KD-SS: 40K Decay-Scheme Measurement

• KD-SS is an experimental framework for measuring the rare ground-state electron-capture branch of 40K decay via coincidence detection of low-energy X-rays/Auger electrons and accompanying 1460 keV γ emissions.
• It employs a composite architecture with a silicon drift detector and a Modular Total Absorption Spectrometer to achieve high gamma-tagging efficiency and precise calibration.
• Accurate measurement of 40K decay improves background models in NaI(Tl) dark matter searches and refines K/Ar dating, enhancing rare-event analyses and geochronological studies.

KD-SS is presented in the literature as part of the KDK effort to measure the $^{40}$K decay scheme by coincidence detection of the low-energy electron-capture signature and the accompanying de-excitation products in an outer calorimeter. In this usage, KDK means Potassium Decay, and the central experimental objective is the ratio

$\rho = \frac{I_{EC}}{I_{EC^*}},$

namely the branching ratio of direct electron capture to the $^{40}$Ar ground state relative to electron capture to the excited state. The work is motivated by the fact that the ground-state electron-capture branch had never been experimentally observed before this study, despite its relevance to NaI(Tl)-based rare-event searches, K/Ar and $^{40}$Ar/$^{39}$Ar dating, and nuclear-structure tests of a unique third forbidden electron-capture transition (Stukel et al., 2020).

1. Terminology, scope, and experimental logic

In the terminology of the experiment, the inner detector measures the keV-scale X-rays and Auger electrons produced by electron capture, while the outer detector measures the accompanying $\gamma$-ray, mainly the 1460 keV line associated with decay through the excited state of $^{40}$Ar. Events are classified as EC, meaning electron capture directly to the $^{40}$Ar ground state with no accompanying 1460 keV $\gamma$, or EC$^*$, meaning electron capture to the excited state of $\rho = \frac{I_{EC}}{I_{EC^*}},$0Ar followed by the 1460 keV $\rho = \frac{I_{EC}}{I_{EC^*}},$1 (Stukel et al., 2020).

This classification defines the experimental problem. The quantity to be extracted is not merely a count rate, but the relative population of two electron-capture channels with different coincidence structure. The setup is therefore organized around a veto-and-tag architecture: low-energy deposition in the inner detector establishes an electron-capture candidate, and the presence or absence of a coincident $\rho = \frac{I_{EC}}{I_{EC^*}},$2 signal in the outer detector discriminates EC$\rho = \frac{I_{EC}}{I_{EC^*}},$3 from EC.

The notation can be a source of ambiguity. In unrelated hadron-spectroscopy work, $\rho = \frac{I_{EC}}{I_{EC^*}},$4 denotes kaon–$\rho = \frac{I_{EC}}{I_{EC^*}},$5-meson scattering, for example in studies of $\rho = \frac{I_{EC}}{I_{EC^*}},$6 from $\rho = \frac{I_{EC}}{I_{EC^*}},$7 (Albaladejo et al., 2015). In the present context, by contrast, KD-SS/KDK refers to a nuclear-decay measurement program centered on $\rho = \frac{I_{EC}}{I_{EC^*}},$8K.

2. Physical motivation and the unresolved $\rho = \frac{I_{EC}}{I_{EC^*}},$9K branch

The unresolved issue is the electron capture directly to the $^{40}$0Ar ground state. The study emphasizes that this branch had never been experimentally observed before the reported work, while theory gives a wide spread of values. The quoted range for the direct EC branching fraction is

$^{40}$1

This spread is large for a rare branch and propagates directly into applications that depend on the $^{40}$2K decay scheme (Stukel et al., 2020).

For rare-event searches, the significance is immediate. Natural potassium contamination is a major background in low-background detectors, especially NaI(Tl)-based dark-matter searches such as DAMA/LIBRA, ANAIS, COSINE-100, COSINUS, DM-Ice17, and SABRE. The problematic feature is that $^{40}$3K electron capture can produce low-energy X-rays and Auger electrons around $^{40}$4 keV, directly in the signal region used by many rare-event analyses. If the direct-to-ground-state EC branch is not known precisely, background models remain uncertain, the interpretation of low-energy excesses becomes less secure, and the contribution of $^{40}$5K to the 2–6 keV region cannot be accurately quantified.

