Measurement of the coincidence efficiency for detecting positron annihilation
gamma rays in NaI detectors.
Introduction and motivation
An experiment to measure the cross section for the 12C(n, 2n)11C reaction has recently been performed using
the 4.5 MV tandem van de Graaff accelerator at Ohio University. This measurement is needed to support the
development of an inertial confinement fusion (ICF) diagnostic for the National Ignition Facility (NIF).
The primary ICF reaction is the DT fusion reaction, in which deuterons and tritons in the nuclear fuel fuse to
produce 4He nuclei and release 14.1 MeV primary neutrons. These neutrons can then scatter elastically from
fuel ions, producing “knock-on” ions. These knock-on ions, which now have higher energies, can then fuse
with other fuel ions to produce so-called “tertiary” neutrons, with energies ranging up to 30 MeV. The ratio of
the tertiary to primary neutrons goes as (𝜌𝑅)2, and can also be used to study the hydrodynamic stability of
the implosion.
By placing graphite discs in the NIF target chamber the number of tertiary neutrons can be measured using the
12C(n, 2n)11C reaction. Since the threshold for this reaction is 20.2 MeV, tertiary neutrons are the only
neutrons produced in the implosion with enough energy to initiate this reaction; the reaction does not occur
for the much more numerous primary neutrons, with only 14.1 MeV. Once the graphite discs have been
activated by the tertiary neutrons, they can be removed and the number of 11C nuclei in each disk determined
by counting 11C beta decays. This is possible since the half-life of 11C is 20.334 minutes. From the number of
11C nuclei, the number of incident tertiary neutrons can be determined using the 12C(n, 2n)11C cross section.
Unfortunately, this cross section is not well measured. Figure 1 shows all known measurements [3-9] for the
12C(n, 2n)11C cross section. These measurements vary by as much as a factor of two in the energy region from
threshold up to 30 MeV. Even near threshold, where the measured cross section curves converge, the cross
sections still do not agree.
An experiment to measure this cross section in the 20-30 MeV energy range of interest was carried out during
the summers of 2012 and 2013 by researchers from Houghton College, SUNY Geneseo and Ohio University. In
this experiment, which was described in detail in the 2013 report [1] to the Laboratory for Laser Energetics
(LLE), deuterons from the accelerator were allowed to strike a thin tritium target, producing monoenergetic
neutrons via 3H(d,n)4He. As shown in in Figure 2, these neutrons could then hit two 12C-containing targets and
cause the 12C(n, 2n)11C reaction: a 1.64 mm thick, 2.54 cm diameter polyethylene target located 7.0 cm from
the tritium target, and a 7.62 cm diameter 0.89 cm thick graphite disc located 14.4 cm from the tritium target.
Neutrons striking the polyethylene target could also scatter elastically from the hydrogen nuclei present in the
material. A 17.46 mm hole drilled through the center of the graphite disc allowed these protons to be
counted by a dE-E detector telescope behind the graphite disc. By using the np elastic scattering cross section,
which has been well measured [2], the neutron flux on the polyethylene target was determined.
Figure 1. Previous measured and calculated cross sections [3-9] for 12C(n, 2n)11C. 3456789
Figure 2. The activation setup. Beam deuterons hit the tritium target just inside the end of the beam line.
Neutrons produced in the 3H(d,n)4He reaction then hit the polyethylene and graphite targets. The detector
telescope measures the rate of elastic np scattering.
Activated polyethylene and graphite targets were counted at three counting stations located in an adjacent
room, shown in Figure 3. After each was activated simultaneously, the graphite and polyethylene targets
were placed between pairs of 3 inch diameter by 3 inch thick NaI detectors. Coincidence events consisting of
two back-to-back 0.511 keV gamma rays from positron annihilation could be selected and counted as a
function of time. This allowed the decay curve of 11C to be measured and fit in order to determine the number
of 11C nuclei present. Pulses from all of these detectors were sent to a FastComTech MPA-4 system, which
recorded the pulse heights and timing information.
Figure 3. Three counting stations were used for the graphite target, the polyethylene target, and the graphite
shields. Positron annihilation gamma rays detected in coincidence were digitized and recorded using an MPA4 multiparameter system.
Cross sections can be extracted from the measured number of 11C nuclei, 𝑁𝐶11 , the number of elastically
scattered protons detected, 𝑁𝑃 , and the activation time, t, since
𝜎=
𝑁𝐶11
𝜆
𝑁𝑃 1
(
)
𝑇𝐶 1 − 𝑒 −𝜆𝑡 𝑁𝑛 𝑁𝑃
(1)
where 𝜆 is the decay constant for 11C, 𝑇𝐶 is the thickness in terms of carbon nuclei (carbon nuclei/cm2) and
𝑁𝑝 /𝑁𝑛 is the number of protons detected, 𝑁𝑝 , for a given number of neutrons, 𝑁𝑛 , striking the polyethylene
target. This quantity can be calculated using the geometry and the known 3H(d,n)4He [10] and np elastic
scattering [2] cross sections. The number of 11C nuclei can be determined by fitting the measured decay curve
with
𝑅(𝑡) = 𝑅0 𝑒 −𝜆𝑡 + 𝐴
(2)
where 𝑅(𝑡) is the rate at which positron annihilation gamma rays are detected at time t and A is the rate of
accidental background coincidences. The number of 11C nuclei present in the sample, 𝑁𝐶11 , is then
𝑁𝐶11 =
𝑅0 𝑒 𝜆 𝑡𝑡𝑟𝑎𝑛𝑠
𝜆 ∙ ε
where 𝑡𝑡𝑟𝑎𝑛𝑠 is the time between the end of activation and the start of counting, in other words, the time
required to transfer the samples to the counting station.
