Search for two neutrino double electron capture of ¹²⁴Xe and ¹²⁶Xe in the full exposure of the LUX detector

An undiscovered property of the neutrino is its Majorana nature—is it its own antiparticle [1–4]? An equivalent question is whether the mass of the neutrino is purely of Dirac type, or whether there is also a Majorana mass contribution. If the latter, then neutrinos may participate in lepton-number violating processes, with consequences including their possible seeding of a matter–antimatter asymmetry in the extreme environment of the early Universe [5]. Experimental access to this problem is mainly being sought through searches for neutrinoless double beta decay (0νββ) [2–4]. Neutrinoless double electron capture (0νDEC) is a second-order weak nuclear process that, if observed, would similarly indicate a Majorana mass contribution [6]. In most situations the lifetime for this process is expected to be several orders of magnitude larger than that of 0νββ, but a possible resonant 0νDEC process might occur [7] in which the close degeneracy of the initial and final (excited) atomic states could enhance the decay rate by a factor as large as 10⁶, making it observable. A number of studies have since pursued this possibility [6–15].

Simultaneous capture of two electrons with the emission of two neutrinos, i.e. two-neutrino double electron capture (2νDEC), is a related decay process that is allowed by the standard model [16–18]. This decay mode has been observed in ⁷⁸Kr [19], ¹³⁰Ba [20, 21] and more recently in ¹²⁴Xe [22] with measured lifetimes in the range of (0.6–18) × 10²¹ years. These lifetimes provide knowledge of the underlying nuclear matrix element, M_2ν, through the relationship

$$\begin{equation}{\left({T}_{\frac{1}{2},2\nu }\right)}^{-1}={G}_{2\nu }^{\mathrm{2}\mathrm{E}\mathrm{C}}{g}_{\mathrm{A}}^{4}\vert {m}_{\mathrm{e}}{c}^{2}{M}_{2\nu }{\vert }^{2},\end{equation} \tag{ 1 }$$

where g_A is the axial coupling constant and ${G}_{2\nu }^{\mathrm{2}\mathrm{E}\mathrm{C}}$ is the phase space factor for this decay [23]. Comparison of experimentally informed nuclear matrix elements of two neutrino double beta decay or double electron capture with the predictions of nuclear models provides a valuable test for these models, which may then use this information to improve their calculations of the unknown nuclear matrix elements of neutrinoless double-beta decay [22, 24–26]. Searches for 2νDEC provide particular input to the calculation of nuclear matrix elements on the proton-rich side of the mass parabola for even–even isobars [27].

Natural xenon consists of eight isotopes, including 0.095% ¹²⁴Xe and 0.089% ¹²⁶Xe (by mass) that may undergo 2νDEC. The decay process is similar for both isotopes:

$$\begin{equation}{}^{A}\mathrm{X}\mathrm{e}+2{\mathrm{e}}^{-}{\to \enspace }^{A}\mathrm{T}\mathrm{e}+2{\nu }_{\mathrm{e}},\end{equation} \tag{ 2 }$$

where A is the atomic number. The reaction Q-value is 2864 keV for ¹²⁴Xe and 919 keV for ¹²⁶Xe. This energy is carried by the neutrinos, which easily escape without being detected, while the nuclear recoil energy is of the order of 30 eV and therefore negligible. The atomic de-excitation following the double electron capture leads to a cascade of x-rays and Auger electrons being emitted from the daughter Te atom as the newly created vacancies are refilled. The branching ratio for events in which both captured electrons are from the K-shell dominates, and leads to a total energy deposit signal of 64.57 keV of which 64.3 keV can be detected [22] (the difference corresponding to energy depositions at the end of the cascade that are too small to produce ionisation or scintillation in the xenon). The signal region will be dominated by ¹²⁴Xe, due to the Q⁵ dependence of the phase space factor.

In fact, ¹²⁴Xe has the highest Q-value amongst DEC candidate nuclei, opening the possibility for two additional decay channels: 2β⁺ (possible in only six nuclides) and the mixed mode β⁺EC. Since the nuclear matrix elements for each of the three decay modes will be similar [28], the lifetimes may be expected to differ only by factors determined by phase space differences [23]. Consequently, one might expect lifetimes of the order of 10²³ years for β⁺EC and 10²⁷ years for 2β⁺, and their detection is therefore out of the reach of LUX. On the other hand, they have very distinct topologies, with multiple energy depositions per decay (from the atomic de-excitation, the kinetic energy of the positrons and the 511 keV γ-rays from the annihilations), which can be explored to discriminate them from the background with high efficiency in larger detectors.

