The decays of
(radon) and
(thoron), as well as their daughters, are illustrated in Fig. 1 with the half-lives, \(\mathscr {Q}\)-values and branching ratios used throughout this work [11]. Radon and thoron are produced in the decay chains of the primordial nuclides
and
, respectively. Both of these nuclides are present, at least at trace level, in all materials, making it necessary to carefully screen and select all detector components [12]. The radon concentration of the air underground at LNGS, emanating from the surrounding rock, has been found to be of \(\mathscr {O}(100\,\hbox {Bq}/\hbox {m}^{3})\) [10]. For this reason, the inner cavity of the detector’s shield is continuously flushed with boil-off nitrogen [5], minimizing the amount of ambient radon and thoron that could potentially enter.
Levels of radon and thoron inside the LXe target of XENON100 are determined by the emanation of either isotope from surfaces inside the detector and the xenon purification system. Additionally, one period before SR1 and two periods during SR2 and SR3, were identified where air leaks of \(\mathscr {O}(10^{-3}\,\hbox {mbar 1}/\hbox {s})\) and \(\mathscr {O}(10^{-5}\,\hbox {mbar 1}/\hbox {s})\), respectively, developed at the purification system’s diaphragm pump, leading to a variation of the radon background over time (see [13] and Sec. 3.3).
After entering the LXe, radon and thoron are able to reach the fiducial volume used for the WIMP search via diffusion and convection [14]. As a consequence, \(\beta \)-decaying daughter nuclides of both isotopes can contribute to the low-energy ER background. Contributions from \(\alpha \)-decays are not relevant because the involved \(\alpha \)-particle energies are two orders of magnitude larger than the energies expected from WIMP-induced NRs, which are at \(\mathscr {O}(10\,\hbox {keV})\) [10].
Some of the progeny of the chains’ nuclei have short half-lives compared to the event window of XENON100, which has a length of \(400\,{\upmu \,s}\) and is centered on the triggering signal [5]. This aspect results in two decays being recorded within the same event (delayed coincidence signature). An example for this are decays of
(radon chain) and
(thoron chain) which are followed by the decays of their polonium daughters (BiPo coincidence). This causes multiple S1 and S2 signals to be present in an event, making it possible to identify and reject them (see Sec. 3.2).
Of the \(\beta \)-decaying nuclides in either chain, many have a significant likelihood of decaying under prompt emission of \(\gamma \)-rays, which gives the same kind of signature as mentioned above. However, certain \(\beta \)-decaying nuclides from either chain are able to decay without \(\gamma \)-ray emission. If they are well-separated in time from accompanying decays, they are very likely to elude identification. Such nuclides are
,
(radon chain) and
(thoron chain).
Radon and thoron concentrations in the LXe target can be inferred by selecting and counting events from decays of their chains. Especially suited for this task are \(\alpha \)-decays, as they produce large, monoenergetic signals resulting in a distinct event signature. Another explicit signature is the BiPo delayed coincidence as outlined above. This coincidence has already been successfully utilized by, for instance, the Borexino and SuperNEMO collaborations for estimating radioactive background levels inside their detectors [15, 16] and by the XENON collaboration for assessing the suitability of a thoron source for calibrating tonne-scale LXe detectors [14]. The focus of this section is to describe the selection of \(\alpha \)-decays and BiPo events. Results thereof are presented in Sec. 3.3.
Alpha event selection
For the analysis of \(\alpha \)-decaying nuclides in XENON100,
and
are used because they are the cleanest \(\alpha \) populations available as explained further below.
is covered in Sec. 3.2 as part of the BiPo coincidence.
To select \(\alpha \)-decays, a set of cuts, based on criteria described in [10, 17], is applied to the data. We require at least one S1 signal with a minimum of two PMTs in coincidence. Any secondary S1 signal has to be below \(1600\,\hbox {PE}\) (motivated in [17]) to avoid decay pileup and multi-scatters. In addition, at least one S2 signal must be present with at least \(25\,\%\) of its area observed by the top PMT array to reject mis-identified signals. Due to the large signal sizes of \(\alpha \)-decays, which are found to be of \(\mathscr {O}(10^4\,\hbox {PE})\) for S1s and \(\mathscr {O}(10^5\,\hbox {PE})\) for S2s, acceptance losses due to the above mentioned cuts are considered to be negligible.