(3)
The only remaining quantity to be measured before the 12C(n, 2n)11C cross section can be determined is
therefore the efficiency, 𝜀. Not all the gamma rays that result from 11C decay enter the NaI detectors and are
counted – some go the wrong direction; some enter the detector but do not interact. The fraction of the 11C
decays that result in gamma rays being detected by the NaI detectors is called the absolute efficiency. If we
require that the full 511 keV of each positron annihilation gamma ray be deposited into each detector, this is
called the full-peak absolute efficiency, if we allow the gamma rays to Compton scatter and only deposit part
of their energy into the NaI detectors, then it is the total absolute efficiency. In order determine the full-peak
coincidence efficiency, a series of smaller experiments are being performed. These efficiency measurements
are being used to benchmark a Monte Carlo simulation. Once the simulation successful predicts the measured
efficiencies, it will be used to calculate the efficiencies needed to compute the cross sections for the
polyethylene and graphite targets in the 12C(n, 2n)11C experiment.
Direct Integration and Simple Monte Carlo Simulation
The simplest approach to calculating the efficiency of the NaI detectors is to use direct integration.
Unfortunately, this is only practical for point sources along the symmetry axis of the cylindrical detectors.
When considering extended sources located off axis and absorbers between the source and detector, it
becomes necessary to use Monte Carlo techniques.
In the simplest model [11], a gamma ray that interacts in the detector is considered to be detected. Since this
does not restrict counted events to those in which the gamma ray deposits its full energy into the detector,
this assumption leads to the total absolute efficiency. In order to obtain the full-peak efficiency from this, one
would need to know the peak-to-total ratio for the detector and geometry. This approximation may also
overestimate the efficiency because it assumes that any interaction will always result in a detected pulse. This
may not be true if the detection threshold is higher than the minimum pulse height.
3
2
N
aI

1
𝜃1
𝜃2
Figure 4. Point source along the axis of a cylindrical NaI detector. Gamma rays leaving the source can (1) miss
the detector, (2) enter the front face and exit the side, or (3) enter the front face and exit the back.
Figure 4 shows a point source along the axis of a cylindrical NaI detector. Gamma rays leaving the point
source can miss the detector, enter the front face and exit the side, or enter the front face and exit the back.
For those gamma ray paths that travel through the detector, distance Δ can be computed. This is the distance
the gamma ray travels through the detector. The probability that the gamma ray is transmitted through the
detector is 𝑒 −𝜇Δ where µ is the attenuation coefficient for NaI, so the probability of interaction is 1 − 𝑒 −𝜇Δ . If
the gamma rays are emitted isotropically, the solid angle can be integrated to obtain the total absolute
efficiency
𝜃1
∫0 (1
𝜀=
−𝑒
−
𝜇𝐻𝑑
cos 𝜃 ) sin 𝜃𝑑𝜃
1 − cos 𝜃1
𝜃2
∫𝜃 (1
1
+
−𝑒
−𝜇(
𝑅𝑑
𝑑
−
)
𝑠𝑖𝑛𝜃 cos 𝜃
1 − cos 𝜃1
(4)
) sin 𝜃𝑑𝜃
.
This technique can be extended [12] to include distributed sources that are off axis, and absorbers between
the source and detector. To do this, a Monte Carlo simulation was created which generates random gamma
rays properly distributed from within the source, with an isotropic angular distribution. The distance each
gamma ray travels through each absorber and the detector is then calculated and used to determine the
probability that the gamma ray will interact and be detected. Summing these probabilities allows the total
absolute efficiency to be calculated. A Monte Carlo code was developed using CINT and the ROOT data
analysis framework [13] to make these calculations and generate efficiency predictions for the experiments
described later. Approximately 100,000 gamma rays must be simulated to converge to a few percent
uncertainty in the efficiency for a distance of 10 cm. This takes about 12 hours on a 3.1 GHz core i5 computer.
Figure 5. Plot created by the Monte Carlo code in calculating the total efficiency for the off center, extended
source and NaI detector used in experiments described later. Gamma rays leaving the source (red points)
enter (dark blue) and exit (light blue) the steel case surrounding the silicon detector. They then travel to the
NaI detector where they enter (dark green) and exit (light green). The distance the gamma ray travels in the
absorbing material and the NaI detector allowed the probability of interaction, and hence the total absolute
efficiency, to be calculated.
Experiment Concept
Before looking at the actual experiment, let’s first consider how the positron annihilation detection efficiency
could be measured for a single detector using a beta coincidence technique. As shown in Figure 6, a 22Na
source emits a positron which can enter a silicon detector where it is detected and annihilates, emitting two
511 keV gamma rays at 180 to each other. One of these gamma rays could enter the NaI detector and be
detected. The full-peak absolute efficiency of the NaI detector is the fraction of the times when the silicon
detector indicates a positron annihilated that a 511 keV gamma ray is also detected in the NaI detector. To
first order, the fact that some positrons annihilate in other places does not matter, nor does it matter if the
efficiency of the silicon detector is less than 100%, since events that do not trigger the silicon detector are not
counted. However, positrons that are detected by the silicon detector but do not stop in the silicon detector
and annihilate elsewhere will affect the determined efficiency, as will Compton scattering events which scatter
gamma rays back into the NaI detector or knock Compton electrons into the silicon detector. These
occurrences can be reduced by making the silicon detector the proper thickness and decreasing the amount of
unwanted material surrounding the source.