Searches for 2νDEC in Xe typically look for the mode with both captured electrons coming from the K-shell (2νKK). Several of these searches reported no indications of a signal and set lower limits for its half-life (e.g. [29–31]), with XMASS achieving the most stringent (90% C.L.) limits at 2.1 × 10²² years for ¹²⁴Xe and 1.9 × 10²² years for ¹²⁶Xe. Recently XENON1T, which uses the same detector technology as LUX but has a larger fiducial mass of 1500 kg, announced the first observation of the 2νKK mode of this decay in ¹²⁴Xe with a half-life of 1.8 × 10²² years and a 4.4σ statistical significance [22].

In this work we examine data from the large underground xenon detector (LUX) for evidence of 2νKK decay from ¹²⁴Xe or ¹²⁶Xe. Details of the experimental approach, of the LUX detector and the specific conditions in which the data used in this analysis was acquired are discussed in section 2, while the details of the data analysis and the statistical method used are presented in section 3. Finally, results from this study are presented and discussed in section 4.

The detection of the atomic de-excitation signal following 2νKK decay is achievable in large-scale two-phase time projection chambers (TPCs) used as dark matter detectors such as LUX, as was first proposed by Mei et al [32] and Barros et al [33] and recently confirmed by the XENON1T collaboration [22]. These detectors provide excellent sensitivity to energy depositions of this magnitude and, despite the relatively low isotopic abundance of both isotopes, have targets of sufficient size to provide a significant isotope-specific exposure.

The LUX detector has been extensively described in [34]. Briefly, it consists of a low-radioactivity titanium vessel partially filled with liquid xenon such that above the liquid a thin layer of gaseous xenon is maintained. A vertical electric field of 181 V cm⁻¹ is established in the xenon target volume (with a mass of 250 kg of natural xenon) via a gate grid placed just below the liquid surface and a cathode at the base of the liquid (total drift length of 48.3 cm). Energy depositions in the xenon target lead to scintillation, ionization and heat. The scintillation, which has a narrow band of wavelengths centered at 175 nm, is directly observed by UV-sensitive high quantum efficiency photomultiplier tubes (PMTs) arranged in two arrays above and below the xenon volume (producing what is usually referred to as the S1 signal). Simultaneously, the electric field drifts a fraction of the ionized electrons to the liquid surface, where a stronger field extracts them to the gaseous xenon region where they produce secondary electroluminescence that is also registered by the PMTs (S2 signal). Horizontal positions are reconstructed using the S2 light distribution in the top array [35], while the delay (0–322 μs) between the S1 and the S2 provides the vertical position [36]. Single electrons extracted from the liquid produce signals with an average of 24.7 detected photons [37] and are easily observed, providing a very low energy threshold for experimental searches (see e.g. [38]). The instrument is immersed in a 7.6 m diameter and 6.1 m high tank with ultrapure water to reduce the background from external sources, and installed at a depth of 4850 feet at the Sanford Underground Research Facility, the underground location providing shielding equivalent to 4300 m of water from cosmic radiation (a reduction of $\mathcal{O}\left(1{0}^{-7}\right)$ in the rate of cosmic muons compared to the surface) [39].

LUX was operated from 2013 through to 2016, in two separate WIMP search campaigns. The first, between April and August 2013 (WS2013), collected 95 live-days of data, while a second longer run (WS2014-16) between September 2014 and May 2016 collected 332 live-days. As a result of an in situ grid 'conditioning' performed before the start of the second run significant changes were observed in the paths of the drifting electrons, from having been near-vertical in WS2013, to being strongly deflected by electric charge of the S2 signals building up on the walls of the detector during WS2014-16 [40, 41]. The accumulated charge leads to a time and space varying electric field magnitude, with direct impact in the recombination of electron–ion pairs and thus the light and charge yields. Section 3 details how these effects were dealt with in data analysis.

