calibrate det 1.....

Orsay: real data

40 MeV ¹⁴C on gold: require at least one good event (both ends of the strip fire) in det 1; ignore quad. Energy vs position (along strip) spectra for all strips in det 1:



80 MeV ¹⁴C on gold: at least one good event in det 1. Energy vs position for det 1:



40 MeV ¹⁴C on nat C: at least one good event in det 1, plus at least one good event in the quad. Energy vs position for det 1:



...and energy vs position for det 4 (the best of the quad):



80 MeV ¹⁴C on nat C: at least one good event in det 1, plus at least one good event in the quad. Energy vs position for det 1:



...and energy vs position for det 4:



80 MeV ¹⁴C on nat C: at least one good event in det 1, plus at least TWO good events in the quad. Energy vs position for det 1:



...and energy vs position for det 4:

Orsay: simulate elastic scattering and reaction for 80 MeV

These are the things we're most likely to see from the 80 MeV natC run: elastic scattering (both particles) from the target ¹²C and the ¹⁶O contamination; and reaction products (¹⁸O and α). The simulations were done for all angles, without reference to the detector locations or energy ranges; those are indicated by the dotted black lines.
In detector 1, all of the elastic scattering products will be practically indistinguishable, with the ¹⁸O at a somewhat lower energy. In the quad, the forward detectors (4 and 5) may see two elastic scattering loci (or even three--the angular range for the 16O scattering is probably larger than I've shown) and some alphas, while the backward detectors (2 and 3) will see more alphas but no elastic scattering at all.

18Ne(d,p)

Alison says:

18Ne beam at 54 MeV with 8mm (probably FWHM) beam spot on CD2 target of 410 ug/cm2 thickness.
Detecting protons from (d,p) at backangles with LEDA at 74mm.
want to know resolution of protons, taking into account beam straggling, dead layer, angular width of strip and straggling, everything basically
excited states at 2.5 MeV, 4.033MeV, 4.140MeV and 4.329 MeV

Here's some results...
Simulated energy spectra for the innermost, middle, and outermost strips of the upstream LEDA:

When I try fitting a gaussian to the lowest energy peak in strip 0, I end up with a sigma of something like 300 keV.
Energy vs effective angle of strip: colours and sizes of markers indicate number of hits:

Orsay: simulate elastic scattering

80 MeV ¹⁴C on carbon



40 MeV ¹⁴C on carbon



80 MeV ¹⁴C on gold



40 MeV ¹⁴C on gold



These simulations include energy loss/straggling in the target and dead layer, along with the detector's energy resolution.
Bottom line: the gold runs should provide well-separated lines in det 1 and nothing at all in quad (so ignore it; no requirements at all on goodness-of-events in the quad), while the carbon events should be coincidences between det 1 and quad--maybe initial energy calibration of det 1?

Orsay status report

Two types of progress....

1. Data analysis.

• I have a working sort code, with various bells and whistles, including the ability to count the number of "good strips"--if a strip in det 1 has a good energy signal in both ends, the good strip count for det 1 is incremented. Similarly for the quad.
  
• I have reasonable gain-match parameters for detectors 2,3, and 4. Detector 5 may not have been biassed, and the gain-matching parameters look dodgy. These parameters are derived from the alphas--since we irradiated only the quad, the only way to gain-match detector 1 will be elastic scattering.
  
• I sorted the data for the alpha run and extracted the energy spectra of all the individual strips. Here's the results, for several of the better strips for one of the better detectors...
  

The energy spectra for several strips are displayed (jaggedy coloured lines) together with triple-Gaussian fits (red smooth lines) courtesy of Igor. X axis is channel number, not keV. (These spectra are for an intermediate stage in gain-matching, and were used to obtain the final parameters: the parameters were adjusted so that the centroids of the fitted peaks were all the same.) What emerges from these spectra is that the detectors have an energy resolution with σ=110 keV.
UPDATE: Here are simulations done using that value for the detector resolution, compared with a few of the better strips' data. The agreement is decent.

• The actual data...well, various different ways of sorting are presented pell-mell in this previous blog entry. Basically, the most conspicuous feature in the quad energy-position spectra is either noise or an artefact of the joining boards. As to which sorting option is the best, see...
  

