High precision half-life measurement of ¹²⁵Cs and ¹²⁵Xe with $\gamma$-spectroscopy

The decay parameters of the reaction products enter into the calculations, consequently their precise values must be known and their uncertainty contributes to the uncertainty of the obtained experimental cross sections. About 50 years ago three experiments were devoted to measure the half-life of ¹²⁵Cs [14, 15, 16]. The values were determined in these works with relatively large uncertainties (2.2%, 10.2% and 8.7%, respectively) and furthermore, the data of [16] is available only in an unpublished thesis and the work of [14] provides only very limited experimental information. In the compilations before 1981 [17] the weighted average (45.2 $\pm$ 1 min) of the half-lives was given as the recommended value. However, this was changed – without any detailed explanation – in the compilations issued after 1993 [18] and the unweighted average of the three measurements [14, 15, 16] (46.7 min) was given. The uncertainty assigned to this unweighted value (0.1 min)[18] is obviously a typo.

The situation is somewhat different in the case of ¹²⁵Xe: although more (the half-life data is based on five measurements [19, 20, 21, 22, 23]) and better documented data is available, the p-value of the weighted mean is only 0.3% which indicates that the systematic uncertainties of one or more measurements might be underestimated. Moreover, similarly to the ¹²⁵Cs case, the relative uncertainties are large (5.0%, 2.2%, 6.0%, 2.0% and 2.3%, respectively) and in these works there are very limited discussions about the experimental setup and on data analysis. In the first compilation issued in 1972 [24] the unweighted average (17.0 $\pm$ 0.3 h) of the results presented in [22, 23] was given as the recommended value. This value was changed in 1981: the weighted average of [22, 23] (16.9 $\pm$ 0.2 h) is indicated as the recommended value in the more recent compilations [18]. The above discussed ¹²⁵Cs and ¹²⁵Xe half-life data are listed in Table 1.

In summary, an independent confirmation of the half-lives or providing more reliable data is of crucial importance for our forthcoming ¹²⁴Xe(p,$\gamma$)¹²⁵Cs activation measurements. The aim of this paper is to present our experimental procedure to provide more precise half-life values. This paper is organized as follows: after a short introduction to our motivation in Sect. 1, in Sect. 2 the technical details of the experimental procedure — including the description of the source preparation and the $\gamma$-counting setup — are presented and the data analysis is explained, while in Sect. 3 the results are given.

Recently, a thin window gas-target system [26] was designed at Atomki in order to measure low energy $\alpha$-induced reaction cross sections relevant for the $\gamma$-process and for measuring the ³He($\alpha$,$\gamma$)⁷Be reaction using the activation method [27, 28]. This chamber was slightly modified according to the special experimental requirements of the ¹²⁴Xe(p,$\gamma$)¹²⁵Cs cross section measurement. Namely, the length of the chamber was reduced to 4.2 mm, for the entrance window a 10.2 $\mu$m thick aluminum foil was used and the ¹²⁵Cs recoils were implanted into a similar high purity aluminum (catcher-) foil. The ¹²⁵Cs sources were produced by the ¹²⁴Xe(p,$\gamma$)¹²⁵Cs reaction, the proton beam was provided by the MGC-20 cyclotron accelerator of Atomki. Six sources were produced with proton bombarding energies of 6.0 MeV, 6.5 MeV (carried out twice), 7.0 MeV, 7.4 MeV and 7.5 MeV. In this energy region the proton capture cross section reaches its maximum values according to the statistical model calculations carried out by the NON-SMOKER code [32]. The isotopic purity of the ¹²⁴Xe gas was better than 99.9% and the lengths of the irradiation varied between 70 and 180 minutes. Between the end of the irradiation and the beginning of the $\gamma$-counting 30-60 minutes elapsed.