3.1. Data and event selection

Events included in this analysis were selected by requiring that the PMT waveforms contain a single S1 and a single S2, as the timescale for the atomic de-excitation following 2νKK decay and the range of the emitted x-rays and Auger electrons are too short for individual interactions to be resolved in the detector. Safeguards were put in place to prevent events in which the main S1 and/or S2 are followed by small spurious pulses from being discarded. More specifically, except at very small energy depositions (≲10 keV), S2 pulses are typically followed by a trail of single electrons extracted from the liquid, which are the result of photoionisation caused by the S2 light in the grids and in impurities in the xenon bulk. These isolated single electrons can overlap in time and produce pulses that resemble legitimate S2s following the main S2, leading to the event being mistakenly identified as a multiple scatter and thus discarded. If not accounted for, this effect leads to an efficiency penalty that increases with event energy, reaching ∼20% at the 2νKK energy. Allowing for additional small spurious pulses after the main S1 and S2 recovers the 98.8% efficiency determined for low energy single scatter events [37].

^83mKr calibrations were carried out frequently throughout the detector operation, for calibration and monitoring. ^83mKr has a half-life of 1.83 h and decays via two transitions, of 32.1 and 9.4 keV, in quick succession (with an intervening half-life of 154 ns) [42], which are often seen as a single interaction in the detector, with a total energy of 41.5 keV. While such signals have been shown to not contaminate other rare event searches conducted by LUX, the summed energies of these decays, smeared by the experimental energy resolution, results in possible contamination of the control region used to estimate the background in the 2νKK region (which starts at 48.1 keV, as discussed in detail in section 3.4). Consequently, the data used for this work excludes acquisition periods following ^83mKr injections such that possible contamination of the data by emissions from this isotope is at a negligible level compared to the background rate, at a large (34%) live-time penalty.

An important background for this search results from the calibrations of the response of the LUX detector to nuclear recoils, which were performed at the end of WS2013 and at various occasions during the WS2014-16 campaign using a deuterium–deuterium (DD) neutron generator [43]. These calibrations lead to the production of unstable isotopes via neutron activation (e.g. ¹²⁵Xe, ¹²⁷Xe, ^129mXe, ^131mXe, ¹³³Xe, ¹³⁵Xe and ¹³⁷Xe). Of these, the isotope of most concern to this analysis is ¹²⁵I, resulting from the decay of ¹²⁵Xe produced by neutron activation of ¹²⁴Xe:

$$\begin{equation}{}^{\mathrm{124}}\mathrm{X}\mathrm{e}+n\rightarrow {\enspace }^{\mathrm{125}}\mathrm{X}\mathrm{e}+\gamma \end{equation} \tag{ 3 }$$

$$\begin{equation}{}^{\mathrm{125}}\mathrm{X}\mathrm{e}\underset{16.9\enspace \mathrm{h}}{\overset{\mathrm{E}\mathrm{C}}{\rightarrow }}{\enspace }^{\mathrm{125}}\mathrm{I}+{\nu }_{\mathrm{e}}+\gamma +\mathrm{X}\end{equation} \tag{ 4 }$$

where X represents the set of x-rays and Auger electrons from the atomic de-excitation. ¹²⁵I decays to the 35.5 keV excited state of ¹²⁵Te via EC, with the resulting nuclear transition and atomic de-excitation leading to a total energy deposit of 67.3 keV in most decays (when the EC is from the K-shell, which occurs in >80% of the decays) [44]:

$$\begin{equation}{}^{\mathrm{125}}\mathrm{I}\underset{59.4\enspace \mathrm{d}}{\overset{\mathrm{E}\mathrm{C}}{\rightarrow }}{\enspace }^{\mathrm{125}}\mathrm{T}\mathrm{e}+{\nu }_{\mathrm{e}}+\gamma +\mathrm{X}\enspace \left(67.3\enspace \mathrm{k}\mathrm{e}\mathrm{V}\right)\end{equation} \tag{ 5 }$$

which in LUX is just slightly more than one sigma (2.7 keV) away from the 2νKK signal and therefore contaminates the signal region. Furthermore, while ¹²⁵Xe decays quickly with a half-life of only 16.9 h, ¹²⁵I has a much longer half-life of 59.4 d—but has been observed to be removed from LUX by the purification system (which uses a hot zirconium getter) with a decay constant of 5.4 ± 0.4 d. Data with high ¹²⁵I rate following DD calibration campaigns were used to characterise the energy resolution of the detector in this energy range (see figure 1 and discussion in section 3.2), but excluded from the 2νKK analysis in order to minimise contamination of the signal region. These exclusion periods were defined as 4 effective ¹²⁵I removal periods (22 calendar days) after the end of DD calibrations. Together with the exclusion periods following ^83mKr calibrations, this resulted in a final live-time of 242.2 days (<60% of the available exposure).

