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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Influence of Linker Identity on the Photochemistry of Uranyl-Organic Frameworks

While uranyl-based metal–organic frameworks (MOFs) boast impressive photocatalytic abilities, significant questions remain regarding their excitation pathways and methods to fine-tune their performance due to the lack of information regarding heterogeneous uranyl catalysis. Herein, we investigated how linker identity and photoexcitation impact uranyl photocatalysis when the uranyl coordination environment remains constant. Toward this end, we prepared three uranyl-based MOFs (NU-1301, NU-1307, and ZnTCPP-U2) and then examined the structural and photochemical properties of each through X-ray diffraction, X-ray absorption, and photoluminescence. We then correlated our observations to the photocatalytic performance for fluorination of cyclooctane. The excitation profile from NU-1301 and NU-1307 exhibited spin-forbidden linker transitions and uranyl vibronic progressions, with uranyl excitation and emission being most dominant in NU-1301. Consequently, NU-1301 was a more active photocatalyst than NU-1307. In contrast, the excitation profile from ZnTCPP-U2 contained transitions associated with the porphyrin linker exclusively. Photocatalytic activity from ZnTCPP-U2 significantly underperformed in comparison to that of the other two MOFs. Furthermore, these data suggest that linkers’ photophysical properties can be used to predict the photocatalytic behavior of uranyl-containing MOFs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Modulating Chemical Environments of Metal–Organic Framework-Supported Molybdenum(VI) Catalysts for Insights into the Structure–Activity Relationship in Cyclohexene Epoxidation

Solid supports are crucial in heterogeneous catalysis due to their profound effects on catalytic activity and selectivity. However, elucidating the specific effects arising from such supports remains challenging. We selected a series of metal–organic frameworks (MOFs) with 8-connected Zr 6 nodes as supports to deposit molybdenum(VI) onto to study the effects of pore environment and topology on the resulting Mo-supported catalysts. As characterized by X-ray absorption spectroscopy (XAS) and single-crystal X-ray diffraction (SCXRD), we modulated the chemical environments of the deposited Mo species. For Mo-NU-1000, the Mo species monodentately bound to the Zr 6 nodes were anchored in the microporous c-pore, but for Mo-NU-1008 they were bound in the mesopore of Mo-NU-1008. Both monodentate and bidentate modes were found in the mesopore of Mo-NU-1200. Cyclohexene epoxidation with H 2 O 2 was probed to evaluate the support effect on catalytic activity and to unveil the resulting structure–activity relationships. SCXRD and XAS studies demonstrated the atomically precise structural differences of the Mo binding motifs over the course of cyclohexene epoxidation. No apparent structural change was observed for Mo-NU-1000, whereas the monodentate mode of Mo species in Mo-NU-1008 and the monodentate and bidentate Mo species in Mo-NU-1200 evolved to a new bidentate mode bound between two adjacent oxygen atoms from the Zr 6 node. This work demonstrates the great advantage of using MOF supports for constructing heterogeneous catalysts with modulated chemical environments of an active species and elucidating structure–activity relationships in the resulting reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Customizable Aperture Geometry in Metal–Organic Frameworks for Kinetic Hydrocarbon Separation

Precise control of aperture dimensions is crucial in adsorptive separations of hydrocarbons, as it directly affects key parameters such as selectivity, capacity, diffusion, and recyclability. The development of metal–organic frameworks (MOFs) has enabled the fine-tuning of local pore environments to address important hydrocarbon separations. However, customizing the aperture geometry to tune the kinetic separation performance remains challenging. Here, we deploy a mixed-linker synthesis strategy, combining long and short linkers on fcu net Zr-MOFs with equilateral triangular apertures to construct isoreticular multivariate MOFs, NU-415 and NU-416, with tailored isosceles triangular apertures suitable for the separation of hexane isomers. Sorption, liquid batch separation, and X-ray diffraction measurements demonstrate significantly improved selectivity, capacity, stability, and recyclability of NU-415 and NU-416 compared with Zr-muconate and MOF-801. Notably, both NU-415 and NU-416 achieve uptake capacities of 2.2 mmol g –1 in 1 min with an n-hexane to 2,2-dimethylbutane selectivity over 200 in an equimolar ternary mixture at ambient conditions, comparable to leading reported materials. Mechanistic studies confirm that separation performance is predominantly governed by significant kinetic differences rather than by thermodynamics. Furthermore, the successful customization of aperture geometry not only enables superior linear to monobranched hexane selectivity in NU-415 but also demonstrates the mixed-linker synthesis strategy as a promising solution for precise and predictable pore architecture control in MOFs.