For geochronology, $^{40}$6K is central to K/Ar and $^{40}$7Ar/$^{40}$8Ar dating. The ground-state EC branch affects how the decay scheme is normalized and interpreted, so an unmeasured or poorly known branch introduces uncertainty into age determinations and the underlying nuclear decay model.

For nuclear structure, the direct ground-state EC transition is an experimentally accessible unique third forbidden electron capture,

$^{40}$9

A plausible implication is that the KD-SS/KDK program is simultaneously a background-measurement campaign, a decay-scheme normalization effort, and a test of nuclear-structure calculations.

3. Composite architecture: SDD, enriched thin-film source, and MTAS

The principal implementation is a composite method in which a large-area silicon drift detector serves as the inner low-energy detector and the Modular Total Absorption Spectrometer serves as the outer $^{40}$0-detector (Stukel et al., 2020). The source is a thin thermally deposited enriched KCl film on graphite, placed very close to the SDD and inside the MTAS central cavity. The configuration is designed so that the SDD resolves the $^{40}$1 keV electron-capture signature while MTAS provides nearly $^{40}$2 coverage for the accompanying $^{40}$3-ray.

The instrumental components are specified in detail. MTAS consists of 19 NaI(Tl) modules, has a total mass close to a metric tonne, includes a central module with a through-hole for the inner detector, can use an extra NaI plug to improve gamma containment, and is read out with Pixie-16 digitizers. Its intrinsic background includes the 1460 keV $^{40}$4K line, the 2614 keV $^{40}$5Tl line, and neutron-capture features. The SDD has active area $^{40}$6, thickness $^{40}$7, thin dead layers on the entrance side, an integrated FET, cooling to about $^{40}$8C, and readout through a spectroscopy preamplifier and shaping amplifier.

Source development is a central technical component of the system. Two fabrication methods were explored:

Method	Outcome	Status
Ion implantation	About 10% of the activity ended up in the substrate; much was lost to the Faraday cup; $^{40}$9Sb contamination appeared	Abandoned
Thermal deposition	KCl thermally evaporated onto graphite disks; deposition efficiency 30–50%	Adopted

For thermal deposition, the best conditions were found at about 18.9 A heater current for 2 minutes under $^{39}$0–$^{39}$1 Torr. The final source was 16.1(6)% enriched KCl, with about $^{39}$2 atoms of $^{39}$3K and an estimated thickness of about 5.1(9) $^{39}$4m. The stated significance of this thinness is that it reduces self-absorption of the 3 keV X-rays.

4. Homogeneous source-detector implementation with $^{39}$5

The study also examines a homogeneous method using $^{39}$6, in which the crystal acts simultaneously as the source of $^{39}$7K decays and the detector of the low-energy X-rays and Auger electrons (Stukel et al., 2020). Because potassium is uniformly distributed in the scintillator bulk, the low-energy capture products have almost zero chance to escape without being absorbed, giving nearly total inner-detector efficiency for those products.

The crystal used in the reported configuration was cut to $^{39}$8, wrapped in teflon, housed in aluminum with nitrogen atmosphere, and coupled to two PMTs for double-ended readout; it also included a small window for low-energy calibration light. The paper presents this approach as promising, but notes a specific modeling limitation: the gamma-tagging efficiency is harder to simulate precisely because the PMT assembly and surrounding material are not yet well constrained. The authors suggest replacing PMTs with smaller, better-characterized SiPMs in future work.

Validation of the low-energy signature was performed using Eu activation in the KSI crystal, which confirmed that the $^{39}$9 keV X-ray/Auger peak is visible and can be isolated in coincidence with MTAS. This suggests that the homogeneous method is particularly attractive for maximizing low-energy containment, while the composite method is more mature in its geometric and efficiency characterization.

5. Calibration, efficiency model, and event classification errors

The SDD calibration used $\gamma$0Mn, $\gamma$1Zn, $\gamma$2Y, and $\gamma$3K, with the signal region blinded during calibration. The calibration was linear, with slope 229.8(1) Channel/keV and intercept 10.4(2) Channel. Performance metrics were a resolution of 198 eV FWHM at 8.04 keV and a noise threshold of 370 eV, placing the low-energy threshold well below the $\gamma$4 keV $\gamma$5K signal region (Stukel et al., 2020).