Finally, the detector volume used for this analysis is restricted to \(R = \sqrt{X^2+Y^2} < 135\,\hbox {mm}\) and \(10\,\hbox {mm}< Z < 260\,\hbox {mm}\) (\(\hat{=}\ 40.5\,\hbox {kg}\) LXe or \(65.3\,\%\) of the active volume). This excludes regions close to the TPC walls, which suffer from reduced light and charge collection efficiencies, and regions with insufficient separation between
and
.
A potential
population close to the PTFE wall enclosing the TPC is also selected for further studies. Selection criteria are the same as above, with the following differences: \(R \ge 135\,\hbox {mm}\) is required, and the largest S2 signal must be smaller than \(8\times 10^4\,\hbox {PE}\). The latter criterion is motivated by the observation of S2 signals well below those seen from
and
for wall population events. Reduced S2 signals correspond to charge losses which can result from, for example, decays happening close to or within the walls. In the latter case, decay products can still enter the TPC, but lose energy in the process as they need to traverse the wall material. The S1 signal cannot be used as the only parameter for nuclide discrimination in this case, as the detector’s energy resolution is insufficient to separate the peaks of
and
in the S1 spectrum (see Fig. 2).
The largest S1 and S2 signals are interpreted as belonging to an \(\alpha \)-decay and are correspondingly named S1\(_{\alpha }\) and S2\(_{\alpha }\). A position-dependent area correction for \(\alpha \)-decays [17] is applied to S1\(_{\alpha }\) in order to account for PMT saturation, which affects both the observed signal size and position reconstruction. Looking at the corrected S1\(_{\alpha }\) spectrum for events happening at \(R < 135\,\hbox {mm}\) (Fig. 2, red circular markers), we identify two peaks, which are attributed to the \(\alpha \)-decays of
and
, respectively.
To determine peak positions and extents while accounting for slight tailing, we fit a sum of two Crystal Ball functions (defined in equation (F-1) of [18]) and a constant to the peaks. Events are classified as containing a
or
decay if the area of their S1\(_{\alpha }\) is within \(3\sigma \) of the respective peak mean (bounds as shown in Fig. 2). This choice is valid as the peaks are, in good approximation, symmetric. Fits are done separately for each SR due to changes of detector parameters affecting positions and widths of both peaks [8]. In all SRs, the peak bounds determined according to this method do either not overlap, or overlap negligibly. In the latter case, the bound separating both peaks is determined by the arithmetic mean of the overlapping bounds in order to ensure events to be attributed to a single peak only. Leakage of the peaks beyond the boundaries assigned to them are estimated to be \(< 1\,\%\) and are thus considered negligible. For consistency, the same procedure is utilized for the wall population, as it also shows a peak in the S1 spectrum (Fig. 2, green triangular markers), using a single Crystal Ball function plus a constant for fitting.
In the thoron chain, the number of \(\alpha \)-decays from
and
can, in principle, be inferred from the S1\(_{\alpha }\) spectrum via peak fitting (see [19]). However, in the XENON100 background, the
peak overlaps the
peak region due to insufficient energy resolution. In addition, there is no indication of
being present in the S1\(_{\alpha }\) spectrum of the fiducial volume used, while, at the same time, it is negligible in the rest of the sensitive volume compared to the wall population. As thus no direct evidence of them exists in the fiducial volume,
and
are not taken into account in this analysis, even though they are present in the detector as demonstrated by
being measured, which belongs to the nuclei discussed in detail in the following section.
BiPo event selection
The decays of
and
are often recorded within the same event as the decays of their daughter nuclei,
and
. This is due to the short half-life of the polonium isotopes compared to the event window recorded by the XENON100 data acquisition system. The S1 signals generated by the \(\beta \) decays of the bismuth isotopes (S1\(_{\beta }\)) are smaller than those generated by the \(\alpha \)-decays of the polonium daughters (S1\(_{\alpha }\)), because the \(\beta \)-decay \(\mathscr {Q}\)-values (see Fig. 1) and ionization densities are lower than those of the \(\alpha \)-decays [20].
