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The Standard Model Theory of Neutron Beta Decay

We review the status of the Standard Model theory of neutron beta decay. Particular emphasis is put on the recent developments in the electroweak radiative corrections. Given that some existing approaches give slightly different results, we thoroughly review the origin of discrepancies, and provide our recommended value for the radiative correction to the neutron and nuclear decay rates. The use of dispersion relation, lattice Quantum Chromodynamics, and an effective field theory framework allows for high-precision theory calculations at the level of 10 –4 , turning neutron beta decay into a powerful tool to search for new physics, complementary to high-energy collider experiments. We offer an outlook to the future improvements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Critical and Californium Source-Driven Noise Analysis Subcritical Measurements with an Unreflected Cylindrical Tank of Mixed Uranium-Plutonium Nitrate Solution

The reported experiments were performed by Oak Ridge National Laboratory (ORNL) at the Battelle Northwest Laboratory’s (now Pacific Northwest National Laboratory) critical experiments facility at Hanford, Washington in 1981 and used 16 days of critical facility time, not including 10 days for setup and removal of ORNL equipment. These measurements were to assess the capability of the Cf source-driven noise analysis (CSDNA) method to measure the subcriticality (keff) of mixed U-Pu nitrate solutions. In addition to the CSNDA measurements, measurements were also performed near delayed criticality where CSDNA measurements cannot be performed. This report documents the experiments that were not reported at that time by presenting the ORNL experimental results and any online analysis performed during and shortly after the measurements. The mixed nitrate solution had a U concentration at 188 grams per liter (g/L), a Pu concentration of 280 g/L, free acid normality of 2.80, H ion molarity of 5.9 and a specific gravity of 1.754 g/cm 3 , a 240 Pu isotopic content of 7.981 wt. %, and a 235 U isotopic content of 0.724 wt. %. The stainless-steel tank for the solution had an inside diameter of 35.38 cm, an outside diameter of 35.53 cm, a height of 56.72 cm, and bottom thickness of 0.9525 cm. A Zircaloy pipe with a 3.1496 cm outside diameter, a 2.7788 cm inside diameter, and bottom thickness of 0.635 cm was available for insertion of the Cf source in the center of the fissile solution. The Cf source was also located at the outside surface of the tank (solution height varied from 10 to 53 cm) and in the center of the solution (solution height varied from 10 to 60.7 cm). The CSDNA measurements were not analyzed online to determine the subcritical neutron multiplication factors. At all subcritical states, the break frequency noise analysis data was fitted to obtain the prompt neutron decay constant. The neutron multiplication factors were determined for the two configurations of the measurements near delayed criticality. The subcritical neutron multiplication factors from the CNSDA measurements can be obtained with further analysis. However, the near delayed critical configuration, the prompt neutron decay constants, the count rates, and the measured cross and auto power spectral densities can be calculated directly for benchmarking. Much of data presented in this report are from ORNL notes—not in the ORNL logbooks. For the final benchmark analysis, the data from the Battelle Northwest Laboratory (which operated the critical facility in 1981) critical facility logbook should be consulted and be incorporated where appropriate. The purpose of this report is to document the experimental information for the measurements performed so that at a later date researchers could perform the required uncertainty and calculational analyses and documentation to use these data for an International Criticality Safety Benchmark Program (ICSBEP) or Nuclear Energy Agency benchmark. The data from these measurements are available from the ORNL Records Management Services Department, and the logbook is available from ICSBEP at Idaho National Laboratory. Preparation of the present report is part of a larger cooperative effort between Idaho National Laboratory (INL) and Oak Ridge National Laboratory (ORNL) to document more than 15 undocumented critical and subcritical experiments enumerated in ORNL/TM-2019/18 and performed by ORNL at ORCEF and other USDOE critical experiments facilities using more than 500 operational days of critical facility time.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Radiative Corrections to Neutron Beta Decay and (Anti)Neutrino-Nucleon Scattering from Low-Energy Effective Field Theory