2. Simulations and other calculations

• I've got a geometric code for my monte-carlo sims that reproduces (to good-enough accuracy) the final positions of the detectors. (It characterises their positions in terms of the radial distance and the thetaφ angles of their centres--thus omitting the slight skew-ness of all of the quad detectors.)
  
• the most basic kinematic calculations, done using jrelkin and neglecting all energy loss/straggling effects:
  

Energy vs. angle curves for all the elastic scattering reactions we did. (click for a larger version.) The dotted lines represent the energy/angular ranges of the detectors (det 1 and quad).


Angle-vs-angle curves: the angle of the scattered beam particle is plotted against the angle of the knocked-out target particle. The dashed boxes represent the areas where both particles' angles take them towards a detector....

...but the above graph doesn't really tell the whole story about what's a coincidence and what's not. In order for an elastic scattering event to give a coincidence, not only must both particles go in the appropriate directions, but they must also both have energies within the range of the detectors.
Update:


(sorry about the random change of sign on the x axis.) The above plot was made using cunning energy requirements on both particles: if a particle's angle is less than 40', its energy must be between 1 and 100 MeV, but if its angle is greater than 40', its energy must be between 1 and 25 MeV. The lines are drawn for the cases where those conditions are met for both particles and so the energies of both particles are such that coincidences can be detected. The lines that fall within the boxes indicate when the angles of both particles permit coincidences.
What this graph seems to indicate:

• There are no ES coincidences from the gold runs at either energy
• For the 12C and 13C runs, we don't lose much of the data by requiring coincidences
• There are absolutely no coincidences for which either particle is above 90', so no way of using ES data to get a position-to-angle measurement for detectors 2 and 3. It should, on the other hand, be possible to calibrate dets 1 and 4 and maybe 5.
  

Other things I'm checking out:

• the total efficiency of the detectors: both percent of solid angle and efficiency for detecting a triple coincidence from the reaction, taking into account the energy thresholds
• the resolution we can expect in the Q value we calculate

...but the most urgent question is really the one about the elastic scattering: if we can identify ES loci in all the detectors, we can confirm that the gainmatching parameters are good, and we can maybe get some kind of position-on-detector to theta calibration. So far it's clear that there is stuff present, at least in dets 1, 4, and 5 (dets 2 and 3 seem mostly to show randoms), but I haven't yet managed to identify any of it.
The way forward: do simulations quickly for a few elastic scattering cases, to give me an idea of what I'm looking for in the data; then move on to sorting actual runs. Use as a condition that there be at least one good strip in both the quad and det 1; also veto quad events on the complementary strip's signal, to get rid of the weird top features. (That's for the carbon(12/13) targets; for the gold target require at least one good strip total because we don't expect real coincidences.)

18F(d,p): various factors affecting resolution

The idea: use an ¹⁸F beam of some energy between 14 and 100 MeV on deuterated polyethylene target of some thickness between 10 and 100 μg/cm²: the reaction is ¹⁸F(d,p)¹⁹F*(α)¹⁵N. Detect either just the protons or all three final particles (p, α, ¹⁵N). Calculate the Q value corresponding to the final energies and deduce the excitation energy of ¹⁹F. See whether we can resolve the 6.497, 6.528 MeV levels. Because of the beam's energy loss and straggling through the target, using the proton's final energy to calculate Q might not give very accurate results, whereas the alpha's energy might be a more precise indicator of ¹⁹F's energy.

The input:

• 90 MeV ¹⁸F beam (corresponds to optimum beam energy of 5 MeV/u)
• 20 μg/cm² DH₂ target
• detectors with arbitrary granularity (i.e. pixel size): take the S2 as a starting point: test the effect of changing the theta (annular) strip pitch from 0.5 mm to 1 mm; test the effect of having 16 or 32 phi (radial) strips.
• energy/angular straggling parameters derived from SRIM

Things I've left out

• energy spread of the beam entering the target
• exact cross section (have assumed isotropic distribution in the centre of mass frame).
  

