ACTA DE INFRACCIONES LABORALES
4. INFORME SOBRE LOS CONTRATOS MERCANTILES CON RESPECTO AL BUQUE “POBRE MITROFÁN”
4.1 CONTRATOS DE EXPLOTACIÓN DEL BUQUE
Energy calibrations of the HPGe detectors were performed using room background lines and with nuclear reactions. Well-known room background lines below 3 MeV (40K, 208Tl) were used as low energy calibration points. In addition, spectra using natMgO were recorded by populating the well-known24Mg excited state atEx = 9967.8(3)keV, which decays to the first excited state
atEx = 1368.675(6) keV [End90] with the emission of nearly isotropic radiation. This isotropic
radiation yields a further energy calibration point.
During the experiment, gain instabilities caused peaks to shift in the spectrum several times. Fig.
5.9shows an example of this gain shift. These shifts meant that the calibration from24Mg could not be used without first applying a correction to the spectra recorded each day. In the experiment, there were two sets of runs: the calibration run in which decays from24Mg were observed, and the data runs containing room background lines. The data runs could initially be calibrated so that all background peak channels (Ci, whereirefers to the run number) coincide with the calibration run channels (Ccal). The second energy calibration using room background and24Mg could then be applied.
The initial calibration between data runs,i, and calibration run was performed according to
Ccal=aiCi+bi, (5.9)
whereaiandbiare the calibration coefficients needed to shift the channels of each run,i, to those of
the calibration run. The energy,E, is related to the calibration run through:
E =aCcal+b (5.10)
Combining these equations gives an expression with which each run can be individually calibrated:
E =aiaCi+ (abi+b) (5.11)
The parameters are obtained through separate linear model least-squares fits of known background γ-ray lines and the oneγ-ray observed in24Mg(γ,γ′). The known background lines used were from
1470 1480 1490 1500 1510 1520 1530 Channels 0 500 1000 1500 2000 Counts Run 5 Run 6
Figure 5.9: Effect of gain shift on detected peaks. The shift occurred during run number 6, and occurred
suddenly because two distinct peaks are visible for that run. This shift appears in all detectors. The cause of such shifts has not been found.
208Tl at E
γ = 1460.851(6)keV [Cam04], and from40K at Eγ = 2614.529(10)keV [Mar07].
Detector efficiencies must be known in order to obtain spin-parity assignments and decay branch- ing ratios. A combination of radioactive source measurements and Monte-Carlo simulations was used to obtain the full-energy peak efficiencies of the detectors (escape peaks were not used in the analy- sis). The radioactive sources used were60Co and56Co, which yield efficiencies up to aboutEγ= 3.5
MeV. The sum-peak method [Kim03] was used with60Co to obtain absolute efficiencies, independent of source activities.
Coincidence summing also occurs in the efficiency measurement of decays from 56Co. In this case, however, the effect can be assumed to be negligible because the decay is highly fragmented and the solid angles of the detectors are relatively small. For example, in the60Co spectrum for detector 1, the number of counts observed in the sum-peak (Eγ = 1173 + 1332keV) was 0.2% of the number
of counts in the Eγ = 1173keV peak. Any summing out effects, where counts are lost from a peak
caused by coincidence summing, will therefore be negligible. The56Co full energy peak efficiencies were then normalised to those measured with 60Co. The photo-peak efficiency of a detector can be approximated by [Tra99]:
ln εpγ
=a+bln(Eγ) +cln(Eγ)2, (5.12)
0 1000 2000 3000 4000 0.0010 0.0020
Photopeak Efficiency
0 1000 2000 3000 4000 0 1000 2000 3000 4000Energy (keV)
0.0010 0.0020 0 1000 2000 3000 4000 (1) (2) (3) (4)Figure 5.10: The full energy peak efficiencies of the four detectors used for the quantum number assignments
of excited states in26Mg. Detector 3 has consistently lower efficiencies because of its45◦ placement; the diameter of the beam pipe requires that the detector is moved to a further distance from the sample.
This approximation for the photo-peak efficiency is fit to the56Co data. The value of the fit at Eγ =
1173keV was used to normalise the 56Co efficiencies to the60Co data. The normalised photo-peak efficiencies of the four detectors are shown in Fig.5.10.
Monte Carlo simulations were then used to extrapolate full-energy peak efficiencies to higher energies covered in the present experiment. The Monte-Carlo code used for this experiment was Geant4 [Ago03]. A schematic of the geometry used in the simulation is shown in Fig. 5.11. The entire setup, including all four detectors was included in the simulations. This accounted for Compton scatteredγ-rays from one detector to another. The beam pipe was also included in the simulations to account for scattering of beam photons into the detectors. The effect of atomic absorption ofγ- rays in the sample was accounted for by including an extended MgO source, which emittedγ-ray s isotropically.
Figure 5.11: Geometry used in the Geant4 efficiency simulations. See text for details.
Simulations were performed at a variety of energies, up to about 12 MeV. Two separate simulations for60Co were also performed. One using an extended source, and one for a point source, to simulate the radioactive source measurements. This enables the correction of the source measurements to allow for a finite sample size. The simulated efficiencies can then be normalised to the radioactive source measurements. The normalisation factors needed to match simulated efficiencies with experimental efficiencies are shown in table5.3. In addition to an absolute normalisation of simulated efficiencies, the normalisation as a function of energy was calculated. If the normalisation is not constant over the energy range covered by radioactive sources, the geometry used in the simulation does not accurately reflect that of the true detector setup and efficiencies cannot be reliably extrapolated to high energies. Figure5.12shows the ratio of simulated and experimental photo-peak efficiencies for56Co as a func- tion of energy, which shows a slope consistent with unity. The simulated efficiencies, therefore, agree with experimental efficiencies. To reduce the uncertainties in the fit, a more extensive study would be required, which is outside the scope of the current project.
The results of the simulations are shown in figure 5.13. Detection efficiencies for individual full-
Detector Normalisation εp εT 1 1.0157 1.0538 2 1.0668 1.0730 3 1.0368 1.1556 4 0.9513 1.0299
Table 5.3: The normalisation factors needed to match simulated and experimental efficiencies.
1000 1500 2000 2500 3000 3500 Energy (keV) 0.6 0.8 1 1.2 1.4 Ratio
Figure 5.12: Ratio of simulated and experimental peak efficiencies versus energy. The solid line represents
a linear fit to the ratios, while the dotted lines represent the uncertainties of the fit. The fit parameters for the equationR=aE+barea= 1.4(1.6)×10−5
0
3000
6000
9000
12000
Energy (keV)
1e-05
1e-04
1e-03
1e-02
Full Energy Peak Efficiency
Detector 1 Detector 2 Detector 3 Detector 4
0
1000
2000
3000
4000
Energy (keV)
6.0e-04
2.0e-3
1e-03
Figure 5.13: Peak efficiencies for the four 60% HPGe detectors, as simulated in Geant4 (upper panel). These
efficiencies have been normalised to the60Co experimental point atE
γ = 1173keV, which in turn is corrected
for finite sample size. Differences in absolute magnitude of efficiency are because of differences in detector sizes, as shown in table5.1. The lower panel shows the agreement of simulated efficiencies with measured56Co
photo-peak efficiencies for detector 1.
energy peaks were obtained by cubic spline interpolation between simulated full-energy peak efficien- cies. The uncertainty of full-energy peak efficiencies nearEγ = 11MeV, arising from uncertainties
in both detector geometry and other experimental uncertainties were assumed to be 5%.