Figure 6. Coincidence technique for measuring detector efficiency. Positrons from 22Na that annihilate in the
silicon detector produce gamma rays that can be detected in the NaI detector.
Feasibility Test
A preliminary experiment was performed to test the feasibility of this technique using only NIM electronics
and visual scalars. Figure 7 shows the setup of the detectors and source.
Figure 7. Detector setup for the feasibility test. Gamma rays from the small 22Na source annihilated is the
silicon detector, producing gamma rays which could be detected in the NaI detector.
Approximately 1 Ci of 22Na in a sodium chloride and water solution was deposited into a shallow indentation
in a 0.7 mm thick polyethylene disc and the water was allowed to evaporate. This disc was then sandwiched
between two 0.09 mm thick aluminum foils and placed over the entrance to an ORTEC silicon surface barrier
detector with 1500 m depletion depth and an active area of 25 mm2. A polyethylene end cap held the
assembly together and made a light-tight seal. Figure 8 shows the silicon detector source assembly. This
design minimizes the amount of material annihilation gamma rays leaving the silicon must penetrate to reach
the NaI detector.
Figure 8. Construction of the detector and source assembly used in the feasibility and singles efficiency
experiments. A 22Na source was deposited in front of a silicon surface barrier detector.
The surface barrier detector and source assembly was mounted to an optical rail with was used to position the
detector and source relative to the ORTEC 905-4, 3 inch diameter by 3 inch thick NaI detector, which was
powered by an ORTEC 296 integrated preamp photomultiplier base. In this detector, the NaI crystal is
surrounded by a 0.51 mm thick aluminum housing.
Figure 9. The electronics used in the feasibility experiment, which was implemented purely with NIM
hardware.
Figure 9 shows the electronics used in the experiment, which was implemented entirely in hardware using
NIM modules. Pulses from the silicon detector and NaI detector were amplified then selected using the timing
single channel amplifiers (TSCA). The time-to-amplitude converter (TAC) produced a pulse with amplitude
proportional to the time difference between the start (NaI detector) and the stop (surface barrier detector).
Using the single channel analyzer only coincidence events were selected and counted (𝑁𝑐𝑜𝑖𝑛 ). Another
counter was used to count the number of positron annihilations in the silicon detector (𝑁𝛽 ). According to the
argument above, the efficiency should then be
𝜀=
𝑁𝑐𝑜𝑖𝑛𝑐
.
𝑁𝛽
(5)
Figure 10 shows typical singles energy spectra produced by the silicon and NaI detectors. For the silicon
detector, the lower and upper limits of the TSCA were adjusted so that the entire positron spectrum was
included. For the NaI spectrum, the limits were adjusted to only include the peak at 511 keV, hence, this was
a measurement of full-peak absolute efficiency.
(a)
(b)
Figure 10. Histograms of the energy spectra from the (a) silicon and (b) NaI detectors. All events in the
positron spectrum were selected, but only gamma rays in the 511 keV peak (shaded) were counted.
Figure 11 (a) shows the pulse height spectrum from the TAC. A coincidence peak is clearly present, having a
FWHM of about 250 ns. Examining channels far from the peak allows an estimate to be made for the
accidental coincidence rate, which is relatively quite small.
In order to test the validity of the assumptions that were made in the design of this experiment, a series of
measurements of the full-peak efficiency were made with the lower level of the silicon detector TSCA set to
different voltages. At least to first order, changing the TSCA level should have no effect on the measured
efficiency since it is the fraction of positron decays that are detected by the NaI detector that is being
measured. Figure 11 (b) shows the results of this experiment, which are constant as predicted.
(a)
(b)
Figure 11. (a) Histogram of time differences between the NaI detector (start) and silicon detector (stop). Full
scale is approximately 2 µs. (b) Measured efficiency as a function of the lower level setting for the silicon
detector TSCA. For these measurements the source was centered 2 cm from the face of the NaI detector.
A measurement of the efficiency as a function of distance was made by setting the detector and source
assembly to various positions along the optical rail. The results of this measurement are shown in Figure 12,
along with previous measurements and calculations, and with the efficiencies calculated using Equation (4)
and with the Monte Carlo code. Because these calculations give the absolute total efficiency, to determine
the full-peak efficiency it is necessary to multiply by the peak-to-total ratio. Previous researchers [11] found a
value of 0.63 for this ratio, giving the light blue curve when applied to the results of Equation (4). The other
curves in Figure 12 are normalized to the measured value of the full-peak efficiency at 10 cm.