Zoom In Zoom Out Reset image size

Although neutron activation of Xe isotopes can also occur due to ambient neutrons in the underground laboratory [45] while xenon is outside the water tank during circulation, the small mass of this unshielded xenon and the reduced abundance of ¹²⁴Xe in natural xenon make this mechanism for production of ¹²⁵Xe negligible (<2 atoms per month) compared to the overall background.

3.2. Energy calibration and resolution

The energy has been reconstructed from S1 and S2 signal areas using the expression

$$\begin{equation}E=\left({\mathrm{S}\mathrm{1}}_{\mathrm{c}}/{g}_{1}+{\mathrm{S}\mathrm{2}}_{\mathrm{c}}/{g}_{2}\right)W,\end{equation} \tag{ 6 }$$

where S1_c and S2_c (measured in phd, representing the number of photons detected) are the S1 and the S2 signals corrected to equalize the detector response throughout the active volume; g₁ and g₂ are the gain factors, defined by the expectation values $\left\langle \mathrm{S}\mathrm{1}\right\rangle ={g}_{1}{n}_{\gamma }$ and $\left\langle \mathrm{S}\mathrm{2}\right\rangle ={g}_{2}{n}_{\mathrm{e}}$, with n_γ and n_e representing the initial number of photons and electrons produced by the interaction, respectively; and W = (13.7 ± 0.2) eV is the mean work function for the production of either a photon or an electron in xenon (see [46] for a detailed discussion on this energy model). The energy calibration was based on fits to γ-ray lines in the 5.2 to 661.7 keV range, from decays of ¹²⁷Xe, ^83mKr, ^131mXe, ^129mXe, ²⁰⁸Tl, ²¹⁴Bi and ¹³⁷Cs. The g₁ and g₂ values used for the WS2013 data are those reported in [47], while in the WS2014-16 dataset they were found to slightly vary throughout the acquisition period [40], with g₁ decreasing from 0.100 ± 0.001 to 0.098 ± 0.001 phd per emitted photon and g₂ from 19.40 ± 0.45 to 18.75 ± 0.29 phd per electron. The periods following nuclear recoil calibrations of the detector with the DD generator have a high rate of ¹²⁵I, offering an opportunity to estimate the energy resolution in this energy range. This was done using data from two high ¹²⁵I rate periods, as shown in figure 1, with a centroid of 67.5 ± 0.4 keV and a resolution of 4.2 ± 0.6% (in good agreement with the expectation from [36] for this energy).

3.3. Data quality cuts

Events that passed the single scatter criterion were subjected to further data quality cuts, designed to remove pathological populations while minimising the impact in the signal detection efficiency.

• We require a minimum size of 10 phd and 1000 phd for S1 and S2 pulse areas, respectively, which removes random coincidence background but does not impact the signal acceptance.
• Energy depositions in the xenon gas produce a long continuous signal which can be classified as an S2 and mimic a single scatter event when accidentally paired with an isolated S1. This small population of events (<0.5% in the region of interest) was excluded by requiring that σ_S2 > 0.4 μs (where σ_S2 is the width of a Gaussian fit to the S2 pulse).
• Finally, a cut was designed to remove a special class of multiple scatter events (dubbed Gamma–X events) in which one of the interactions occurs in the active region of the detector (producing an S1 and an S2) and one or more energy depositions take place under the cathode, in the reverse field region, where only the S1 is detected. The multiple S1 pulses are merged and only one S2 is detected, leading to an incorrect energy reconstruction for the event.

Although mostly negligible in the low energy WIMP search range, the rate of these Gamma–X events increases considerably for higher energies and is a relevant background in the 2νKK region. Occurring under the cathode, very close to the bottom PMT array, these additional scatters are expected to lead to events with a higher fraction of the S1 signal in a single bottom PMT compared to single scatters in the fiducial volume (well above the cathode), a feature that can be explored to identify them with high efficiency.