Test, independently, all the different possible contributions to the final Q resolution:

• energy loss/straggling and angular straggling of beam through the target
• energy and angular straggling of the outgoing particles through the target (assume we can reconstruct the energy perfectly, so count the energy straggling but not the energy loss)
• energy straggling of particles in the detectors
• energy resolution of detectors
• beam spot size
• granularity of detectors

Doing the calculations

• Monte Carlo simulation of reaction
• use relativistic energy/momentum to calculate Q (n.b. this is different from e.g. the LLN experiment, where non-relativistic energy/momentum were good enough)

Results
(click on the image for a larger version)

What the graph shows: the standard deviation of the Q values calculated using each different method.
"Qp" means the Q value calculated using only data from the protons; "Qa15" means that only data from the alpha and ¹⁵N are used; Qcalc means that a complicated bit of algebra is done to eliminate the proton and ¹⁵N energies and to reconstruct the beam energy before the reaction.
the different cases:

• "perfect": no energy losses: Q is calculated using the initial energies/angles of all particles
• "beam in target": the reaction takes place at a randomly chosen depth in the target, and uses the beam's modified energy/angle at that point
• "detector energy resolution": see what effect the detector's resolution has: add a gaussian with 15 keV fwhm to a particle's energy
• "particles in target": calculate energy/angle straggling of outgoing particles through the target
• "particles in deadlayer": calculate energy straggling of particles in the deadlayer: assume that the detector is flat and perpendicular to the beamline
• "particles in deadlayer, incidence angle = 0": same as above, only assume that the particles always hit the detectors square on.
• "beamspot size": assume that the beam has a circular profile, with gaussian shapes in the both x and y directions, with σ=1 mm: calculate the precise position of the particles on the detectors, 500 mm down- and upstream.
  
• "detector granularity (standard)": the detectors have 0.5 mm strip pitch and 32 strips in φ,are of infinite extent, and are located 500 mm down- and upstream: calculate the effective position of the particles on the detectors: i.e. the location of the middle of the pixels that the particles hit.
  
• "detector granularity: 16 phi strips": decrease the number of phi strips
• "detector granularity: strip pitch 1 mm": increase the strip pitch

The clever algebra method, Qcalc, does indeed do a better job than the α+¹⁵N method in accounting for the beam energy loss in the target, but that's about its only strength. In general it is decent when it comes to things that mostly affect particles' energies, but it's very sensitive to the particle's angles, so it can't handle granular detectors: the Q values for the realistic detectors range between positive and negative infinity.
The α+¹⁵N method isn't as bad as Qcalc for the granular-detector cases, but it's still pretty bad.
For Qp, the sizes of the spreads in Q introduced by the various factors are all roughly on the same order. They also all depend on the angle of the protons: in some cases they're stronger at backward angles, and in some cases weaker.

Calculate Qp, using all factors combined, and see what the total angular dependence is.
Input: detectors are perpendicular to the beam line, located at 500 mm from the target, and have 0.5 mm theta strip pitch and 32 phi strips; the beam has σ=1 mm; Q is calculated using (proton energy = initial energy + straggling through target + straggling through dead layer + detector resolution factor) and (proton angle = initial angle + angular straggling through target) and (beam energy = average beam energy half way through the target).
Results: Q value as a function of angle, for the two states of interest...

Distribution of Q values for high-angle protons (i.e. theta > 120')

It looks like it's at least possible in theory to make this measurement!

sketches for TuDragon

The drawings are on 1 cm grid paper, and are either to scale or to half scale.
The drawing of the lid indicates two o-ring grooves in the lid; those should go in the top surfaces of the inner and outer gas cells themselves.

Unsimulated Orsay data again

All images here use data from run 105 (80 MeV ¹⁴C on 50 μg/cm^{2 nat}C)

Singles data from all detectors
detector 1 (forward)


detector 2 (backward in quad)


detector 3 (backward in quad)


detector 4 (forward in quad)


detector 5 (forward in quad, possibly not biassed, and with dodgy gain-matching)


detector 1, requiring exactly 1 good quad event (and incidentally at least one good det 1 event)


detector 4, requiring exactly 1 det 1 good event and 1 quad good event.


detector 4, requiring exactly 1 quad event (and however many det 1 events; automatically eliminates complementary-detector events)


detector 4, requiring exactly one good event in det 1 (and as many quad events as you like)


detector 1, requiring exactly one good event in det 1


detector 4, requiring one good event in det 1 and at least 1 good event in the quad


detector 4, requiring one good event in det 1 and at least 1 good event in the quad: veto events with signals in the complementary strip


detector 4, requiring at least 1 good event in the quad: veto events with signals in the complementary strip