Detector Efficiency

The γ-ray detection efficiency in the running geometry was measured using three radioactive sources and the14N(p,γ)15O reaction, and was simulated using the Monte Carlo code Geant4 [26]. Two types of detection efficiencies were evaluated. Peak efficiency is the probability of detecting the full energy of aγ-ray emitted from a source. Total efficiency is the probability of detecting a nonzero energy of an emittedγ-ray. Combining the simulations and measurements, the peak and total efficiencies as a function ofγ-ray energy were constructed. The sum-peak method for a60Co source described in Ref. [29] was employed. The advantage of this method is that the source activity cancels out of the final equations and the measurement precision is determined solely by counting statistics.

The peak efficiency of detecting the Eγ= 1173 keVγray,ηp_γ1173, becomes

η_γp₁₁₇₃ = 1 W (θ) s Nγ1173Nγ22505 NtotalNγ1332Nγ2505+Nγ1173Nγ21332 . (4.1)

The number of counts in the Eγ = 1173 and 1332 keV full energy peaks of the 60Co spectrum are

given by Nγ1173and Nγ1332, respectively. The number of counts in the full energy sum peak located at Eγ = 2505 keV is denoted by Nγ2505and the total number of room background subtracted counts

Nγ1173 Nγ1332 Nγ2505 Ntotal W(θ)

112374_±349 105990_±330 2124_±47 750690_±866 1.0494

η_γp₁₁₇₃ η_γp₁₃₃₂ η₁₃₃₂t

0.01744 _±0.00031 0.01644_±0.00029 0.0829_±0.0012 Table 4.3: Measured efficiencies for Eγ= 1173 and 1332 keV lines from a60Co source.

due to the60Co source from Eγ = 0 - 2505 keV is denoted byNtotal. The measured γ-ray spectra

were extrapolated to zero pulse height for the determination of Ntotalto account for the low energy

thresholds of the electronics. Similarly, for the Eγ= 1332 keVγ-ray the peak efficiency is

η_γp₁₃₃₂ = 1 W (θ) s Nγ1332Nγ22505 NtotalNγ1173Nγ2505+Nγ1332Nγ21173 . (4.2)

The average total efficiency due to both the Eγ= 1173 and 1332 keV lines is given by

η_γt₁₃₃₂ = 1 W (θ) − 1 W(θ) s Nγ1173Nγ1332 NtotalNγ2505+Nγ1173Nγ1332 . (4.3)

The angular correlation coefficient,W(θ), is a function of the distance between the detector and target, the geometry of the HPGe crystal and the angular distribution of the radiation from the source [1, 29]. The angular correlation attenuation factor, described in Sec. 3.5.4, was calculated using a code written by Richard Longland that performs an analytical integration of the angular correlation between the two emittedγ-rays over the solid angle covered by the detector. Using Eqs. 4.1, 4.2 and 4.3, along with the measured count rates listed in Tab. 4.3, the peak and total efficiencies of an Eγ= 1173 and

1332 keVγ-ray were calculated. The results are presented in Tab. 4.3. These measured efficiencies were then used to normalize all other measured and simulated efficiencies.

The next step was to use56Co and152Eu sources to construct a relative efficiency curve. Since the 56Co source was weak it could be placed in the target position with the HPGe detector in the normal running position. No pile-up was observed in the detector. This close geometry required the application of coincidence summing corrections to the data. Coincidence summing occurs when two or more γ-rays from the same decaying nucleus interact with the detector. This is more likely to occur at highγ-ray detection efficiencies. The effects of coincidence summing will depend on the

total and peak detection efficiencies and can be corrected for if the branching ratios of each decay are known. These corrections were performed using a C program, sump.c, written by Richard Longland, following the matrix formalism presented in Ref. [30]. The summing corrected data points were then fit by an R code and normalized to the measured60Co efficiencies. The152Eu source was very strong, which required positioning the detector at a distance of 30 cm from the source, to reduce the effects of pile up. Summing corrections were, therefore, negligible and the detection efficiencies were simply scaled to the normalized56Co data using the Eγ= 1112 and 1299 keV lines from152Eu. This

produced a normalized efficiency curve for Eγ= 120 - 3600 keV.

The higher energy efficiencies were measured using the Elab_r = 278 keV resonance in14N(p,γ)15O. This reaction produces decays ranging in energy from Eγ= 763 - 7556 keV and spans the entire range

of energies needed for measurement of the direct capture component in17O(p,γ)18F at Elab_{p ≤}500 keV. These data were summing corrected and normalized using the normalized56Co fit and the Eγ=

1380 and 2373 keV lines. The result is a data set of measured efficiencies ranging from Eγ= 120 keV

- 7.56 MeV.

The running geometry was then simulated in Geant4 and the peak and total efficiencies were esti- mated. The resulting peak and total efficiencies were normalized to the measured Eγ= 1173 and 1332

keV efficiencies. Figure 4.3 displays the normalized Geant4 peak efficiency simulations, the mea- sured efficiencies from56Co,152Eu and the14N(p,γ)15O resonance data. The simulated efficiencies correspond well with the experimental data with the exception of efficiencies measured at Eγ <400

keV. This suggests that either the material thicknesses modeled in Geant4 are incorrect, or the actual detector geometry is incorrectly modeled. The152Eu source data were collected at a greater distance from source to detector than the running geometry. The first test was then to adjust the detector posi- tion in the Geant4 simulation and compare the simulated and measured efficiencies at Eγ <400 keV.

Simulations for detector to target distances of 28 and 33 cm were normalized using the same method as the simulations of the running geometry. Figure 4.4 compares the results of these simulations to the measured efficiencies from152Eu. Simulating the detector at a greater distance from the source pro- duces efficiencies that more closely correspond with the measured efficiencies than the simulations of the original running geometry. This suggests that the original discrepancy between the running geom- etry simulations and the measured efficiencies at Eγ <400 keV can be explained by a large source to

0 0.005 0.01 0.015 0.02 0.025 0.03 0 1000 2000 3000 4000 5000 6000 7000

Efficiency

Energy (keV)

Figure 4.3: Peak efficiency measurements in the 55◦ detection geometry compared to a normalized Geant4 simulation.

detector distance for the152Eu data. Also, the major peak of interest in the17O(p,γ)18F direct capture measurement will be the decay of the first excited state to the ground state (Eγ = 937 keV). At this

energy the measured and simulated efficiencies are in agreement.