Half-life of the nuclear cosmochronometer $^{176}$Lu measured with a windowless 4π solid angle scintillation detector

The Lu-Hf isotopic system is widely used as a cosmochronometer for dating astrophysical events, planetary differentiation, and terrestrial orogenic processes. Despite its importance, published experimental half-lives of 176Lu vary, and Lu-Hf isochron studies yield two discordant decay constants when applied to meteorites versus terrestrial rocks of known U-Pb ages. This discrepancy undermines precise geochronology and interpretations of early Solar System and planetary evolution. The study aims to obtain an accurate and precise laboratory half-life for 176Lu using a detection method that minimizes dependencies on nuclear-structure data, detection efficiency calibrations, and sample contaminants, thereby resolving discrepancies and validating consistency with high-precision U-Pb chronometry.

Prior determinations of the 176Lu half-life include γ-ray counting, γ-γ coincidence, γ-sum coincidence, and liquid scintillation methods, yielding values that scatter between roughly 3.2–4.3 × 10^10 years. Isochron-derived values from terrestrial rocks (calibrated against U-Pb) support a shorter decay constant (T1/2 ≈ 3.72 × 10^10 y), whereas some meteorite classes (eucrites, some chondrites, and an angrite) imply a shorter half-life than terrestrial isochrons, while other meteorites (Richardton chondrite and Acapulco) and terrestrial rocks indicate a longer value consistent with the present result. Complexities in coincidence analyses, especially when multiple γ-rays are emitted per decay, require non-trivial corrections (e.g., pile-up of three γ-rays), contributing to discrepancies. The community has considered astrophysical or cosmic-ray-induced processes to explain meteorite-based anomalies. The present work seeks to provide a direct laboratory half-life with minimized systematics to benchmark these approaches.

Overview: The total energy from photons and electrons emitted in 176Lu decay was measured with a windowless 4π BGO scintillation detector enclosing a natural Lu sample to achieve near-unity detection efficiency. No external activity calibration is required for the Lu measurement, and sensitivity to nuclear-structure parameters is minimized. Samples: Two natural Lu metallic foils (Nilaco Co.) with elemental Lu fraction 99.9% (±0.1%) were used. Approximate dimensions: 8 mm × 8 mm × 0.125 mm. Masses: 125.26 ± 0.05 mg and 121.43 ± 0.05 mg. Isotopic abundance of 176Lu in natural Lu: 2.5987 ± 0.0012%. Atomic mass for natural Lu: 174.967. Potential long-lived impurities (40K, 87Rb, 138La, 147Sm, 187Re, 232Th, 235,238U) were assessed via ICP-MS on a 40 µm × 180 µm area: K 0.001%, Rb 0.001%, Re 0.005%, Th 0.017%; La, Sm, U below ~0.001% detection limit. While not a bulk average, results suggest impurities unlikely to affect decay counting. Detector system: Two BGO crystals (cylindrical 3 in. × 2 in., and well-type 3 in. × 3 in. with 10 mm × 15 mm hole). The Lu sample was placed at the bottom of the well. Surfaces: top/bottom polished; sides and hole interior unpolished, wrapped with PTFE reflective tape. Readout via PMT (Hamamatsu R1307-07), Ortec 113 preamplifier, Ortec 672 spectroscopy amplifier, and APG7400A MCA. Shielding: ~15 mm Cu plus ~150 mm Pb. Typical counting rates: ~12 cps (with sample), ~4 cps (background). To mitigate long-timescale cosmic-ray background fluctuations, each Lu sample and the background were measured for 48 h each. Detection efficiency modeling: PHITS code simulated detection probability with full detector geometry and homogeneous source distribution, including self-absorption in the sample. A detected event required deposit energy ≥30 keV (validated by clear observation of ~31 keV Cs x-rays from 133Ba). Photon detection probabilities for 200–350 keV are >99.5%, ideal for 202 and 307 keV γ-rays from 176Lu. Internal conversion coefficients and electron energies from BrIcc were included. Electron detection probability decreases at low energy due to absorption in the sample. Effective detection probabilities for transitions (including conversion electrons): ~75.2% (88 keV), ~95.0% (202 keV), ~99.6% (307 keV). β rays from 176Lu have a continuous spectrum; calculated β detection probability ~50.8%. Overall total detection probability per 176Lu decay: ~99.9% with ±0.1% uncertainty. Calibration/examination: A 133Ba standard source was used to verify detector response. Outside the detector, individual γ-rays and Cs x-rays were observed; inside, sum peaks (437 and 384 keV) consistent with the feeding of the 437.0 keV (85.4%) and 383.8 keV (14.5%) levels in EC decay of 133Ba were observed. Although BGO thickness is marginal for 133Ba, the sum-peak yield matched the source activity within uncertainty. Spectra and backgrounds: Background features included Pb x-rays and a 570 keV γ-ray from intrinsic 207Bi in BGO, and a 662 keV γ-ray from 137Cs contamination in the room. Subtracting background from Lu spectra revealed Hf x-rays, 202 and 307 keV γ-rays, their 202+307 keV sum peak, and pile-up continuum (700–1000 keV). Half-life determination: The half-life is obtained by T1/2 = ln(2) · t · m · NA · ε · f · I / (Y · A), where t is measuring time, m is sample mass, NA = 6.02214 × 10^23 mol−1, ε total detection efficiency, f elemental Lu fraction, I isotopic abundance of 176Lu, Y measured yield (30–1192.8 keV), A atomic mass of natural Lu (174.967). For the two samples: total counts Y = 1,135,911 ± 1,467 and 1,100,590 ± 1,455; measuring times t = 171,834 s and 171,832 s; ε = 99.9 ± 0.1%; f = 99.9 ± 0.1%; I = 2.5987 ± 0.0012%. Relative uncertainties: ε 0.1%, f 0.1%, I 0.05%, mass 0.04%; time fluctuation <0.01%; NA and A uncertainties negligible. Systematic uncertainty from these contributions is 0.15%. Uncertainty propagation applied to Eq. (1) for total uncertainty.