Adsorption↗
DOE OSTI2022

Coherent elastic neutrino-nucleus scattering: Terrestrial and astrophysical applications

Coherent elastic neutrino-nucleus scattering (CE$\nu$NS) is a process in which neutrinos scatter on a nucleus which acts as a single particle. Though the total cross section is large by neutrino standards, CE$\nu$NS has long proven difficult to detect, since the deposited energy into the nucleus is $\sim$ keV. In 2017, the COHERENT collaboration announced the detection of CE$\nu$NS using a stopped-pion source with CsI detectors, followed up the detection of CE$\nu$NS using an Ar target. The detection of CE$\nu$NS has spawned a flurry of activities in high-energy physics, inspiring new constraints on beyond the Standard Model (BSM) physics, and new experimental methods. The CE$\nu$NS process has important implications for not only high-energy physics, but also astrophysics, nuclear physics, and beyond. This whitepaper discusses the scientific importance of CE$\nu$NS, highlighting how present experiments such as COHERENT are informing theory, and also how future experiments will provide a wealth of information across the aforementioned fields of physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Modeling and evaluating 239 Pu and 235 U PFNS and average prompt-neutron multiplicity [Slides]

The following are currently in VIII.1 LANL and IAEA test files: 239 Pu nu-bar including CGMF modeling and CEA data, 239 Pu PFNS including Chi-Nu & CEA data, 239 Pu(n,f) cross section including fission TPC data. The following are currently being tested: 235 U nu-bar including CGMF modeling and 235 U PFNS including Chi-Nu data. Upcoming tasks include the correction of 235 U Chi-Nu PFNS at higher E inc , benchmarking 235 U PFNS and nu-bar evaluations, and getting 238 U nu-bar.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

New results from the CUORE experiment

The Cryogenic Underground Observatory for Rare Events (CUORE) is the first cryogenic experiment searching for neutrinoless double-beta ($0\nu\beta\beta$) decay that has been able to reach the one-ton scale. The detector, located at the Laboratori Nazionali del Gran Sasso in Italy, consists of an array of 988 TeO$_2$ crystals arranged in a compact cylindrical structure of 19 towers. Following the completion of the detector construction in August 2016, CUORE began its first physics data run in 2017 at a base temperature of about 10 mK. Following multiple optimization campaigns in 2018, CUORE is currently in stable operating mode. In 2019, CUORE released its 2\textsuperscript{nd} result of the search for $0\nu\beta\beta$ with a TeO$_2$ exposure of 372.5 kg$\cdot$yr and a median exclusion sensitivity to a $^{130}$Te $0\nu\beta\beta$ decay half-life of $1.7\cdot 10^{25}$ yr. We find no evidence for $0\nu\beta\beta$ decay and set a 90\% C.I. (credibility interval) Bayesian lower limit of $3.2\cdot 10^{25}$ yr on the $^{130}$Te $0\nu\beta\beta$ decay half-life. In this work, we present the current status of CUORE's search for $0\nu\beta\beta$, as well as review the detector performance. Finally, we give an update of the CUORE background model and the measurement of the $^{130}$Te two neutrino double-beta ($2\nu\beta\beta$) decay half-life.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Data-driven Techniques for $v^{e}$ Signal and Background Predictions in NOνA