Once normalized to the efficiency at 10 cm, all of the curves – the point source direct integration of Equation
(4), and the Monte Carlo predictions for a point source and an extended source – agree well with the
measurements for large distances. This can be most clearly seen in the inset, which expands the scale for
distances greater than 5 cm. Moreover, for large distances the effect of the extended source is negligible, and
the extended source predictions agree with the point source model. At shorter distances, however, it is
observed that the extended and point source models disagree, as expected, and that predictions all
overpredict the measured efficiency. The previous measurements also follow this pattern -- they [14, 15]
agree for large distances, but they [12] are larger at shorter distances than we measured.
It was hypothesized that his behavior was due to 1275 keV gamma rays, which are emitted at the same time
as the positron in 22Na decay, entering the NaI detector and summing with the 511 keV gamma rays making
these pulses too large to be counted as full-peak events, and causing the measured full-peak efficiency to be
reduced.
Figure 12. Absolute full-peak efficiency as a function of the distance between the active silicon detector
(which acted as the positron annihilation gamma source) and the NaI detector. The measured efficiencies
(blue squares) are compared to the manufacturers value [14] (green triangle) and a previous measurement
[15] (light green diamond) at 10 cm. The full-peak efficiency was calculated from Equation (4) using the peakto-total ratio of 0.63 given by Tsoulfanidis [11] (light blue curve), and normalized to the value at 10 cm (dark
blue curve). The simple Monte Carlo code was used to predict the total efficiency the extended source (green
curve), which was then normalized to 10 cm requiring the peak-to-total ratio of 0.58.
Singles Efficiency Measurement
In order to test this idea, a new experiment was designed (Figure 13a) that would eliminate the possibility of a
1275 keV gamma ray entering the NaI detector at the same time as a 511 keV gamma ray. Just as before, 511
keV gamma rays from positron annihilation in the silicon detector were detected in the NaI detector. The
fraction of the silicon triggers for which the NaI detector detected a gamma ray is the absolute efficiency –
full-peak if the gamma ray deposited 511 keV, total otherwise. In this case, however, we also required that a
1275 keV gamma ray be detected in the “veto” detector, since we know if it was in the veto detector it could
not be in the other NaI detector.
(a)
(b)
Figure 13. (a) Experimental setup for measuring the efficiency without the effect of 1275 keV gamma rays.
Positrons annihilated in the silicon detector into 511 keV gamma rays with could be detected by the NaI
detector. Only those events for which a 1275 keV gamma ray was detected in the “veto” detector were
counted. (b) CAMAC and NIM electronics digitized the time difference between the detectors and the pulse
heights.
The silicon and NaI detectors were the same as used in the previous experiment. The “veto” detector wa
s a 3 inch diameter, 3 inch thick Bicron NaI well detector, with a 22 mm diameter, 1.5 inch deep well.
Introducing this new detector and its associated coincidence requirements meant it would be very difficult to
implement using NIM electronics only. Instead, the CAMAC system shown in (Figure 13b), was used to digitize
the time difference between pulses from the NaI and veto detectors and the silicon detector, and to digitize
the pulse heights from all of the detectors.
Figure 14 shows the electronics diagram for the experiment. Signals from each detector were amplified and a
logic timing pulse produced for each by the TSCA modules. The silicon timing pulse was used to start a LeCroy
3377 time-to-digital converter, the stop pulses were the timing pulses from the other two detectors. The
event trigger was the pulse from the silicon detector. Following an event trigger pulse, a gate generator was
used to deactivate the circuit for approximately 7 µs to allow time for the ADC conversion.
The timing pulse from the silicon detector was also used to form the gate for the ORTEC 413AD analog-todigital converter, which digitized the pulse heights from each of the detectors. A LeCroy 2551 scaler was used
to record the number of timing pulses generated by each detector for the purpose of calculating the live time.
The CAMAC modules were read out using the SCSI interface of a Jorway 73A CAMAC crate cpntroller into a PC
microcomputer running Linux. A custom C++ data acquisition code was written using the SJY CAMAC drivers
[16] from Fermilab and the ROOT data analyses framework [13]. The data were analyzed using a set of custom
ROOT macros.
Figure 14. Electronics diagram for the CAMAC system used to digitize time differences and pulse heights from
all three detectors.
In order to extract the efficiencies from the timing and pulse height information that were collected,
coincidence events were selected. Figure 15 shows a typical histogram of the time difference between the
silicon detector (start) and the NaI detector (stop). Events within the box were considered to be coincidence
events. The time spectrum for the veto detector was treated similarly. Figure 18 (a) and (c) show the energy
spectra from the NaI and veto detectors. The events selected are those in which 511 keV and 1275 keV were
deposited, respectively. Figure 18 (b) is the positron energy spectrum from the silicon detector. Figure 18 (d)
histograms the NaI detector pulse height for three-detector coincidence events having a 1275 keV gamma ray
in the veto detector and a good positron energy in the silicon detector.
The absolute full-peak efficiency is the ratio, 𝜀𝐹𝑃 = 𝑁𝐹𝑃 ⁄𝑁𝛽, of the number of coincidence events (𝑁𝐹𝑃 ) having
a 511 keV deposited in the NaI detector (the red box in Figure 18 (d)) to the number of positron annihilation
events in the silicon detector with a 1275 keV gamma ray in the veto detector (𝑁𝛽 ).
Figure 15. Histogram of the time difference between the timing pulse from the silicon detector and the NaI
detector. The x-axis is channels. FWHM of the coincidence peak is about 250 µs. The box represents the cut
that was applied to select good coincidence events.
