In this study, we explored the potential of a NaI(Tl) scintillator-based gamma spectrometer for the accurate determination of burial dose rates in natural geological samples using a full spectrum analysis (FSA) approach. In this method, an iterative reweighted least-square regression is used to fit calibration standard spectra (^{40}K, and ^{238}U and ^{232}Th series in equilibrium) to the sample spectrum, after subtraction of an appropriate background. The resulting minimum detection limits for ^{40}K, ^{238}U, and ^{232}Th are 4.8, 0.4 and 0.3 Bq·kg^{–1}, respectively (for a 0.23 kg sample); this is one order of magnitude lower than those obtained with the three-window approach previously reported by us, and well below the concentrations found in most natural sediments. These improved values are also comparable to those from high-resolution HPGe gamma spectrometry. Almost all activity concentrations of ^{40}K, ^{238}U, and ^{232}Th from 20 measured natural samples differ by ≤5% from the high resolution spectrometry values; the average ratio of dose rates derived from our NaI(Tl) spectrometer to those from HPGe spectrometry is 0.993 ± 0.004 (n=20). We conclude that our scintillation spectrometry system employing FSA is a useful alternative laboratory method for accurate and precise determination of burial dose rates at a significantly lower cost than high resolution gamma spectrometry.

#### Keywords

- NaI(Tl) detector
- scintillation gamma spectrometry
- full spectrum analysis (FSA)
- minimum detection limit (MDL)
- burial dose rate measurement
- OSL dating

In the trapped charge dating community, no matter what techniques and facilities are used, it is important to compare results between different laboratories to show they are all able to measure the same age for the same sample. Such intercomparisons have been well carried out in radiocarbon dating (Scott

In a recent preliminary study, Bu ^{40}K, ^{238}U, and ^{232}Th activity concentrations of 25, 4.8, and 2.5 Bq·kg^{–1}, respectively. (MDL is defined here as the activity or activity concentration for which the random uncertainty is 30%, Bu ^{–1}, respectively. Even though these MDLs are close to or below the lower limits found in most natural sediments, lower MDLs, especially for ^{238}U and ^{232}Th, are desirable to achieve a burial dose rate with lower uncertainty.

In this study, we investigate the potential of a different approach – full spectrum analysis (FSA) (Dean, 1964; Hendriks ^{40}K, ^{238}U and ^{232}Th series in equilibrium) to the unknown spectrum (after subtraction of an appropriate background). When compared to the three-window approach, FSA uses considerably more statistical information from each spectrum, and the additional degrees of freedom provide a direct estimate of uncertainties from the fitting process; this is in contrast to the uncertainties in a three-window analysis, which are based only on counting statistics. Here we investigate the benefits of the FSA approach. The revised MDLs are compared with those from both the three-window analysis of Bu

The configuration of the experimental setup used in this study is essentially the same as the one reported in Bu

Because of atmospheric ^{222}Rn, there can be a correlation between background count rate and atmospheric pressure, season and room ventilation (Mentes and Eper-Pápai, 2015; Schubert ^{222}Rn contamination. Using this configuration, we have been unable to detect a significant change in background count rate in 6 measurements over a period of 33 weeks.

All natural samples were ignited at 450°C for 24 hours (to determine organic content) before grinding to <200 μm, and then mixing with high viscosity wax (Bottle wax, blend 1944, British Wax Refining Company) on a hotplate at ~80°C. A typical wax:sample mass ratio of ~1:2 gives a typical sample mass of 250–300 g in the final counting geometry. Sample and calibration standards are cast in the same cup-shaped geometry, with a wall thickness of 10 mm, an internal diameter of 80 mm and an internal height of 60 mm. Samples are stored for >20 days before counting, to allow ^{222}Rn to reach secular equilibrium with its parent ^{226}Ra. Inverted, the sample cups are placed over the top of the NaI detector for counting. Murray

