Determination of the gamma and X-ray emission intensities of terbium-161

In this study, the gamma and X-ray emission intensities of 161Tb were determined using a high-purity germanium spectrometer. The samples used were previously standardised by coincidence counting and Triple to Double Coincidence Ratio (TDCR) methods. A total of 28 gamma-rays and 4 X-rays were measured and compared with previous measurements performed more than 30 years ago. Most of the lines are in agreement, while large discrepancies are observed for 5 lines. The uncertainties have been dramatically decreased with respect to previous measurements giving a better knowledge of the 161 Tb day.


Introduction
Terbium-161 (E β-av = 154 keV (100%), T 1/2 = 6.953(2) d (Duran et al., 2020) is considered as an attractive radionuclide for targeted radionuclide therapy (Hindié et al., 2016;Lehenberger et al., 2011;Grünberg et al., 2014;Müller et al., 2014;Haller et al., 2016). It emits a considerable amount of conversion and Auger electrons per decay, which may cause an increased therapeutic efficacy over the clinically applied 177 Lu radionuclide (Champion et al., 2016). Recent preclinical studies performed with 161 Tb-PSMA-617 showed better in vitro and in vivo results as compared to 177 Lu-PSMA-617, which also support an additive therapeutic effect of conversion and Auger electrons of 161 Tb (Müller et al., 2019). In addition, its low energy gamma rays emission allows imaging using Single Photon Emission Computed Tomography (SPECT), where a good quality image can be obtained with an energy window centered at 74.6 keV (Marin et al., 2020).
Precise nuclear data information such as decay emission(s), the energy of the emission(s) and half-life are important to perform precise activity measurements, which is crucial for activity dosing and absolute image quantification. Terbium-161 decays to the ground and excited states of stable 161 Dy via nine main beta branches with endpoint energies ranging between 43 and 593 keV (Reich, 2011) (Fig. 1). The half-life of 161 Tb, 6.953(2) days, was recently measured by Duran et al., (2020). The present study aims at measuring the emission intensities of gamma and X-rays of 161 Tb.
Previous measurements of gamma intensities were performed before the 90's (Brockeimer and Rogers, 1965;Funke et al., 1966;Berg and Malmskog, 1969;Prasad and Nielsen, 1974;Hnatowicz and Dragoun, 1983;Vylov et al., 1984) and the different databases give close or compatible values, but with quite different relative standard uncertainties, which are more than 5-10% for the Joint Evaluated Fission and Fusion (JEFF), (JEFF, 2020) and lower for the Evaluated Nuclear Structure Data File (ENSDF), (ENSDF, 2020). Table 1 shows the intensities of the gamma lines in the different databases. Large uncertainties reported in all the previous measurements enhance the need for more precise emission intensity measurements.
In this work, the emission intensities 161 Tb lines are measured using the gamma-ray spectrometry set-up of the Institute of Radiation Physics (IRA) described in (Talip et al., 2021). The Paul Sherrer Institute (PSI) provided the mother solution which was diluted and characterized at IRA using a reference ionisation chamber (CIR). This chamber was calibrated using standardisation measurements as described in (Nedjadi et al., 2020). As a 160 Tb impurity is measured in the solution, the interfering gamma lines corresponding to this impurity were taken into account. The results of the gamma-ray emission intensities are presented and compared with the literature. 161 Tb was produced by irradiating highly enriched (98.2%) 160 Gd 2 O 3 targets in SAFARI-1 (South African Nuclear Energy Corporation, 2.10 14 n.cm − 2 .s − 1 ) nuclear research reactor. After irradiation, a twocolumn system was applied for the separation of 161 Tb from the target material at PSI (Gracheva et al., 2019).

Source preparation for activity measurement
The PSI provided a 161 Tb solution with 400 MBq activity in 1 mL. A carrier solution consisting of 0.1 mol L − 1 HCl solvent with a Tb +3 -ion concentration of 25 μg g − 1 was used to dilute at IRA the PSI sample by a factor of about 15 to prepare the master solution. Two 3 g aliquots of the master solution were dispensed into 5 mL glass ampoules for activity measurements in the CIR (Fig. 2.).

Source preparation for gamma spectrometry
The measured activity concentration given by the CIR measurement was 24.39(15) MBq/g at the reference date, 16.01.2020 at 12:00 UTC. An aliquot of 45.80(24) mg of the master solution was diluted into a 20 ml Zinsser plastic vial prefilled with terbium carrier so that the total mass was 20.02627(11) g. The total activity in the vial was 1116.84 (890) kBq at the reference date, 16.01.2020 at 12:00 UTC. This vial, then, was used for the gamma-ray spectrometry measurements (Fig. 2).

Gamma-ray spectrometry
The γ-ray spectrometry was performed using a n-type high purity germanium (HPGe) cylindrical detector, with 52 mm diameter and 53 mm height of germanium crystal. The detector is equipped with a 500 μm beryllium window and a 3.27 mm polyethylene absorber. The detector is surrounded by a cylindrical shielding with wall thicknesses of 10 cm of lead and 2 mm of copper. More details about the data acquisition and peak processing are given in (Talip et al., 2021).

Efficiency calibration
The data acquisition system as well as the full energy peak (FEP) efficiency calculation and the validation of the measurement method using reference samples are described in (Talip et al., 2021). The correction factors for coincidence summing are taken into account and calculated using the GEANT4 Monte Carlo simulation software with a decay scheme based on ENSDF data file (Allison et al., 2016).