(a)
(b)
(c)
(d)
Figure 16. Histograms of (a) NaI (b) silicon and (c) veto detector energy spectra, with the x-axis in channels.
The box in each case represents the cut that was applied to the spectrum to select 511 keV gamma rays,
positrons, and 1275 keV gamma rays, respectively. Energy spectrum (d) is a histogram of the energy
deposited in the NaI detector for coincidence events with 1275 keV deposited in the veto detector. The box
represents the cut applied to select events to use in calculating the full-peak efficiency.
The absolute total efficiency is similarly the ratio 𝜀𝑇 = 𝑁𝑇 ⁄𝑁𝛽, where 𝑁𝑇 is the total number of events in the
spectrum in Figure 18 (d). By using the total number of events in the spectrum, events where the gamma ray
Compton scatters in the NaI detector were included in the efficiency calculation. In this spectrum, the
Compton scattered gamma rays which deposit less than 511 keV are visible, and below the Compton minimum
energy of about 170 keV no events are present. It is not clear what is causing the small number of events with
pulses larger than 511 keV.
Using this technique, it is also possible to measure the peak-to-total ratio for the NaI detector as a function of
the distance from the source to the NaI detector. This was done by simply taking the ratio 𝑁𝐹𝑃 ⁄𝑁𝑇 , yielding
the results shown in Figure 17. The ratio over the region from 0.6 to 8 cm decreases slightly with distance,
and has a weighted mean of 0.5899 ± 0.0032, which can be compared to the value of 0.63 reported by Heath
[15].
Figure 17. Peak-to-total ratio for the 3x3 NaI detector as a function of distance to the source, with the source
along the axis of the detector. The ratio decreases slightly with distance, and has weighted mean is 0.59 over
the range from 0.6 to 8 cm.
A measurement of the efficiency as a function of distance was made by setting the detector and source
assembly to various positions along the optical rail and recording the timing and pulse height information for
about 24 hours. The results of this experiment are shown in Figure 18. In Figure 18 (a), the distance from the
source to detector was changed by sliding the source and silicon detector assembly along the optical rail, while
in (b) the distance was held at 0.6 cm and the source and detector assembly was scanned across the face of
the NaI detector. Both the total and full-peak singles efficiencies predicted by the Monte Carlo code agreed
well with the measured values in this experiment, which was taken as encouragement to proceed to the next
step, measuring the coincidence efficiencies.
(a)
(b)
Figure 18. (a) Efficiencies as a function of distance from source to NaI detector. (b) Efficiencies as a function
of source positon along the face of the NaI detector for a distance of 0.6 cm. In both plots, the absolute total
(red) and full-peak (green) measured efficiency (symbols) and the Monte Carlo calculation for the physical
silicon detector (dark curves) agree well. The Monte Carlo total efficiency for a point source (light red curve)
overpredicts the efficiency, and the measured full-peak efficiencies that are not corrected for 1275 keV
gamma rays (blue symbols) are below the prediction.
Coincidence Efficiency Measurement
Given the agreement of the Monte Carlo predictions for the singles efficiencies with the measured values
using the coincidence technique described above, the experiment was modified to measure the coincidence
efficiency, which is needed to extract cross sections from the data in the 12C(n, 2n)11C experiment. To do this, a
second NaI detector was included into the circuit, and a different silicon detector was used.
The silicon detector and source assembly in Figure 8, which was used in the singles experiments described
previously, was not well suited for the coincidence measurements. Annihilation gamma rays leaving the front
of the silicon detector penetrated very little material, but gamma rays exiting the back would travel through
the steel case, the microdot connector, and possibly the coaxial cable. In addition, since the 22Na source is
only on one side of the silicon, the distribution of positron annihilation events within the 1.5 mm thick silicon
would not be symmetric. For these reasons the silicon detector and source assembly was redesigned to use a
thin, transmission-mounted silicon detector. Figure 19 (a) shows the construction of the detector and source
assembly. Approximately 1 µCi of 22Na was deposited on the side of the polyethylene source foil facing the
Canberra fully-depleted PIPS silicon detector with active area 150 mm2 and depletion depth 300 µm. Because
this detector was so thin, the positrons deposited very little energy in the detector, and the pulse heights were
very small, at most a few tens of millivolts. In addition, although the positrons would annihilate in the silicon
with a uniform distribution, they could also punch through the detector and annihilate at an unknown location
further away. These facts, and also the large surface area of the detector, made it more difficult to simulate
and may partially explain the disagreement with model predictions later on.
The second ORTEC 905-4 NaI detector was mounted on the optical rail with its axis collinear to the first NaI
detector, as shown in Figure 19 (b), with the silicon detector and source assembly mounted between on a
vertical and horizontal fine-positioning stage. Figure 20 shows the additional channel for the second NaI
detector added to the electronics.
(a)
(b)
Figure 19. (a) Construction of the detector and source assembly used to measure the coincidence efficiency.
A 22Na source was deposited in front of a very thin, transmission-mounted silicon surface barrier detector. (b)
Experimental setup for coincidence efficiency experiments, showing the second NaI detector and new silicon
detector and source assembly.
Efficiencies were measured using the same technique as the singles efficiency measurement described above.