NOν \nu A is a long baseline neutrino oscillation experiment, using two functionally identical detectors to measure νe \nu_e appearance and νμ \nu_\mu disappearance at the Far Detector (FD) with the NuMI Beam at Fermilab. The Near Detector (ND) measures the beam before oscillations, which will allow us to make a measurement of the signal flux before it has oscillated and the background components which can mimic νe \nu_e at our FD. We use the ND in three different ways to predict the amount of signal and background expected at the FD to partially cancel systematic uncertainties. The background prediction has three components: Charged Current (CC) νμ \nu_\mu , νe \nu_e and Neutral Current (NC) events. We need to determine the fraction of the selected ND sample in each of these components because some oscillate significantly (CC νμ \nu_\mu ) and some do not oscillate at all (NC). This poster will present details of these three data-driven techniques for predicting the FD spectrum.

Yu, Shiqi [Argonne; IIT, Chicago]↗
DOE OSTI2020

Reticular exploration of uranium-based metal—organic frameworks with hexacarboxylate building units

We report that the rational reticular design of metal–organic frameworks (MOFs) from building units of known geometries is essential for enriching the diversity of MOF structures. Unexpected and intriguing structures, however, can also arise from subtle changes in the rigidity/length of organic linkers and/or synthetic conditions. Herein, we report three uranium-based MOF structures—i.e., NU-135X (X = 0, 1, 2)—synthesized from trigonal planar uranyl nodes and triptycene-based hexacarboxylate ligands with variable arm lengths. A new chiral 3,6-connected nuc net was observed in NU-1350, while the extended versions of the ligand led to 3-fold catenated MOFs (NU-1351 and NU-1352) with rare 3,6-connected cml-c3 nets. Lastly, the differences in the topology of NU-1350 and NU-1351/NU-1352 could be attributed to the slight distortions of the shorter linker in the former from the ideal trigonal prism geometry to an octahedral geometry when coordinated to the trigonal planar uranyl nodes.

3,6-connected net↗
DOE OSTI2024

Constraining Flexibility in the MIL-88 Topology through Integration of 3-Dimensional Linkers

Metal–organic frameworks (MOFs) are a class of crystalline, nanoporous materials that are recognized for their tunability. While some MOFs demonstrate flexibility, this characteristic can pose challenges in achieving precise pore control or establishing permanent porosity. Specifically, MIL-88B, is notable for its high flexibility, as it is constructed from metal trimer clusters and 2-dimensional linkers (2DLs) featuring planar, aromatic cores, allowing significant structural changes. In this study, we synthesized two new MOFs, NU-2010 and NU-2011, which are structurally analogous to MIL-88B but incorporate ditopic 3-dimensional linkers (3DLs) with sterically bulky cores and higher symmetry. Our aim was to investigate whether the introduction of 3DLs could mitigate the flexibility observed in MIL-88B. We employed a combination of single crystal and powder X-ray diffraction techniques to assess the flexibility of MIL-88B, NU-2010, and NU-2011 under various conditions including thermal activation, solvent exchange, and temperature changes. Furthermore, our findings indicate that incorporating 3DLs significantly reduces framework flexibility in NU-2010 and NU-2011 relative to MIL-88B.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Tuning the Conductivity of Hexa-Zirconium(IV) Metal–Organic Frameworks by Encapsulating Heterofullerenes

Electrical conductivity in metal–organic frameworks (MOFs) has a great potential for energy storage applications and electrocatalysis. Zirconium-based MOFs such as NU-901 and NU-1000 have a low electrical conductivity due to the redox innocence of Zr–oxo bonds. Recently, it has been shown that the electrical conductivity of NU-901 can be increased by 11 orders of magnitude by physically encapsulating fullerene (C 60 ) in its diamond pore. This effect is due to the host–guest interaction between the electron-rich 1,3,6,8-tetrakis(p-benzoate)pyrene (TBAPy 4– ) organic linkers of NU-901 (host) and the electron-poor fullerene (guest). Herein, we used density functional theory to study heterofullerene (C 59 X; X = B, Al, Ga, In, Si, Ge, and Sn) encapsulation in NU-901. Furthermore, our study suggests that encapsulated heterofullerenes enhance the electrical conductivity of the NU-901 MOF even further than C 60 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Nanocluster Rearrangement Forms a Family of Ordered Cerium–Titanium Bimetallic Metal–Organic Frameworks with Three Different Nodes, Nanocavities, and Thermal Stabilities