In order to prepare uranium and thorium calibration standards, the appropriate IAEA certified reference material BL-5 (7.09 ± 0.03% U, NRCAN-1) or OKA-2 (2.893 ± 0.058% Th, NRCAN-2) was diluted in low activity quartz-rich sand (M32, Sibelco Belgium; ^{226}Ra 1.39 ± 0.08; ^{232}Th 0.85 ± 0.06, ^{40}K 6.8 ± 0.7 Bq·kg^{−1}, measured by an HPGe gamma spectrometer), ground to <200 μm. The diluted reference materials were then mixed with wax to give individual parent activities of ∼800 Bq per cup. For potassium calibration standards, analytical grade K_{2}SO_{4} (14.20 Bq·g^{–1} assuming stoichiometry, purity given by the manufacturer as 100.4%) was mixed directly with wax to give ∼2700 Bq per cup. From the calculation, the expected uncertainties arising from the weighing process are <<1%. Three standards were prepared from separate dilutions for each radionuclide (named as K1-3, U1-3 and Th1-3, respectively). A background sample cup was prepared by casting pure wax. In order to correct for the gain drift caused by temperature changes during counting the algorithm described in Bu ^{40}K, ^{238}U and ^{232}Th. This spectrum was derived from a mixed sample of ^{40}K, ^{238}U and ^{232}Th (named KUTh reference), prepared by diluting BL-5 and OKA-2 in K_{2}SO_{4} to give a sample cup containing ∼2700 Bq of ^{40}K and ∼70 Bq of ^{238}U and ^{232}Th, respectively. The activity ratios of the three nuclides in this KUTh reference sample are chosen to be similar to the average ratio of ^{40}K, ^{238}U and ^{232}Th activities in natural geological samples (e.g., Ankjærgaard and Murray, 2007 and references therein).

Because our NaI(Tl) scintillation detector is insensitive to low energy photons, photons emitted by ^{222}Rn short-lived daughters dominate the U-series spectrum; given secular equilibrium between ^{222}Rn and ^{226}Ra (ensured by casting in wax and storing), our U analyses are actually ^{226}Ra analyses.

The full spectrum analysis algorithm used in this study requires considerably more stringent energy stability across the entire spectrum than does the three-window algorithm. After the measurement, spectra from unknown samples, and background and ^{40}K, ^{238}U and ^{232}Th calibration standards were all energy corrected to the common reference spectrum from the KUTh reference sample before spectrum analysis. The linear correction algorithm (with an intercept) corrects two specific peaks in each spectrum to the two corresponding peaks in the reference spectrum. The correction algorithm is described in Bu ^{40}K calibration standard spectra (in which other peaks are only derived from the background, and so are poorly defined).

The gamma spectra from the background, ^{40}K, ^{238}U and ^{232}Th calibration standards and unknown natural samples all have characteristic peaks of very different absolute and relative intensities; as a result, the most useful reference peaks are dependent on the spectrum to be drift corrected. For example, natural samples usually contain significant activity concentrations of ^{40}K, ^{238}U and ^{232}Th, and so drift correction employs the ubiquitous ~85 keV peak (X-ray) from U and Th, and the 1.46 MeV gamma-ray peak from ^{40}K. The same is true of background spectra although all the intensities are, of course, much weaker. However, this choice is impractical when we select reference peaks for the gamma spectra from calibration standards, e.g., in the ^{40}K standard spectrum, the X-ray peak is not detectable, and so the 1.46 MeV from ^{40}K emission and its Compton backscatter peak (measured at 226 keV) are used. This is in contrast to the more conventional choice of Bu ^{40}K) and the background 2.61 MeV peak from the ^{232}Th series were employed. We now prefer the backscattered peak because the background 2.61 MeV peak is too weak to allow accurate determination of the peak centroid. For the ^{238}U and ^{232}Th calibration standards, we selected the same peaks as those described in Bu et al. (2018), ^{238}U calibration standard with negligible ^{40}K, we employ the X-ray peak and the ^{214}Bi peak (1.76 MeV, U series); for ^{232}Th calibration standard, we use the X-ray peak and the ^{208}Tl peak (2.61 MeV).