Events were selected in the same way as shown in Figure 16, with the addition of another cut on the 511 keV
events in NaI 2. Therefore, by using the proper criteria for selecting events, it was possible to determine the
singles efficiencies in both NaI detectors and the coincidence efficiency. The full-peak coincidence efficiency is
the ratio 𝜀𝐹𝑃 = 𝑁𝐹𝑃 ⁄𝑁𝛽, where the number of coincidence events,𝑁𝐹𝑃 , included events with all three TDC
time differences within the coincidence gates, 511 keV deposited in each NaI detector, 1275 keV deposited in
the veto detector, and a good positron energy. The number of positron annihilations in the silicon detector,
𝑁𝛽, contains events with good TDC coincidence time differences between the veto and silicon detector, 1275
keV deposited in the veto detector, and a good positron energy. The absolute total efficiency is similarly the
ratio 𝜀𝑇 = 𝑁𝑇 ⁄𝑁𝛽, where 𝑁𝑇 includes all events in the ADC spectra for NaI 1 and NaI 2 rather than just the
events in the 511 keV peak.
A measurement of the efficiency as a function of distance was made by coaxially setting the two NaI detectors
to approximately the same distance from the source and silicon detector assembly, and recording the timing
and pulse height information for about 24 hours. This was repeated for several NaI detector positons. It was
later discovered that the positioning of the silicon detector was incorrect, and, in fact, NaI 2 was about 0.65
cm closer to the center of the silicon detector than NaI 1. This fact was taken into account in the Monte Carlo
code predictions.
Figure 21 show the peak-to-total ratio (i.e. the ratio 𝑁𝐹𝑃 ⁄𝑁𝑇 ) obtained for this measurement. As before this
ratio is basically constant with distance from the source, and for the singles ratio is in agreement with the
value we measured previously. The coincidence peak-to-total ratio is also consistent with being constant, but
at a slightly lower value.
Figure 20. Electronics diagram for the coincidence measurement. An additional channel, identical to the first
NaI detector and the veto detector, was added for the second NaI detector.
Figure 21. Peak-to-total ratio for NaI 1 singles (blue), NaI 2 singles (red), and coincidences (green) as a
function of distance between the source and detector, with the source and detector coaxial. The line
segments represent linear best fits. In each case the measured ratio is consistent with constant peak-to-total
ratio.
The predictions of the Monte Carlo code are compared with the measured singles efficiencies as a function of
distance from the source in Figure 22. In this case the agreement is not as good as the agreement obtained
with the other silicon detectors (see Figure 18). For NaI 1, the code always underpredicts the total efficiency,
even at large distance where one might expect it to agree. For NaI 2 the code overpredicts at short distances
and underpredicts are large distances. The behavior for the full-peak is similar: at short distances the code
underpredicts for NaI 1 and overpredicts for NaI 2. Because of the symmetrical nature of the detector
arrangement, one would expect the plots for NaI 1 and NaI 2 singles to be the same. Since the only nonsymmetry is the silicon detector and source assembly, it seems reasonable that the difference is somehow
related to the source. Figure 23 shows the measured absolute total and full-peak efficiencies, which are
always smaller than the prediction of the Monte Carlo code.
(a)
(b)
Figure 22. Singles efficiencies for (a) NaI 1 and (b) NaI 2 as a function of distance from the source to the front
face of both NaI detectors. In both plots, the absolute total (red) and full-peak (green) measured efficiency
(symbols) and the Monte Carlo calculation for the physical silicon detector (dark curves) disagree, especially
for small distances. Also shown are the Monte Carlo total efficiency for a point source (light red curve), the
calculation from Equation (4) (blue curve), and the measured full-peak efficiencies not corrected for 1275 keV
gamma rays (blue symbols).
(a)
(b)
Figure 23. (a) Absolute total (red) and (b) full-peak (green) coincidence efficiencies. Predictions with no
absorbing material (light curve) and the physical detector and source assembly (dark curve) are compared
with measured values (symbols).
Another set of measurements was made by keeping the distance from the center of the silicon detector to the
front face of each NaI detector at 2 cm, and scanning the silicon detector and source assembly across the face
of the detectors. The results are shown in Figure 24 (a) and (b). In this experiment, the agreement with the
model for the singles efficiencies seems much better than for the distance measurements – more so than
would be allowed by Figure 22. The fact that the prediction agrees with the radial measurements while the
distance measurements, for which the offset mistake was modeled in the code, do not, indicates the distance
measurements may need to be repeated, with the source properly centered. Figure 24 (d) shows the
corresponding coincidence efficiencies as a function of radial position across the face of the detectors. In this
case, the models overestimate the efficiencies in agreement with Figure 22 at 2 cm. Interestingly, the
agreement is the best near the edges of the detector. The peak-to-total ratios plotted in Figure 24 (c) do not
depend on the position for the singles measurements, but seem to peak near the center of the NaI detectors
for coincidence measurements.
(a)
(b)
(c)
(d)
Figure 24. Singles efficiencies for (a) NaI 1 and (b) NaI 2, (c) peak-to-total ratio and (d) coincidence efficiency
as a function of source position across the face of the NaI detectors, for a source to detector separation of 2
cm. In (a), (b) and (d), predictions with no absorbing material (light curve) and the physical detector and
source assembly (dark curve) are compared with measured values (symbols) and the measured full-peak
efficiencies not corrected for 1275 keV gamma rays (blue symbols). In (c) the curves are linear or quadratic
fits.