The MTAS $\gamma$6-tagging efficiency was first measured experimentally with $\gamma$7Mn at 835 keV, where the decay is almost purely through the excited state. The measured efficiencies were 0.9775(1) at 1 $\gamma$8s, 0.9778(1) at 2 $\gamma$9s, and 0.9778(1) at 4 $^{40}$0s. Geant4 simulations were then used to scale to the $^{40}$1K energy. For $^{40}$2K, the scaled efficiency was 0.9791(5) from simulation, and after live-time correction the values were 0.9789(6) at 1 $^{40}$3s and 0.9792(6) at 2 and 4 $^{40}$4s. For $^{40}$5Zn, the final corrected efficiency was 0.9793(6).

Dead time was modeled as paralyzable: $^{40}$6 with inversion

$^{40}$7

and dead-time percentage

$^{40}$8

The live-time corrections were reported to be very small, around the 0.01% level, with representative live times around 0.9977–0.9987 depending on coincidence window and source.

The paper gives explicit definitions of classification errors. A false negative occurs when EC$^{40}$9 appears as EC because the $^{40}$0 is not tagged by MTAS. Its expected rate is

$^{40}$1

where $^{40}$2 is source activity, $^{40}$3 is the probability that the X-ray/Auger reaches the SDD and triggers it, and $^{40}$4 is the MTAS tagging efficiency. A false positive occurs when an EC event accidentally coincides with an unrelated MTAS background event. The probability model uses

$^{40}$5

with $^{40}$6 the MTAS background rate. Measured $^{40}$7 values were around 0.0075–0.0230 depending on window and isotope, and the paper quotes source-background terms of order

$^{40}$8

in the low-energy SDD region.

For the low-energy capture signature, the experiment introduces $^{40}$9, the probability that the X-ray/Auger electron from EC escapes the source, reaches the SDD, and passes the chosen energy gate. The relevant relations are

$\gamma$0

and with an energy gate,

$\gamma$1

For the two-decay convolution component,

$\gamma$2

and for the gated K-shell case,

$\gamma$3

This yields

$\gamma$4

Measured $\gamma$5 values were a weighted average of 25.9 $\gamma$6 3.9% for $\gamma$7Mn and 21.5 $\gamma$8 1.1% for $\gamma$9Zn. The paper explicitly notes that these are not the final total efficiency of the experiment.

6. Decay-scheme relations, sensitivity target, and significance

The decay-scheme structure used in the experiment includes dominant $^*$0 decay to $^*$1Ca, electron capture to excited $^*$2Ar, much rarer $^*$3 decay, and the unobserved direct EC to the ground state of $^*$4Ar (Stukel et al., 2020). The quoted ratios are

$^*$5

$^*$6

and a formerly extrapolated estimate

$^*$7

The theory spread for $^*$8 includes 45.2(11), 190, and 215.0(31), which map onto the broad range already quoted for the direct EC branching fraction.

The experimental design goal mentioned in the study was about 0.2%, and the sensitivity studies show that the composite setup is capable of reaching that precision. At the same time, the work does not report a final $^*$9K ground-state branching-ratio result. Instead, it validates a measurement framework: the SDD + MTAS composite system is technically viable, the SDD resolves the low-energy $\rho = \frac{I_{EC}}{I_{EC^*}},$00K signature, the MTAS gamma-tagging efficiency is high and well characterized, dead-time and background effects are quantified, and the system has enough sensitivity to measure the rare direct EC branch.

A common misconception is to treat the reported apparatus paper as though it already established the final branching ratio. The paper does not make that claim. Its contribution is methodological and metrological: it demonstrates a controlled procedure for separating true $\rho = \frac{I_{EC}}{I_{EC^*}},$01K EC events from background-induced coincidences and missed-$\rho = \frac{I_{EC}}{I_{EC^*}},$02 events. In that sense, KD-SS/KDK occupies a specific place in the $\rho = \frac{I_{EC}}{I_{EC^*}},$03K literature: it is an experimental platform for converting a long-standing inferred quantity into a directly measured decay-scheme parameter.