The result is a delayed coincidence signature of one S1 signal being followed by a larger one. For selecting such events, we require at least two S1 signals with at least twofold PMT coincidence and the correct time order (S1\(_{\beta }\) before S1\(_{\alpha }\)). Both signals need to be larger than \(200\,\hbox {PE}\) and S1\(_{\alpha }\) has to pass a data quality cut on the fraction of its area observed by the top PMT array to reject signals seen almost exclusively by the bottom array. Such a signal topology is virtually impossible to occur for an \(\alpha \)-decay happening inside the TPC due to the large amounts of scintillation photons generated (see Sec. 3.1).
In order to distinguish delayed coincidences from Bi and Po decays (called BiPos in the following) from either chain additional constraints are applied exploiting the fact that
has a much shorter half-life than
(\(T_{1/2} = 300\,\hbox {ns}\) vs. \(T_{1/2} = 162\,{\upmu }\hbox {s}\)).
are selected by requiring S1\(_{\alpha }\) to occur at least \(7\,{\upmu }\hbox {s}\) after S1\(_{\beta }\), which removes more than \(99.99\,\%\) of
events. For
, the time difference has to be between \(0.5\,{\upmu }\hbox {s}\) and \(2\,{\upmu }\hbox {s}\). The lower bound ensures that both signals are individually identified with \(\sim 100\,\%\) efficiency by the data processor, while the upper bound removes about \(99\,\%\) of
events.
Due to the possibility of \(\gamma \)-radiation accompanying the Bi-decays, the S2\(_{\alpha }\) signal falling outside the event window, and signal losses because of the spatial distribution of events as detailed in Sec. 3.3, no constraints are required on the number of S2 signals and their parameters. In fact, as the number of S2 signals is expected to vary and event reconstruction is not optimized for pairing S1 and S2 signals when multiple physical interactions are present, signal matching has to be done separately. A match requires the absolute time difference between a pair of S2 signals to be within \(\sim 1\,{\upmu }\hbox {s}\) of the one between the S1 signals (detailed in [21]). The S2 which occurs earlier is assigned to S1\(_{\beta }\). If no match is found, the largest S2 is assigned to S1\(_{\beta }\). We then recalculate positions and signal corrections (for S1\(_{\alpha }\) and those mentioned in [5]) for each event, as both depend on pairing S1 with S2 signals. Events without any S2 signal are not rejected, but are assumed to have occurred in a charge-insensitive region such as below the cathode, with a set of default coordinates assigned to them (\(R = 0\,\hbox {cm}\), \(Z = -30.5\,\hbox {cm}\)).
The data processor does not search for S1 signals occurring after a sufficiently large S2 signal within the same event [5]. This behavior is intentional as the processor has been developed for the analysis of single interaction events. However, this reduces the acceptance of the BiPo event selection because the S1\(_{\alpha }\) signal might occur after the first S2 signal of the Bi-decay which happens after S1\(_{\beta }\) within the maximum drift time of \(176\,{\upmu }\hbox {s}\) [5]. This loss in acceptance as well as the one resulting from the finite size of the event window is accounted for by summing up weights \(\varepsilon \) for each BiPo event, defined by
$$\begin{aligned} \varepsilon ^{-1} = \exp \left( -\lambda \ \varDelta t_{ min }\right) -\exp \left( -\lambda \ \varDelta t\right) . \end{aligned}$$
(1)
\(\lambda \) is the decay constant of the corresponding polonium isotope, \(\varDelta t\) is the time difference between S1\(_{\beta }\) and the first S2 peak (or the end of the event window, if no S2 is present), and \(\varDelta t_{ min }\) is the minimum time difference between S1\(_{\alpha }\) and S1\(_{\beta }\) allowed by the selection criteria. Thus, the right side of equation (1) is the probability of a polonium decay to occur within the given constraints in time.