Metal–organic frameworks (MOFs) provide a versatile platform for incorporating multiple metal ions within a single crystalline framework, yet achieving spatial and stoichiometric order in heterometallic nodes remains a synthetic challenge. Building on our previously reported, highly thermally stable Ce/Ti bimetallic MOF NU-3000, we identified and isolated two additional crystalline phases, NU-2998 and NU-2999, that arise from the same Ce/Ti nanocluster precursor under modified solvothermal conditions. Systematic variation of reaction temperature, time, solvent ratio, and modulator concentration directs the assembly of these distinct frameworks. Structural analysis and comprehensive characterization studies reveal that these MOFs each feature an unreported nodal geometry with nanocavities of different sizes. NU-2998 even adopts an unreported topology, denoted nui , that features an elongated pore spanning 4 nm. Together, these findings establish a synthesis route that starts with a nanocluster and ends with a set of bimetallic MOFs, offering a glimpse into the pathway-dependent assembly of multimetallic porous materials. Finally, we evaluated the thermal stability of each additional analogue and compared them to NU-3000, providing further insight into material stability. NU-3000 maintained the highest thermal stability and was evaluated as a catalyst for CO oxidation at elevated temperatures.

bimetallic MOFs↗
DOE OSTI2021

Neutrino(antineutrino)–nucleus interactions in the shallow- and deep-inelastic scattering regions

In $\nu /\bar{\nu }$–nucleon/nucleus interactions shallow inelastic scattering ($\text{SIS}$) is technically defined in terms of the four-momentum transfer to the hadronic system as non-resonant meson production with $Q^2 \lessapprox 1 \text {GeV}^2$. This non-resonant meson production intermixes with resonant meson production in a regime of similar effective hadronic mass W of the interaction. As $Q^2$ grows and surpasses this $ ≈1 \text{GeV}^2$ limit, non-resonant interactions begin to take place with quarks within the nucleon indicating the start of deep inelastic scattering ($\text{DIS}$). To essentially separate this resonant plus non-resonant meson production from $\text{DIS}$ quark-fragmented meson production, a cut of 2 $\text{GeV}$ in W of the interactions is generally introduced. However, since experimentally mesons from resonance decay cannot be separated from non-resonant produced mesons, $\text{SIS}$ for all practical purposes in this review has been defined as inclusive meson production that includes non-resonant plus resonant meson production and the interference between them. Experimentally then for $W \lessapprox 2 \text{GeV}$ inclusive meson production with $W \gtrapprox (M_N + M_π)$ and all $Q^2$ is here defined as $\text{SIS}$, while for $W \gtrapprox 2 \text {GeV}$, the kinematic region with $Q^2 \gtrapprox 1 \text{GeV}^2$ is defined as DIS$\text{DIS}$degrees of attention from the community. While the theoretical/phenomenological study of $\nu$–nucleon and $\nu$–nucleus $\text{DIS}$ scattering is advanced, such studies of a large portion of the $\text{SIS}$ region, particularly the $\text{SIS}$ to $\text{DIS}$ transition region, have hardly begun. Experimentally, the $\text{SIS}$ and the $\text{DIS}$ regions for $\nu$–nucleon scattering have minimal results and only in the experimental study of the $\nu$–nucleus $\text{DIS}$ region are there significant results for some nuclei. Inasmuch as current and future neutrino oscillation experiments have contributions from both higher $W \text{SIS}$ and $\text{DIS}$ kinematic regions and these regions are in need of both considerable theoretical and experimental study, this review will concentrate on these $\text{SIS}$ to $\text{DIS}$ transition and $\text{DIS}$ kinematic regions surveying our knowledge and the current challenges.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Interplay between fractional quantum Hall liquid and crystal phases at low filling