The half-lives of the ¹²⁵Cs and ¹²⁵Xe isotopes were measured with $\gamma$-spectroscopy. After the irradiations the catcher foil was removed from the gas chamber and transported to the off-line counting setup where the $\gamma$-radiation following the $\beta$ decay of the reaction products was measured using a 100% relative efficiency HPGe detector (Canberra model GR10024), placed into a complete 4$\pi$ multilayered shielding⁵⁵5The type of the shielding, purchased from Tema Sinergie S.P.A (https://www.temasinergie.com/), is Tema Sinergie Mod. GDS 2.. This setup was also used in the past for the precise half-life measurements carried out at Atomki [29, 13, 30]. A similar data acquisition system to [29] was used for this experiment. Namely, the signals from the detector preamplifier were first shaped (the shaping time was set to 3 $\mu$s) and amplified by an ORTEC model 671 module. An ORTEC model ASPEC-927 multichannel analyzer unit was used and the data were collected using the ORTEC A65-B32 MAESTRO software which provides deadtime information found to be precise in the previous works [29, 30]. The energy calibration was carried out using calibrated ⁶⁰Co, ¹³³Ba, ¹³⁷Cs, ¹⁵²Eu and ²⁴¹Am sources (for more details see e.g. [31]).

The activity of each irradiated sample was measured for 29 to 61 hours⁶⁶6Except for the counting of the 2nd source produced at E_p = 6.5 MeV which had to be stopped due to technical problems.. In the first 5 hours of the counting the spectra were saved and then erased in every 3 minutes to derive the half-life of the ¹²⁵Cs isotope and later in every 15 minutes to measure the half-life of the ¹²⁵Xe nucleus. For each spectra the deadtime value, used to correct the corresponding peak area, was provided by the MAESTRO software and was found to be between 0.11% and 2.19%, depending on the time elapsed after the irradiation and on the counting geometry.

Figures 1 and 2 shows a 3 min and a 15 min $\gamma$-spectrum, taken 67 minutes and 15.1 hours after the beginning of the $\gamma$-counting following the E_p = 7.4 MeV proton beam irradiation. In table 2 the details of the gamma countings are summarized.

The sources produced by E_p = 6 MeV and by E_p = 6.5 MeV proton irradiation were placed at 1 cm distance from the end-cap of the detector. The activity measurements of the sources produced by E_p = 7.0 MeV, E_p = 7.4 MeV and E_p = 7.5 MeV irradiations were carried out using two different geometries: these samples were placed at first at 10 cm (far geometry) from the end-cap of the detector and the decay of the ¹²⁵Cs isotope was measured for 1.8 - 2.15 hours. Thereafter, the sources were moved to 1 cm (close geometry) from the end-cap of the detector and the activity was measured again. In these cases the counting length was within 1.4 - 2.75 hours. To derive the half-life of the ¹²⁵Xe isotope the activity was measured similarly first in far geometry and then in close geometry. The total lengths of the countings were about 27-38 hours at both geometries.

Although both isotopes decay by the emission of several $\gamma$-rays [18], unfortunately the relative intensities of most of the transitions were too low for a precise half-life determination. Furthermore, due to the limited resolution of the HPGe detector, it was not possible to resolve the E_γ = 112 keV $\gamma$-ray in ¹²⁵Cs from the E_γ = 113.55 keV $\gamma$-ray in ¹²⁵Xe. Since the subtraction of the parasitic contribution would lead to noticeably higher uncertainties we omit this transition from the half-life determination. Therefore, to derive the half-life of the ¹²⁵Cs isotope the area of the 526 keV peak was determined in each spectra measured for 3 min The determination of the ¹²⁵Xe half-life is based on two $\gamma$-lines, the rates of the E_γ = 188.42 keV and E_γ = 243.38 keV $\gamma$-transitions were sufficient in each 15 min long counting for a precise measurement.

Two methods — resulting in half-lives always within 0.2% — were used to determine the net peak areas. In each spectra the peaks were fitted with a Gaussian plus a linear background and the peak areas were also determined by numerical integration. In the two cases different background regions were selected. As can be seen in figs. 1 and 2 there are parts on both sides of the region of interest where the background for the peak area determination could be fixed with good confidence. A linear function was fitted onto the two background regions and the background was subtracted from the peak areas. The determination of the half-lives was made by fitting an exponential curve — using the least square method (described in details e.g. in [33]) — on the deadtime corrected areas of the $\gamma$-peaks as the function of the elapsed time. Fig. 3 shows the decay curve of ¹²⁵Cs (left side) and ¹²⁵Xe (right side) with the measured points and the fitted exponential function as well as the percentage residuals (bottom).