• Measured half-life of 176Lu: (3.719 ± 0.007) × 10^10 years, corresponding to decay constant λ = (1.864 ± 0.003) × 10^−11 yr^−1.
• Per-sample results: [3.718 ± 0.005(stat.) ± 0.006(sys.)] × 10^10 yr and [3.720 ± 0.005(stat.) ± 0.006(sys.)] × 10^10 yr; combined systematic uncertainty ~0.15%.
• Total detection efficiency achieved: 99.9% ± 0.1%, with near-independence from nuclear-structure inputs (γ emission probabilities, internal conversion) and EC branching to 176Yb.
• The method avoids reliance on external calibration sources for efficiency, and is largely insensitive to sample contamination and branching to unobserved channels.
• The resulting half-life is consistent with values inferred from Lu-Hf isochrons of terrestrial rocks calibrated by U-Pb, reinforcing concordance with precisely known 235U and 238U half-lives.
• The result is shorter than some γ-γ coincidence measurements (e.g., 2003), likely due to complex correction requirements in multi-γ cascades and detector array combinatorics.
• This measurement provides the most precise laboratory half-life for 176Lu among reported methods.

The study addresses long-standing discrepancies in 176Lu half-life determinations by employing a windowless 4π BGO detector to record the total deposited energy per decay with near-unity efficiency, thereby minimizing uncertainties from nuclear-structure parameters and detection efficiency calibrations. The derived half-life aligns with terrestrial rock isochron results, supporting the use of Lu-Hf dating in geochemistry and cosmochemistry and demonstrating consistency with U-Pb chronometry. This strengthens confidence in ages derived from the Lu-Hf system where U-Pb may be unavailable. The method’s four key advantages—insensitivity to γ emission probabilities and EC branching, near-100% efficiency reducing dependence on simulations, no need for external efficiency calibration, and independence from meteorite isochron discrepancies—enhance accuracy and precision. The divergence from certain γ-γ coincidence results likely stems from the challenges of correcting for multiple-cascade coincidences and pile-up effects in complex detector arrays. Regarding meteorite-based shorter apparent half-lives, the authors discuss a plausible astrophysical mechanism: neutron-induced processes generated by cosmic-ray spallation. Neutrons with energies from ~123 keV to a few MeV can inelastically scatter on 176Lu, feeding the short-lived isomer and accelerating effective decay to 176Hf; additionally, 175Lu(n,γ)176Lum followed by decay contributes to 176Hf production. Because 175Lu(n,γ) also creates 176Lu over a wide neutron energy range, net 176Lu abundance changes may be muted, consistent with the lack of observed 176Lu deficits in meteorites. Detailed cross sections for 176Lu(n,n′) feeding the isomer are poorly known and merit further investigation.

This work provides the most precise laboratory determination of the 176Lu half-life to date, T1/2 = (3.719 ± 0.007) × 10^10 years, using an energy-summing, windowless 4π BGO detector that achieves near-unity efficiency and reduces dependence on nuclear-structure inputs and calibration uncertainties. The result validates Lu-Hf isochron ages for terrestrial rocks and supports consistency with U-Pb chronometry, thereby improving confidence in Lu-Hf dating across geoscience and cosmochemistry. The discussion offers a physically plausible explanation—cosmic-ray–induced neutron reactions—for shorter apparent half-lives inferred in some meteorites without requiring global changes to the decay constant. Future work should include: improved measurements and evaluations of neutron inelastic-scattering cross sections feeding 176Lum; expanded tests across different sample matrices and geometries to further validate near-100% efficiency assumptions; and targeted studies of meteorites to quantify potential cosmic-ray neutron effects and their depth/energy dependence.

• The total detection efficiency is modeled (PHITS) and inferred to be ~99.9% ± 0.1%; while close to unity, residual dependence on geometry and low-energy electron self-absorption remains.
• Intrinsic backgrounds (e.g., 207Bi in BGO) and environmental 137Cs were present; subtraction and shielding mitigate but do not eliminate potential systematic effects.
• Impurity assessments via ICP-MS covered a small area and may not represent full-sample averages; however, measured levels suggest negligible impact.
• The approach assumes stability of counting rates and background over multi-day runs; cosmic-ray variations are mitigated by matched background runs but could introduce small residual fluctuations.
• The study does not directly measure neutron-induced cross sections relevant to proposed meteorite scenarios; thus, the astrophysical explanation remains qualitative pending dedicated nuclear data.
• Energy threshold of 30 keV is justified by 133Ba x-rays but could marginally affect detection of very low-energy electrons, though impact on total efficiency is included in uncertainty.