Future Plans
One likely explanation for the difference between the efficiencies modeled by the simple Monte Carlo code
and the measurements is Compton scattering in the silicon detector case. In the Monte Carlo code, no
provision is made for tracking Compton scattered gamma rays and electrons, yet, for the silicon detector and
source assembly used in the measurements described so far, the amount of Compton scattering could be
significant. This is especially true for gamma rays traveling in directions other than directly toward the NaI
detectors, because the silicon detector is surrounded by a relatively thick steel case, which is then placed
inside aluminum and plastic end cap rings which hold foils to keep out ambient light. To address this problem,
two approaches are being pursued:
1. New source and detector assembly
A new detector has been designed to reduce the amount of material near the source. Two of the problems
with the transmission-mounted silicon surface barrier detector used previously was the large amount of
material near the detector and the small pulse heights due to the fact it was so thin. To reduce these
problems, a new small detector was made using a 9.5 mm square by 5.4 mm thick BC-400 plastic scintillator,
with wells milled on each side leaving a 2 mm thick membrane between the two sides. As shown in Figure 25,
approximately 0.5 µCi of 22Na was deposited in each well by dissolving it in water as a sodium chloride
solution, then allowing the water to evaporate. Acrylic cover slides, 0.24 mm thick, were glued across the
wells on both sides using cyanoacrylate glue. The plastic scintillator was glued to a 10.2 cm long acrylic light
guide, which was in turn glued to a Photonis 1-1/8 inch XP2902 photomultiplier tube, using Bob Smith
Industries 5-minute quick-cure epoxy. The light guide was wrapped in white Teflon tape, and then the light
guide and photomultiplier tube were wrapped with black electrical tape to keep out room light. A 0.17 mm
thick square of aluminum foil was placed over the plastic scintillator and taped down to provide a very thin,
light-tight enclosure. Using a home-made base produces pulses of approximately 200 mV.
Figure 25. The plastic scintillator and source assembly. 22Na is deposited in two wells, on each size of a small
plastic scintillator. Light pulses from the scintillator are detected by a phototube after travelling through an
acrylic light guide.
This detector was inserted into the experiment in place of the silicon detector and source assembly. An initial
test was made to ensure that the measured efficiencies did not depend on the energy deposited in the plastic
scintillator, similar to the experiment on the silicon detector in Figure 11 (b). In this experiment, data were
collected with the plastic scintillator TSCA lower level set to 1 V. When there data were replayed, the cut on
the plastic scintillator ADC was made 100 channels wide, and incremented in steps of 100 channels. The
absolute total and full-peak efficiencies were calculated with each ADC cut, and the results plotted in Figure
26. Figure 26 also includes the histogram of the plastic scintillator ADC for comparison. Notice the singles
efficiencies are in good agreement with each other, which is expected. All of the measured efficiencies are
consistent with being constant, as would be expected, out to at least channel 3000, where they begin to fall,
especially the coincidence efficiencies. From the ADC histogram, it is clear that this is near the endpoint of the
positron spectrum, and may be due to events where more energy is deposited in the spectrum than is possible
by the 22Na positrons alone, for example, by Compton scattering of gamma rays.
Figure 26. The absolute total (red) and full-peak (green) efficiencies (left scale) for NaI 1 (light squares) and
NaI 2 (light triangles) singles and coincidences (dark diamonds) as a function of energy deposited in the plastic
scintillator, in 100 channel bins. The energy spectrum from the plastic scintillator detector (blue circles) is
plotted (left scale) to allow comparison. The efficiencies are constant out to approximately channel 3000. The
detectors were coaxial with the source at a distance of 6 cm.
Currently a series of singles and coincidence efficiency measurements are being made as a function of
separation between the source and detectors, and as a function of radial position by scanning the source
across the face of the detectors at a fixed distance. Once these are complete, measurements with the source
inserted various distances into a graphite disc will be made, in order to set up conditions similar to those
encountered in the 12C(n, 2n)11C experiment. Finally, we will repeat these measurements with calibrated 22Na
and 68Ge sources obtained from NIST to check the consistency of the results.
2. New Geant4 simulation
This past summer, Mollie Bienstock, an undergraduate student from SUNY Geneseo, worked with Dr. Ryan
Fitzgerald in the Radiation Physics Division of the Radioactivity Group at the National Institute of Standards
and Technology (NIST). Dr. Fitzgerald is an expert on modeling radiation detectors and gamma ray counting.
This summer they worked on calibrating 22Na and 68Ge sources, which will be sent to Houghton College in the
next few weeks for the experiments described above. In addition, Dr. Fitzgerald has developed an initial code,
using the Geant4 toolkit [17], for the simulating the interactions of the gamma rays, electrons and positrons in
the detectors and source for the purpose of improving the model prediction of the efficiency.
Figure 27..Graphical representation of the graphite disc and NaI detectors produced by the initial Geant4
simulation code.
We plan to use the efficiency measurements to benchmark our Monte Carlo simulations, both the simple code
and the GEANT code. Once we are satisfied that the efficiencies given by the GEANT code are accurate to the
level needed for the 12C(n, 2n)11C experiment, we will use the code to calculate the efficiency for the actual
geometries used in the experiment.