^{40}K, ^{238}U and ^{232}Th calibration standards, a corrected background spectrum, and the KUTh mixed reference spectrum used for drift correction. The shaded region in

Cups from all three sets of ^{40}K, ^{238}U and ^{232}Th calibration standards (9 in total) were each counted for 20 h, then each spectrum was drift corrected to the reference spectrum, and normalised to counting time to give the count rate in each channel (counts·ks^{–1}). The background was counted three times (each for 20 h); after correction and normalisation, these three spectra were averaged. This averaged background spectrum was then subtracted from each ^{40}K, ^{238}U and ^{232}Th normalised spectrum. The detection efficiency (counts·ks^{-1}·Bq^{-1}) of each nuclide was derived by dividing the count rate in each channel with the known activity (Bq). Finally, the detection efficiencies resulting from three standard spectra were averaged to reduce the contribution to scatter resulting from manufacturing (mainly dilution and casting) of the calibration standards.

In FSA, the shape of a large part of the sample spectrum is analysed, and decomposed to determine the contributions from the three individual ^{40}K, ^{238}U and ^{232}Th standard spectra and the background spectrum. The counts in the first prominent peak (as shown in

Formalising the above, in each channel, the measured unknown sample spectrum ^{40}K, ^{238}U and ^{232}Th detection efficiencies _{k}_{k}

As we know the total number of channels in the energy range of interest is _{k}^{40}K, ^{238}U and ^{232}Th activities by minimising the chi-squared:

After obtaining the first estimate of the activities _{k,0}

In

In this way, those channels with a higher fitting error have a higher weight factor, giving a faster convergence. We carried out this process iteratively by continuously using a newly obtained

This process delivers a fitting error contribution of ~0.001 Bq·kg^{–1} for a typical >100 g sample.

The uncertainty analysis on the burial dose rate of natural samples is not a trivial task; there are many sources of uncertainty, both correlated and uncorrelated, contributing to the final propagated uncertainty on the burial dose rate. In this study, as usual, we categorise them into systematic and random uncertainties. The systematic uncertainties depend mainly on the standards we use to calibrate the ^{40}K, ^{238}U and ^{232}Th detection efficiencies on our NaI gamma detector. The random uncertainty includes the uncertainties contributed by the finite counts in each channel (counting statistics) and the fitting uncertainty arising from the fitting algorithm used to determine the activity concentrations. The details of the derivation of systematic and random uncertainties are summarised in the Supplementary Material.

Once the activity concentrations of ^{40}K, ^{238}U and ^{232}Th in the unknown sample are determined, we derive beta and gamma dose rates based on the dose rate conversion factors published by Guérin ^{40}K, and all U and Th decay series from the IAEA (IAEA Live Chart of Nuclides, March 2018). The revised activity concentrations per ppm are listed in

Updated ^{40}K, ^{238}U and ^{232}Th activity concentration per ppm for dose rate derivation.

Radionuclide | Activity concentration (Bq·kg^{–1}) | Uncertainty (Bq·kg^{–1}) |
---|---|---|

^{40}K | 317 | 3 |

^{238}U | 12.922 | 0.025 |

^{232}Th | 4.061 | 0.029 |

During the derivation of field beta and gamma dose rates, radon loss in the field is assumed to be 20% ± 10%; this is the default assumption used in our laboratory. In addition, we assume ^{226}Ra to be in equilibrium with its series parent ^{238}U. Both these assumptions can be varied on a site-specific basis.

The total dry burial dose rate was then calculated by summing the beta and gamma dose rates. Since the activity concentrations of the ^{238}U and ^{232}Th daughter nuclides are all dependent on activity concentrations of ^{238}U and ^{232}Th, respectively, the contributions from their individual uncertainties to the total beta or gamma uncertainties are correlated. In addition, beta and gamma dose rates are also correlated because they are all derived from the same ^{40}K, ^{238}U and ^{232}Th activity concentrations. During the summing of beta and gamma dose rates, propagation of these correlated uncertainties are handled by the uncertainty analysis tool

MDLs for ^{40}K, ^{238}U and ^{232}Th activities (or activity concentrations for a sample with a certain weight) are one of the most important specifications of a gamma spectrometer intended for the measurement of dose rates. In this study, we used the same procedures as described in Bu _{EXP}_{MEAS_20h}

These ten synthesised sample spectra were analysed by FSA and the apparent ^{40}K, ^{238}U and ^{232}Th activities (_{MEAS}^{.} Here we define the MDL as the value of _{EXP}_{MEAS}^{40}K, ^{238}U and ^{232}Th activities of 1.1, 0.09 and 0.07 Bq, respectively. By dividing by the maximum practical sample mass in our cup geometry (0.23 kg), the corresponding MDLs on activity concentrations for ^{40}K, ^{238}U and ^{232}Th are 4.8, 0.4 and 0.3 Bq·kg^{–1}, respectively.