Acceptance losses caused by the S1\(_{\beta }\) size criterion, however, cannot be reliably predicted without depending on measured
and
rates. This is caused by events that happen on the cathode, whose S1 signals are shadowed by the cathode grid which results in a modification of the expected S1\(_{\beta }\) spectrum. The relevance of cathode events is explained in the following section. Losses induced by other quality cuts are negligible.
Results and discussion
The rate evolution of each decay is shown in Fig. 3. To verify that the selected event populations represent the correct nuclei, an exponential decay plus a constant offset is fitted to the rate decrease of
that is observed during the two months of SR1 (Fig. 3, top left). A small air leak was closed before this period, resulting in the decay of the excess radon which is visible in the rate evolution.
The half-life given by the fit is \(T_{1/2} = (3.81\pm 0.12)\,\hbox {d}\), which is in perfect agreement with the literature value for
(\(T_{1/2} = 3.82\,\hbox {d}\)). In addition, the relative positions of the peaks in the S1\(_{\alpha }\) spectrum match the expectations given by the \(\mathscr {Q}\)-values of the individual decays, with a constant light yield of \(\sim 3.7\,\hbox {PE}/\hbox {keV}\) observed for all nuclides. Furthermore, the rates assigned to
,
and
(radon chain) correlate with each other, while no correlation with the rates from
(thoron chain) and
(radon chain) can be seen. While the latter is also part of the radon chain, secular equilibrium is broken due to the long half-life of
(\(T_{1/2} = 22.2\,\hbox {y}\)). While thoron can also enter the detector via leaks, it has a much shorter half-life (\(T_{1/2} = 55.8\,\hbox {s}\)) than
, which results in a large suppression as it is more likely that it decays before reaching the TPC [14].
Table 1 Average specific rates for all SRs (statistical errors only). The leak period of SR1 ends on February 7, 2010, and the leak period of SR3 lasts from June 27, 2013, to December 1, 2013. Note that the
rate concentration is large compared to the other nuclides because it is concentrated at the PTFE wall enclosing the TPC
The condition on the S2 peak size introduced to select decays originating from the TPC’s PTFE walls does not specifically select
. However, considering that its rate is not correlated with the remainder of the radon chain, and taking into account similar observations made by the LUX experiment [22], we conclude that the wall population indeed consists of
. The spatial distribution that includes it (see Fig. 4) shows that it is located almost exclusively at \(R^2 > 200\,\hbox {cm}^{2}\), while the largest fiducial volume used for XENON100 WIMP analyses requires \(R^2 < 200\,\hbox {cm}^{2}\) among other constraints [23]. For \(R^2 < 180\,\hbox {mm}^{2}\), a small number of events, likely caused by
and
leakage, can be seen. However, it is evident that these events are negligible compared to those happening at \(R^2 \ge 180\,\hbox {mm}^{2}\) as well as to those belonging to
and
.
Computing the average specific rates (Table 1) yields \((48.0\pm 0.4)\,{\upmu }\hbox {Bq}/\hbox {kg}\), \((64.3\pm 0.4)\,{\upmu }\hbox {Bq}/\hbox {kg}\) and \((68.3\pm 0.4)\,{\upmu }\hbox {Bq}/\hbox {kg}\) for
in SR1 to SR3 respectively. Periods of increased average rates and fluctuations are observed in SR2 and SR3. These increases are caused by tiny air leaks in the diaphragm pump used in the xenon purification system, leading to a correlation of the
rates inside and outside of the detector [13]. Restricting the rate average to periods not affected by a leak gives \((38.3\pm 0.4)\,{\upmu }\hbox {Bq}/\hbox {kg}\) (SR1) and \((41.8\pm 0.9)\,{\upmu }\hbox {Bq}/\hbox {kg}\) (SR3). We thus conclude that constant emanation of radon from detector materials results in a base rate of, on average, \(40\,{\upmu }\hbox {Bq}/\hbox {kg}\).