Conclusions
In summary, an experiment to measure the cross section for the 12C(n, 2n)11C reaction between 20 and 27
MeV was performed during the summers of 2012 and 2013 using the 4.5 MV tandem van de Graaff
accelerator at Ohio University. This measurement is critical if carbon activation is to be used as a diagnostic at
the National Ignition Facility. This cross section is very difficult to measure; previous results vary by as much
as a factor of two in this energy range. The goal of our experiment, which was designed to address the
weaknesses of the previous measurements, is to measure the cross section to an uncertainty of 5%. The only
unknown remaining is the detector efficiency, which must be determined to an accuracy of about 5%. Work is
currently underway at Houghton College, SUNY Geneseo and NIST to measure and calculate this quantity. The
12C(n, 2n)11C experiment, which includes collaborators from Houghton College, SUNY Geneseo, Ohio
University, the Laboratory for Laser Energetics, and the National Institute of Standards and Technology,
comprises contributions from a number of collaborators with a breadth of expertise.
Presentations
Mark Yuly, Thomas Eckert, Garrett Hartshaw, Ian Love, Keith Mann, Tyler Reynolds, Laurel Vincett, Stephen
Padalino, Megan Russ, Mollie Bienstock, Angela Simone, Drew Ellison, Holly Desmitt, Carl Brune, Thomas
Massey. Ohio University, Ryan Fitzgerald, Mollie Bienstock, Craig Sangster, Sean Regan, “The 12C(n,2n)11C
Cross Section from 20-27 MeV,” Science and Technology Seminar, Laboratory for Laser Energetics, University
of Rochester, Rochester, N.Y., July 18, 2014.
Garrett E. Hartshaw, "A Measurement Of The 12C(n,2n)11C Cross-Section For Use As An Intertial Confinement
Fusion Diagnostic," B.S. thesis, Houghton College, 2014.
Garrett Hartshaw and Mark Yuly, "A Measurement of the 12C(n,2n)11C Cross-Section for Use as an Inertial
Confinement Fusion Diagnostic," XXXIII Annual Rochester Symposium for Physics Students, University of
Rochester, Rochester, NY., April 5, 2014.
Thomas Eckert and Mark Yuly,"Coincidence Efficiency of Sodium Iodide Detectors for Positron Annihilation,"
XXXIII Annual Rochester Symposium for Physics Students, University of Rochester, Rochester, N.Y., April 5,
2014.
Garrett Hartshaw, Ian Love and Mark Yuly, Stephen Padalino, Megan Russ, Mollie Bienstock, Angela Simone,
Drew Ellison, and Holly Desmitt, Thomas Massey and Craig Sangster, "Analysis of a Measurement of
12C(n,2n)11C Cross Sections," 55th Annual Meeting of the APS Division of Plasma Physics, Denver, Colorado,
November 11-15, 2013; Omega Laser Facility Users Group Workshop, Laboratory for Laser Energetics,
Rochester, NY, April 23-25, 2014.
1. S. Padalino, C. Freeman, K. Fletcher, E. Pogozelski, J. McLean, and M. Yuly, “Nuclear and Plasma Diagnostics
for4 the EP-OMEGA Laser Systems and the NIF,” 2013.
2. V.G.J. Stoks, R.A.M. Klomp, M.C.M. Rentmeester, and J.J. de Swart, Phys. Rev. C 48 792-815 (1993); V.G.J.
Stoks, R.A.M. Klomp, C.P.F. Terheggen and J.J. de Swart, Phys. Rev. C 49 2950-2962 (1994).
3. P. J. Dimbylow, Phys. Med. Biol. 25, 637 (1980).
4. B. Anders et al., Zeit. Phys. A 301, 353 (1981).
5. P. Welch et al., Bull. Am. Phys. Soc. 26, 708 (1981).
6. O. D. Brill et al., Dok. Akad. Nauk SSR 136, 55 (1961); F. Nasyrov et al., At. Energ. 25, 437 (1968).
7. T. S. Soewarsono et al., JAERI Tokai Rep. 27, 354 (1992).
8. Uno et al., Nucl. Sci. Eng. 122, 247 (1996); E. Kim et al., 129, 209 (1998).
9. J. E. Brolley Jr. et al., Phys. Rev. 88, 618 (1952).
10. M. Drosg, IAEA report IAEA-NDS-87 Rev. 5 (2000).
11. N. Tsoulfanidis, Measurement and Detector of Radiation, 2nd Ed. (Taylor and Francis, 1995), pp.392-395.
12. S. Yalcin et al., Appl. Rad. Isotopes 65 1179-1186 (2007),
13. Rene Brun and Fons Rademakers, ROOT - An Object Oriented Data Analysis Framework, Proceedings
AIHENP'96 Workshop, Lausanne, Sep. 1996; Nucl. Inst. & Meth. in Phys. Res. A 389 81-86 (1997). See also
http://root.cern.ch/.
14. 905 Series NaI(Tl) Scintillations Detectors manual, available from ORTEC.
15 . R.L. Heath, AEC Report IDO-16880-1, 1964 (revised electronic update, 1997).
16. J. Streets and D. Slimmer, Fermilab Report PN540 v. 1.9.2, 2002.
17. S. Agostinellia, et al., NIM A 506 250-303 (2003); J. Allison, et al., IEEE Trans. on Nucl. Sci. 53 270-278
(2006).