Data from the ¹⁴C calibration performed after the WS2014-16 run [48] was used to define this cut, as it provides a uniformly distributed population of events with energy depositions up to the 156.5 keV β-decay endpoint with minimal contamination of Gamma–X events. As shown in the top panel of figure 2, the S1 raw area fraction in the bottom array PMT with the largest contribution to the S1 signal was plotted and binned as a function of the total uncorrected S1 area. The cut was then defined to keep >99% of the ¹⁴C events in each raw S1 bin. As this fraction naturally increases with depth, and to maximise the signal acceptance efficiency, only events with a drift time longer than 250 μs were used to define the cut. This resulted in an overall efficiency of 99.7% at all depths (flat in the energy region of interest), but actually only events below ∼270 μs are excluded (corresponding to the bottom 7.6 cm and 3 cm of the fiducial volumes in the WS2013 and WS2014-16 datasets, respectively).

Zoom In Zoom Out Reset image size

The bottom panel in figure 2 shows the events from the WS datasets which are excluded by this cut, mainly in the region under the electron recoil band as expected. Consistent with being Gamma–X events created by radioactive decays in the bottom PMT array, their density decreases exponentially with the distance from the bottom of the detector and they are mainly located above the innermost PMTs.

3.4. Statistical approach

The background in the 2νKK decay signal region is expected to be approximately flat, dominated by Compton scattering of high energy γ rays and β decays from contaminants mixed in the xenon (as discussed in more detail in section 4). We therefore use the frequentist statistical approach of Rolke et al [49], wherein a region of interest (ROI) is defined that broadly covers the signal region, and sidebands with the same width are defined to either side. The number of background events in the ROI is estimated as the average of the absolute number of events in the two side bands. The Rolke statistical method is then used to estimate the number of signal events corresponding to the 90% C.L. upper limit given the actual observation in the ROI, as well as the number of signal events corresponding to the sensitivity of the experiment (i.e. the average expected limit in case of no signal), which can be used to estimate the corresponding limit and sensitivity on the half-life of the KK decay mode using:

$$\begin{equation}{T}_{1/2}^{2\nu \mathrm{K}\mathrm{K}}{\geqslant}\frac{\mathrm{ln}\left(2\right)a{N}_{\mathrm{A}}}{A}\frac{{\epsilon}M{\Delta}T}{{\mu }_{\mathrm{u}\mathrm{p}}}\end{equation} \tag{ 7 }$$

where μ_up is the upper limit on the number of signal events, a is the isotope abundance in natural xenon (0.095% for ¹²⁴Xe and 0.089% for ¹²⁶Xe) and A the respective molar mass (123.9 g/mol and 125.9 g/mol, respectively [50]), N_A = 6.022 × 10²³ is Avogadro's number, is the signal detection efficiency, ΔT is the duration of the exposure and M the fiducial mass.

Here, we define the ROI with 95.4% signal acceptance as ±2σ from the signal median of 64.3 keV, which translates to a width of 10.8 keV for a 4.2% energy resolution (measured from the fit to the ¹²⁵I decay peak, see figure 1), extending from 58.9 to 69.7 keV. The acceptance is reduced to 94.0% after applying the flat efficiencies from the data quality cuts and the single scatter selection. The uncertainty in the acceptance of the ROI is calculated as having independent contributions from the error in the reconstruction of the mean energy and the error on the width of the peak, resulting in a final ROI acceptance ${\epsilon}=94.{0}_{-3.2}^{+2.2}$%.

3.5. Fiducial volume definition

Combining the data from the WS2013 and WS2014-16 datasets surviving the exclusion periods and data quality cuts produces the spectrum shown in figure 3. This is a broadly continuous background with a rate of 3.4 × 10⁻³ events/kg/keV/day, consistent with energy depositions from Compton scattering of high energy γ rays from radiological (U, Th, ⁴⁰K, ⁶⁰Co) contamination in detector components and the 'naked' β-decay of ²¹⁴Pb in the ²²²Rn chain and compatible with the expectation from the background model of the detector at low energies [51]. The contribution from the β-decay of ⁸⁵Kr is highly suppressed as a result of purification of the LUX xenon in a dedicated Kr-removal system prior to the detector installation underground [51, 52]. A clear peak is seen around 32 keV due to the decay of the cosmogenically produced ¹²⁷Xe (${T}_{\frac{1}{2}}$ = 36.4 d) isotope, activated while the xenon was on the surface and therefore present at the start of the WS2013 dataset with an initial activity of 490 ± 95 μBq kg⁻¹ [51].