Comparison of MDLs (Bq·kg^{-1}) from different studies.

Nuclide | NaI(Tl) spectrometer (Sample weight: 0.23 kg) | HPGe spectrometer (Sample weight: 0.25 kg) | |
---|---|---|---|

FSA (This study) | 3-Window (Bu | (Murray | |

^{40}K | 4.8 | 21 | 0.6 |

^{238}U | 0.4 | 4.0 | 0.04 |

^{232}Th | 0.3 | 2.1 | 0.03 |

The accuracy of the measurement and analyses can be examined in ^{40}K, ^{238}U and ^{232}Th, respectively. The deviations _{MEAS}_{EXP}^{40}K, ^{238}U and ^{232}Th, are normalised to the expected activity _{EXP}_{EXP}^{40}K, ^{238}U, and ^{232}Th analyses are all consistent with the expected results, without any obvious systematic error, even when the expected activities approach the MDLs.

The precision and accuracy of the FSA algorithm were further evaluated by comparison of our analyses with those from a high resolution HPGe spectrometry facility (Murray _{NaI}_{HPGe}_{HPGe}

In this study, all unknown samples, ^{40}K, ^{238}U and ^{232}Th calibration standard cups, mixed KUTh reference cup for drift correction and background cup were measured at a room temperature of ∼20–25°C for 20 hours. The maximum temperature drift during each measurement was ∼0.4°C.

As shown in _{NaI}_{HPGe}_{HPGe}^{40}K, ^{238}U and ^{232}Th for 20 samples lie within the shaded region of ±5%, with only one data point below -5% line in ^{238}U panel and another two just above +5% line in ^{232}Th panel. For the total beta and gamma dose rates (_{NaI}_{HPGe}_{HPGe}

In addition,

This is also indicated in _{NaI}_{HPGe}_{NaI}_{HPGe}

Average ratios of AC_{NaI}/AC_{HPGe} and DR_{NaI}/DR_{HPGe} (n=20).

Average ratio | |
---|---|

^{40}K | 0.995 ± 0.005 |

^{238}U | 0.984 ± 0.005 |

^{232}Th | 1.005 ± 0.006 |

Total dose rate | 0.993 ± 0.004 |

Another important consideration when using a gamma spectrometer for measuring dose rates in OSL dating applications is the counting time. The required count time is dictated by the required dose rate uncertainty and the sample activity. As discussed above, the total uncertainty on dose rate is mainly derived from random and systematic uncertainty in ^{40}K, ^{238}U and ^{232}Th activity concentrations. While the systematic uncertainty is fixed (at ~2%), the random uncertainty, no matter whether from the fitting error of FSA algorithm or from counting statistics, is mainly determined by the counts in each channel.

Quantitative investigation of the dependency on counting time was carried out by counting the same natural sample (LD962) for different lengths of time, ^{40}K, ^{238}U and ^{232}Th, and total beta and gamma dose rates, respectively, on counting time. The results are compared with those measured on the HPGe spectrometer for 20 hours, ^{-1} for activity concentrations of ^{40}K, ^{238}U and ^{232}Th and 1.09 Gy·ka^{–1} for total dose rate; these values are represented by the thick horizontal dashed lines in each sub-panel in _{NaI}_{HPGe}_{HPGe} (_{NaI}_{HPGe}_{HPGe} (^{40}K, ^{238}U and ^{232}Th and the derived dose rate, e.g. a 30 min count will lead to a ~±10% uncertainty on dose rate.