A direct measurement of the
emanation at room temperature by means of miniaturized proportional counters was performed in summer 2012 between SR2 and SR3 [24]. It resulted in \((9.3\pm 1.0)\,\hbox {mBq}\) and \((2.6\pm 0.5)\,\hbox {mBq}\) being measured for the XENON100 detector and gas system, respectively, leading to an expected specific rate of \((74 \pm 7)\,{\upmu }\hbox {Bq}/\hbox {kg}\) assuming homogeneous mixing of
in the full LXe inventory. Inside the TPC, the assumption of homogeneous mixing is valid, with the exception of
(Fig. 4). The apparent decrease of
events towards the top of the TPC is caused by losses induced by the peak finding algorithm as explained in Sec. 3.2 and by \(\gamma \)-rays, which accompany the
decay, scattering off the LXe at a different position than the original decay. Measurements with an external
source suggest, that the homogeneous admixing of radon throughout the entire LXe inventory takes place within a few hours [19]. The environmental conditions of the direct measurements with proportional counters differed from the standard operation conditions, as the detector and gas system were at different temperatures and exposed to nitrogen or helium, respectively. Both the increased temperature and reduced stopping power are known to impact the emanation rate of
(for example, see [25, 26]) and we consider the direct measurement to be a weak confirmation of our results.
A priori, we expect the radon chain from
to
to be in secular equilibrium, as the longest-lived daughter nuclide in this part of the chain,
, has a half-life of \(26.9\,\min \) (Fig. 1). This is short compared to both the time scales of the SRs, which lasted for several months (Fig. 3), and the time scale of the target purification, which is about \(5\) days per revolution. However, we observe only about \(50\,\%\) of the expected amount of
events and about \(86\,\%\) of
events (Table 1). Acceptance losses due to cuts are negligible for the \(\alpha \)-events from
because of their high-energy signature. Thus, we have to consider additional causes for this mismatch. The most appealing one is radon daughters plating out onto the cathode due to convection and drift in the electric field. Radon daughters which remain ionized were, for example, observed in the EXO-200 TPC [27], and plating of radon progeny onto the cathode of a LXe TPC has already been reported by the ZEPLIN-III collaboration [28]. The precise motivation for the plate-out hypothesis is the observation of a surplus of events in the cathode region for
and
(Fig. 4), which is visible even when rejecting events without a proper S2 signal (which we assign to \(Z = -30.5\,\hbox {cm}\), the height of the cathode, by default). In addition, it has been observed in
calibration data, that the drift field affects the motion of
daughters inside the detector [14]. While nuclide velocities inside the TPC are dominated by convection, which contributes up to \(\sim 5\,\hbox {mm}/\hbox {s}\) to up-/downward motion along the Z axis, a constant contribution of \(\sim 1\,\hbox {mm}/\hbox {s}\) towards the cathode is observed which is attributed to the drift field (500–533\(\hbox {V}\) \(/\) \(\hbox {c}\) \(\hbox {m}\) depending on the SR [8]). As a consequence of the plate-out, decays happening on the cathode are shadowed, leading to losses in the S1 signal and thus a lower acceptance of BiPo and
events.
No cathode accumulation is seen in the
distribution. Such an effect could be hidden due to the reduced discrimination power at the bottom of the TPC between
and
(see Sec. 3.1). In addition, the effect on
is assumed to be enhanced because of the repeated chance of collecting ionized daughters with every decay. A larger fraction of
remaining ionized compared to
, as suggested in [27], might also play a role.
rates are larger compared to those of other radon chain nuclides by a factor of \(\sim 4.2\) in the outermost part of the detector in periods not affected by a leak. However, one has to take into account that the volume within which
is selected is by a factor of \(\sim 4.5\) smaller than a volume without any requirement on R (Sec. 3.1). Averaging the
activity without constraining R gives, for instance, \((38.6\pm 0.3)\,{\upmu }\hbox {Bq/kg}\) in SR1. Because this rate is still larger than the one observed for
and does not correlate with rates of preceding chain decays, we assume surface contamination of the PTFE walls due to air exposure during TPC assembly to be the origin of the
population (analogous to observations made in [29]). Under this assumption, we find a
activity per unit area of PTFE in the range from 0.6–0.9 \({\upmu }\) \(\hbox {Bq}\) \(/\) \(\hbox {cm}\) \(^{2}\).