Zoom In Zoom Out Reset image size

A total of 993 and 991 events are observed in the left and right side bands, respectively, resulting in a background expectation of 992 ± 31 events in the ROI and a 90% C.L. sensitivity to the half-life of the 2νKK decay of ¹²⁴Xe of 3.1 × 10²¹ years (corresponding to an upper limit of 78 signal events). A small (1.3σ) upward fluctuation is visible in the ROI, with the 1031 events actually observed translating in a 90% C.L. upper limit of 120 signal events and a corresponding lower limit for the half-life of this decay mode of 2.0 × 10²¹ years. Similarly, the sensitivity to the half-life of 2νKK decay in ¹²⁶Xe is 2.9 × 10²¹ years while the limit is 1.9 × 10²¹ years.

Data collected during the two science runs of the LUX detector were analysed to search for the 2νDEC decay of ¹²⁴Xe and ¹²⁶Xe, in particular the mode in which the two captured electrons are from the K-shell. No significant excess of events was observed in the 27769.5 kg-days total exposure, which allowed 90% C.L. lower limits to be set for the half life of this decay mode of 2.0 × 10²¹ years for ¹²⁴Xe and 1.9 × 10²¹ years for ¹²⁶Xe.

For the case of ¹²⁴Xe this is an order of magnitude lower than the observed half-life reported by XENON1T, of 1.8 × 10²² years (4.4σ significance) for a fiducial mass of 1.5 ton and 177.7 days exposure. This is a consequence of the much higher mass of XENON1T, which has a direct impact in the size of the available isotope samples but also allows for a more shielded fiducial volume and consequently a lower background rate.

The next generation detector LUX–ZEPLIN [53], with an active mass of 7 ton and an estimated fiducial mass in this energy region of 5.6 ton, will be able to confirm the observation of 2νKK decay of ¹²⁴Xe from XENON1T and reach a discovery level 5σ-significance for this signal in just a few months of operation. Given its foreseen 1000 day long run it will also be able to search for the 2νβ⁺EC mixed decay mode (10²³ years), while the expected very long half life of the 2νβ⁺β⁺ channel (10²⁷ years) puts it out of reach of this generation of detectors. Similarly, the 2νDEC decay of ¹²⁶Xe (with an estimated half-life of $\mathcal{O}\left(1{0}^{24}\right)$ years) will not lead to a statistically significant number of events overlapping the large ¹²⁴Xe 2νDEC signal to claim an observation.

The research supporting this work took place in whole or in part at the Sanford Underground Research Facility (SURF) in Lead, South Dakota. Funding for this work is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics under Contract Numbers DE-SC0020216, DE-FG02-08ER41549, DE-FG02-91ER40688, DE-FG02-95ER40917, DE-FG02-91ER40674, DE-NA0000979, DE-FG02-11ER41738, DE-SC0015535, DE-SC0006605, DE-AC02-05CH11231, DE-AC52-07NA27344, DE-FG01-91ER40618, DE-SC0010010, DE-SC0014223 and DE-SC0019066. This research was also supported by the U.S. National Science Foundation under award numbers PHYS-0750671, PHY-0801536, PHY-1004661, PHY-1102470, PHY-1003660, PHY-1312561, PHY-1347449, PHY-1505868, PHY-1636738; the Research Corporation Grant RA0350; the Center for Ultra-low Background Experiments in the Dakotas (CUBED); the South Dakota School of Mines and Technology (SDSMT). LIP-Coimbra acknowledges funding from Fundação para a Ciência e a Tecnologia (FCT) through the project-Grant PTDC/FIS-PAR/28567/2017. Imperial College and Brown University thank the UK Royal Society for travel funds under the International Exchange Scheme (IE120804). The UK groups acknowledge institutional support from Imperial College London, University College London and Edinburgh University, and from the Science & Technology Facilities Council for PhD studentships ST/K502042/1 (AB) and ST/R504737/1 (EL) and the Commonwealth Scholarship Commission in the UK through the reference (grant) number BDCS-2016-49 (AN). The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. The assistance of SURF and its personnel in providing physical access and general logistical and technical support is acknowledged.