^{–1} of ^{40}K, ^{238}U and ^{232}Th, respectively and a dose rate of 1.09 Gy·ka^{–1}. These data allow the selection of the count time required to achieve a specified uncertainty. For example, even counting for only 1 to 2 hours gives a dose rate with a relative uncertainty ≤5%. A longer count of >5 hours brings down the uncertainty below ±3%. The sample used to illustrate these dependencies is amongst those with the lowest activity concentrations (see

We have investigated the potential of full spectrum analysis (FSA) algorithm for analysing gamma spectra from a low cost, low maintenance laboratory spectrometry system based on a 3”×3” NaI(Tl) crystal, to determine burial dose rates in trapped charge dating. Experimental results have shown that an FSA algorithm employing iterative reweighted least-squares regression is able to significantly lower the minimum detection limits (MDLs), down to 1.1, 0.09, and 0.07 Bq, respectively, for ^{40}K, ^{238}U, and ^{232}Th activities (corresponding to 4.8, 0.4 and 0.3 Bq·kg^{–1} for a 0.23 kg sample). These MDLs are one order of magnitude lower than those based on an improved three-window analysis approach (reported earlier by Bu ^{40}K, ^{238}U, and ^{232}Th from FSA are all almost one order of magnitude lower than those found in almost all natural sediments. We conclude that our NaI(Tl) gamma analyses based on FSA are suitable for determining the dose rate even in samples containing low activity concentrations of ^{40}K, ^{238}U and ^{232}Th.

The accuracy and precision on measurement and analysis of activity concentration and dose rate have been examined in 20 natural samples. The results are also compared to those measured using an HPGe spectrometer, and we found the relative discrepancies are all within 5% on activity concentrations of ^{40}K (RSD 2.2%), ^{238}U (RSD 2.5%), and ^{232}Th (RSD 2.7%), and within 4% on dose rates (RSD 1.6%). The average ratio of dose rates measured on our NaI(Tl) scintillation spectrometer with FSA to those from HPGe spectrometry is 0.993 ± 0.004 (n=20).

Further investigations of the dependence of analyses on counting time indicate that for a sample containing ~250, 10 and 10 Bq·kg^{–1} of ^{40}K, ^{238}U and ^{232}Th, respectively, even a 1–2 hours count time gives a result with uncertainty ≤5%. A longer counting, e.g. for 5 hours quickly brings down the uncertainty below ±3%. This demonstrates that using FSA with our NaI(Tl) spectrometer is capable of rapid and accurate determination of burial dose rate.

Given these results, we conclude that our simple scintillation spectrometry system employing FSA is a useful alternative laboratory method for accurate and precise determination of burial dose rates at a significantly lower cost than high resolution gamma spectrometry. This, combined with the relatively large (and so more representative) sample size, makes it a strong competitor to other analytical methods used in OSL dating.

Supplementary material is available online at ^{40}K, ^{238}U and ^{232}Th activities.

#### Average ratios of ACNaI/ACHPGe and DRNaI/DRHPGe (n=20).

Average ratio | |
---|---|

^{40}K | 0.995 ± 0.005 |

^{238}U | 0.984 ± 0.005 |

^{232}Th | 1.005 ± 0.006 |

Total dose rate | 0.993 ± 0.004 |

#### Comparison of MDLs (Bq·kg-1) from different studies.

Nuclide | NaI(Tl) spectrometer (Sample weight: 0.23 kg) | HPGe spectrometer (Sample weight: 0.25 kg) | |
---|---|---|---|

FSA (This study) | 3-Window ( | ( | |

^{40}K | 4.8 | 21 | 0.6 |

^{238}U | 0.4 | 4.0 | 0.04 |

^{232}Th | 0.3 | 2.1 | 0.03 |

#### Updated 40K, 238U and 232Th activity concentration per ppm for dose rate derivation.

Radionuclide | Activity concentration (Bq·kg^{–1}) | Uncertainty (Bq·kg^{–1}) |
---|---|---|

^{40}K | 317 | 3 |

^{238}U | 12.922 | 0.025 |

^{232}Th | 4.061 | 0.029 |

^{3}He and radiogenic ^{4}He in the CRONUS-P pyroxene standard. ^{3}He and radiogenic ^{4}He in the CRONUS-P pyroxene standard

^{222}Rn) excluding the effects of forced ventilation and radon exhalation from soil and building materials. ^{222}Rn) excluding the effects of forced ventilation and radon exhalation from soil and building materials

^{21}Ne in quartz. ^{21}Ne in quartz

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