The rates of the weaker transitions, corresponding to the decay of ¹²⁵Cs and ¹²⁵Xe, in each 3 min and 15 min long spectra are about factor of 5 to 10 lower. Several spectra were summed up and the rate of the weaker transitions were studied. Although we found that the t_1/2 values based on the counting of these transitions scatter around the t_1/2 value proclaimed here, since their statistical uncertainties are significantly larger (about 2.2 % - 5.1 %), involving these transitions in the weighted mean does not improve the precision of the final result.

The half-lives, measured in far geometry and in close geometry were in agreement within 0.09% (for ¹²⁵Cs) and 0.01% (for ¹²⁵Xe). Furthermore, selecting different background regions and using different methods for the net peak area determination led to a small, 0.2% difference in the derived t_1/2 results. These values — 0.09% (for ¹²⁵Cs), 0.01% (for ¹²⁵Xe) and 0.2% were taken into account as systematic uncertainties.

The new half-life value of ¹²⁵Xe, derived in the present work is based on the counting of two $\gamma$-transitions. There is a small — 0.33% — difference between the half-lives based on the 188.42 keV or the 243.38 keV lines. This difference may be explained by e.g. contributions from weak $\gamma$-background lines located close (within the resolution of the HPGe detector) to the peaks of our interest. The maximum of such a possible systematic uncertainty on the ¹²⁵Cs half-life value was estimated in the following way. Using our HPGe detector it was not possible to resolve the 112 keV $\gamma$-peak of ¹²⁵Cs from the 113.5 $\gamma$-peak of ¹²⁵Xe. We estimated this contribution in each spectra by correcting the 243.38 keV peak areas using the known I_γ(113.50) / I_γ(243.38) branching ratios. After this subtraction the decay curve was fitted again, the resulted ¹²⁵Cs half-lives were found to be in average 0.55% higher then the ones based on the 526.47 keV peak. Therefore, this 0.55% was considered as a systematic uncertainty.

The reliability of the counting setup, namely, the effect of accidental detection efficiency changes and deadtime determination, can be studied using a long-lived reference source with precisely known half-life. The aluminum foil used to catch the ¹²⁵Cs recoils, contained some iron impurity leading to the production of ⁵⁶Co (t_1/2 = 77.2 d) through the ⁵⁶Fe(p,n)⁵⁶Co reaction. This isotope emits several high intensity $\gamma$-lines (1037.840 keV, 1238.282 keV, 1360.215 keV, 1771.351 keV, 2015.181 keV and 2598.459 keV⁷⁷7The 846.77 keV peak of the ⁵⁶Co is not resolved from the E_γ = 846.51 keV line of ¹²⁵Xe, therefore it was not used to monitor the stability of the counting setup.) which could be used to monitor the stability of the counting setup. The deadtime correction provided by MAESTRO has been applied to the net peak areas of this source and the reliability of the deadtime was checked by studying the ⁵⁶Co decay. Fig. 4 shows the decay and deadtime corrected 1238.282 keV yield of the ⁵⁶Co reference source. The figure clearly shows that the decay and deadtime corrected yield is constant in time which proves the reliability of the deadtime values. The slope of the linear fit was always consistent with zero with maximum uncertainty of 0.2% (which is in excellent agreement with a previous work [30]) and this value can be considered as the upper limit of the systematic uncertainty characterizing the counting setup.

The pulse pile-up effect can also influence the results of the $\gamma$-spectroscopy experiments [35, 36]. The initial counting rates characterizing the half-life determination of ¹²⁵Cs, listed in Table 2, varied between 0.54 kHz and 1.33 kHz. No trend in the resulted half-life values as the function of the initial counting rates were observed. The counting rates characterizing the runs used to derive the ¹²⁵Xe half-life were even lower, typically below 0.5 kHz. Therefore, it was concluded that event-loss due to pile-up does not influence the present data. Finally, it has to be noted that noble gasses tend to diffuse out of foils [34], however, this effect was extensively studied in [27] and no loss was observed.