The nature of the state at low Landau-level filling factors has been a long-standing puzzle in the field of the fractional quantum Hall effect (FQHE). While theoretical calculations suggest that a crystal is favored at filling factors $\nu$≲1/6, experiments show, at somewhat elevated temperatures, minima in the longitudinal resistance that are associated with fractional quantum Hall effect at $\nu$ 1/7, 2/11, 2/13, 3/19, 1/9, 2/15, and 2/17, which belong to the standard sequences $\nu$ =n/(6n ± 1) and $\nu$=n/(8n ± 1). To address this paradox, we investigate the nature of some of the low-$\nu$ states, specifically $\nu$= 1/7, 2/13, and 1/9, by variational Monte Carlo, density matrix renormalization group, and exact diagonalization methods. We conclude that in the thermodynamic limit, these are likely to be incompressible fractional quantum Hall liquids, albeit with strong short-range crystalline correlations. Finally, this suggests a natural explanation for the experimentally observed behavior and a rich phase diagram that admits, in the low-disorder limit, a multitude of crystal-FQHE liquid transitions as the filling factor is reduced.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Hint of a new scalar interaction in LHCb data?

Abstract We explain recent LHCb measurements of the lepton universality ratios, $$R_{D^{(*)}}^{\tau /\ell }\equiv \frac{\mathcal {B}(\bar{B} \rightarrow D^{(*)+} \tau ^- \bar{\nu }_\tau )}{\mathcal {B}(\bar{B} \rightarrow D^{(*)+}\ell ^- \bar{\nu }_\ell )}$$ R D ( ∗ ) τ / ℓ ≡ B ( B ¯ → D ( ∗ ) + τ - ν ¯ τ ) B ( B ¯ → D ( ∗ ) + ℓ - ν ¯ ℓ ) and $${R(\Lambda _c^+)}^{\tau /\ell } \equiv \frac{\mathcal {B}(\Lambda _b \rightarrow \Lambda _c^+ \tau ^- \bar{\nu }_{\tau })}{\mathcal {B}(\Lambda _b \rightarrow \Lambda _c^+ \ell ^- \bar{\nu }_{\ell })}$$ R ( Λ c + ) τ / ℓ ≡ B ( Λ b → Λ c + τ - ν ¯ τ ) B ( Λ b → Λ c + ℓ - ν ¯ ℓ ) with $$\ell =\mu $$ ℓ = μ , via new physics that affects $$R_D^{\tau /\ell }$$ R D τ / ℓ and $$R(\Lambda _c^+)^{\tau /\ell }$$ R ( Λ c + ) τ / ℓ but not $$R_{D^*}^{\tau /\ell }$$ R D ∗ τ / ℓ . The scalar operator in the effective theory for new physics is indicated. We find that the forward-backward asymmetry and $$\tau $$ τ polarization in $$\bar{B} \rightarrow D^+ \tau ^{-} \bar{\nu }_{\tau }$$ B ¯ → D + τ - ν ¯ τ and $$\Lambda _b \rightarrow \Lambda _c^+ \tau ^- \bar{\nu }_{\tau }$$ Λ b → Λ c + τ - ν ¯ τ decays are significantly affected by the scalar interaction. We construct a simple two Higgs doublet model as a realization of our scenario and consider lepton universality in semileptonic charm and top decays, radiative B decay, B -mixing, and $$Z \rightarrow b \bar{b}$$ Z → b b ¯ .

Physics↗
DOE OSTI2026

Bayesian Fit to NOvA Data Subsamples for Three Flavor Oscillation Analysis

NOvA (NuMI Off-Axis $\nu_e$ Appearance) is a long baseline neutrino experiment designed to measure the oscillation of muon neutrinos to electron neutrinos over a distance of 810 km. NOvA uses a near and far detector to observe $\nu_\mu$ disappearance and $\nu_e$ appearance of neutrinos produced by the NuMI beam at Fermilab. NOvA uses a Bayesian analysis framework in addition to its Frequentist method to measure neutrino oscillation parameters such as the mixing angles, mass ordering, and CP-violating phase. We report preliminary results of Bayesian fits to representative NOvA datasets. Comparison of fits to $\nu_\mu$ disappearance and $\nu_e$ appearance enables a cross-check of NOvA results with reactor $\bar{\nu_e}$ disappearance measurements. NOvA also searches for violation of Lorentz invariance by analyzing fits of forward horn current (FHC) versus reverse horn current (RHC) samples. The results validate and advance NOvA's contributions to precision measurements of neutrino properties.