Emission intensity
The emission intensity P γ is calculated according to: where N is the net number of counts in the peak area, t is the measurement live-time, A is the source activity and ε γ is the FEP efficiency.
C dec. is the correction factor for the source decay between the start of the measurement and the reference date, C meas. is the correction for the decay during the measurement and C sum. accounts for the coincidence summing correction. Terbium-161 source was measured 3 times on 01.16.2020, 01.20.2020 and 02.03.2020 at a source-detector distance of 15 cm and with a measurement time of 3.807, 1.854 and 1.715 days and a time of 13.5%, 10.6% and 2.5% respectively. Fig. 3 and Fig. 4 show the first spectrum measured where the impurity of 160 Tb can be clearly observed. The activity ratio 160 Tb/ 161 Tb calculated was (5.90 (39)).10 − 5 at the reference date. The contribution of the 160 Tb current produced in the CIR chamber for activity measurement was 0.1%, which was taken into account. As some of the 160 Tb's lines are very close to the ones of 161 Tb (Nucléide-LARA, 2018), the contribution from the impurity, for the X-ray lines at 45.999, 45.2, 52.2 and 53.6 keV as well as for the gamma line at 392.6 keV, is subtracted using the known activity value of 161 Tb, the impurity ratio and the emission probability of the 160 Tb lines. For the four X-ray lines, the 160 Tb contribution is very low, less than 0.1% of the total counts, whereas it contributes up to 6% for the gamma line at 392.6 keV. For the gamma line at 238.6 keV, there are two close lines at 237.6 and 239.7 keV, which can overlap. However, as their emission intensities are very low, only less than 4 and 2 counts respectively are expected to be measured in the detector, therefore, no contribution from 160 Tb is used for this line. For the line at 87.9 keV, the closest line of 160 Tb at 86.8 keV is found in the 3 measurements and no subtraction from 160 Tb is performed.

Terbium-161 gamma and X-ray lines emission intensities
The results of the gamma-ray intensities of 161 Tb measured at IRA are given in Table 1 as well as the values from the different databases. Each value corresponds to the average of the three measurement results. The uncertainty budget is detailed in Table 2 for the lines at 48.91, 74.49, 425.8 and 292.4 keV, chosen as the two most intense, with the largest relative uncertainty and with the smallest relative uncertainty, respectively. The correction factor for the decay during the measurement is 1.2018(2) for the longest measurement and the decay correction factor of the source activity for the reference time is 6.0265(5) for the last measurement performed on 02.03.2020.
A total of 32 lines were measured. The lines at 25 and 28 keV are below the energy threshold where the FEP efficiency is calculated and the line at 43.81 keV is hidden in the Compton continuum and cannot be measured.
For most of the measured lines, the statistical uncertainty is below 2% except for the lines at 315, 348, 425 and 506 keV, for which the largest uncertainty is 2.6% for the 425 keV line. The uncertainty of the efficiency is always below 2%, the largest being 1.9% for the 48.9 keV line and decreasing with the energy down to 1% at 550 keV. For all the lines, the uncertainty of the coincidence summing correction factor is small, around 0.5% or less. The uncertainty on coincidence summing correction factor for the main lines at 48.9, 74.6 and 57.2 keV are respectively 0.1%, 0.1% and 0.2%. Their correction factor is 1.0062, 1.0040 and 1.0048 respectively. As the source-detector distance is rather large, 15 cm, the correction factor is close to 1 for each line. The largest one is 1.0103 for the line at 238.6 keV and the smallest one is 0.9781 for the line at 131.8 keV. It is worth noting that, for the computation of the coincidence summing factor, the full decay scheme considered in GEANT4 is based on ENSDF data files. This may introduce a small bias in the computation of the coincidence summing correction compares to reality.
Among the 28 measured gamma lines, 22 for JEFF and 16 for ENSDF  Table 3 shows all the differences between the results from this work and the databases values. All the X-ray lines are compatible with the databases values at k = 2 except the line at 45.2 KeV, which differs by more than 17%. Compared with the most recent measurement (Vylov, 1984), the lines at 59.2, 84.7, 100.5, 315.1 keV differ markedly from our measurements (factor 5 or more) and only a limit is given for the line at 131.8 keV (<4.64 10 − 5 ) in agreement with our measurement. Eight  other lines are compatible and fourteen disagree with discrepancies of around 20%, except the lines at 81.3 and 506.7 keV for which one finds a difference of 40% and 50% respectively (see Table 3). For other older measurements (Berg and Malmkog, 1969;Prasad and Nielsen, 1974;Hnatowicz and Dragoun, 1983), they measured only 15 or 17 lines, some are in agreement but others differ by 10-20%. They also have larger uncertainties, 10% or more (see Table 3).
In the present work, large reduction of the uncertainties (see Table 1) were obtained thanks to the high radionuclidic purity of the source, a large counting time (6.6 days), a precise measurement of the source activity (Nedjadi et al., 2020), a precise measurement of the 161 Tb half-life (Durán et al., 2020), and a precise Monte Carlo calculation for the coincidence summing correction.

Conclusions
Emission intensities for 32 lines in the decay of 161 Tb were measured Table 2 The uncertainty budget for the lines at 48.91, 74.49, 238.57, 425.8 and 292.4 keV.  Table 3 Measured gamma-ray emission intensities per 100 decays for 161 Tb and difference with databases and data from (Vylov et al., 1984;Hnatowicz and Dragoun, 1983;Prasad and Nielsen, 1974;Berg and Malmkog, 1969 with reduced uncertainties in comparison with previous measurements and values given in different databases. The three most intense lines at 48.9, 57.2 and 74.6 keV were measured with an uncertainty of 2% or less and are in agreement with previous measurements, which had large uncertainties. Most of our results are in agreement with the data reported in existing databases. However, among the 32 intensities measured, 5 lines are very discrepant with a factor of 4 or more. This work improves considerably the emission intensities values and their uncertainties in contrast with the last measurements performed more than 30 years ago. This work contributes to improving the decay scheme for the 161 Tb.