Zhao, Larry [Fermilab]↗
DOE OSTI2021

QED radiative corrections to neutrino-nucleon elastic scattering

Neutrino oscillation experiments at accelerator energies aim to establish CP violation in the neutrino sector by measuring the energy-dependent rate of $\nu_e$ appearance and $\nu_\mu$ disappearance in a $\nu_\mu$ beam. Extracting the correct oscillation rate demands control over QED radiative corrections at the percent level. Focusing on the critical charged-current neutrino-nucleon scattering process, we show that the cross section factorizes into two pieces. The first piece depends on hadron structure but is universal for $\nu_e$ and $\nu_\mu$, and hence constrained by high-statistics $\nu_\mu$ data. The second piece is nonuniversal and suffers large logarithm enhancements, but is computed to high precision using renormalization group improved perturbation theory. Our results provide a missing ingredient for the robust interpretation of current NOvA and T2K experiments, and can be applied to future experiments such as DUNE and HyperK.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Sensitivity of the NEXT experiment to Xe-124 double electron capture

Double electron capture by proton-rich nuclei is a second-order nuclear process analogous to double beta decay. Despite their similarities, the decay signature is quite different, potentially providing a new channel to measure the hypothesized neutrinoless mode of these decays. The Standard-Model-allowed two-neutrino double electron capture (2$\nu$EC EC) has been predicted for a number of isotopes, but only observed in 78 Kr, 130 Ba and, recently, 124 Xe. The sensitivity to this decay establishes a benchmark for the ultimate experimental goal, namely the potential to discover also the lepton-number-violating neutrinoless version of this process, 0$\nu$EC EC. Here we report on the current sensitivity of the NEXT-White detector to 124 Xe 2$\nu$EC EC and on the extrapolation to NEXT-100. Using simulated data for the 2$\nu$EC EC signal and real data from NEXT-White operated with 124 Xe-depleted gas as background, we define an optimal event selection that maximizes the NEXT-White sensitivity. We estimate that, for NEXT-100 operated with xenon gas isotopically enriched with 1 kg of 124 Xe and for a 5-year run, a sensitivity to the 2$\nu$EC EC half-life of 6 × 10 22 y (at 90% confidence level) or better can be reached.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Latest Results from the CUORE Experiment

Abstract The Cryogenic Underground Observatory for Rare Events (CUORE) is the first cryogenic experiment searching for $$0\nu \beta \beta $$ 0 ν β β decay that has been able to reach the one-tonne mass scale. The detector, located at the Laboratori Nazionali del Gran Sasso (LNGS) in Italy, consists of an array of 988 $${\mathrm{TeO}}_{2}$$ TeO 2 crystals arranged in a compact cylindrical structure of 19 towers. CUORE began its first physics data run in 2017 at a base temperature of about 10 mK and in April 2021 released its $$3{\mathrm{rd}}$$ 3 rd result of the search for $$0\nu \beta \beta $$ 0 ν β β , corresponding to a tonne-year of $$\mathrm{TeO}_{2}$$ TeO 2 exposure. This is the largest amount of data ever acquired with a solid state detector and the most sensitive measurement of $$0\nu \beta \beta $$ 0 ν β β decay in $${}^{130}\mathrm{Te}$$ 130 Te ever conducted . We present the current status of CUORE search for $$0\nu \beta \beta $$ 0 ν β β with the updated statistics of one tonne-yr. We finally give an update of the CUORE background model and the measurement of the $${}^{130}\mathrm{Te}$$ 130 Te $$2\nu \beta \beta $$ 2 ν β β decay half-life and decay to excited states of $${}^{130}\mathrm{Xe}$$ 130 Xe , studies performed using an exposure of 300.7 kg yr.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