Herein we study radiative corrections to neutron beta decay and low-energy (anti)neutrino-nucleon scattering within a top-down effective field theory approach. As it was recently shown, a few electromagnetic and electroweak low-energy coupling constants in heavy-baryon chiral perturbation theory are yet to be determined. Performing matching to the four-fermion effective field theory, we relate these low-energy constants to correlation functions of vector and axial-vector currents. Such relations allow us to explicitly clarify scheme dependence for radiative corrections to neutron decay and low-energy charged-current (anti)neutrino scattering, provide a robust prediction of leading in the electromagnetic coupling constant contributions, and achieve a clear separation between short-distance and long-distance contributions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Factorization and resummation of QED radiative corrections for neutron beta decay

Details of the two-loop analysis of long-distance QED radiative corrections to neutron beta decay are presented. Explicit expressions are given for hard, jet, and soft functions appearing in the factorization formula that describes the limit of small electron mass and large electron energy. Numerical enhancements from the infrared region are resummed using renormalization group methods. Power corrections, cancellation of singularities in the small-mass expansion, renormalization scheme dependence, and bound-state effects are also discussed. These results provide the most precise determination of long-distance radiative corrections to neutron beta decay and impact the determination of |𝑉 𝑢⁢𝑑 | from the measured neutron lifetime and thus set a target for uncertainty reductions in the experimental and short-distance inputs.

Beta decay↗

Exploring 𝛽 decay and 𝛽-delayed neutron emission in exotic 46,47 Cl isotopes

In this paper, 𝛽 − and 𝛽-delayed neutron decays of 46,47 Cl are reported from an experiment carried out at the National Superconducting Cyclotron Laboratory using the Beta Counting System. The half-lives of both 46 Cl and 47 Cl were extracted. Based on the delayed 𝛾-ray transitions observed, the level structure of 𝑁=28 46 Ar was determined. Completely different sets of excited states above the first 2 + state in 46 Ar were populated in the 46 Cl 𝛽⁢0⁢𝑛 and 47 Cl 𝛽⁢1⁢𝑛 decay channels. Two new 𝛾-ray transitions in 47 Ar were identified from the very weak 47 Cl 𝛽⁢0⁢𝑛 decay. Furthermore, 46 Cl 𝛽⁢1⁢𝑛 and 47 Cl 𝛽⁢2⁢𝑛 were also observed to yield different population patterns for levels in 45 Ar, including states of different parities. Here, the experimental results allow us to address some of the open questions related to the delayed neutron emission process. For isotopes with large neutron excess and high 𝑄 𝛽 values, delayed neutron emission remains an important decay mode and can be utilized as a powerful spectroscopic tool. Experimental results were compared with shell-model calculations using the FSU and 𝑉 MU effective interactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Study of neutron beta decay with the Nab experiment

The current three sigma tension in the unitarity test of the Cabbibo-Kobayashi-Maskawa (CKM) matrix is a notable problem with the Standard Model of elementary particle physics. A long-standing goal of the study of free neutron beta decay is to better determine the CKM element Vud through measurements of the neutron lifetime and a decay correlation parameter. The Nab collaboration intends to measure a, the neutrino-electron correlation, with accuracy sufficient for a competitive evaluation of Vud based on neutron decay data alone. This paper gives a status report and an outlook.

Baessler, Stefan↗

Pion-Induced Radiative Corrections to Neutron β Decay

In this work, we compute the electromagnetic corrections to neutron β decay using a low-energy hadronic effective field theory. We identify new radiative corrections arising from virtual pions that were missed in previous studies. The largest correction is a percent-level shift in the axial charge of the nucleon proportional to the electromagnetic part of the pion-mass splitting. Smaller corrections, comparable to anticipated experimental precision, impact the β-ν angular correlations and the β asymmetry. We comment on implications of our results for the comparison of the experimentally measured nucleon axial charge with first-principles computations using lattice QCD and on the potential of β decay experiments to constrain beyond-the-standard-model interactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Fundamental Neutron Physics: Theory and Analysis

The goal of the proposed research is the study of the possible manifestations of new physics beyond the Standard model in fundamental neutron physics, with emphasis on fundamental symmetries and "exotic'' interactions. The main part of the research will be focused on theoretical support of the search for Time Reversal Invariance Violation (TRIV) in neutron nuclei scattering. The existence of our universe, and the prevalence of matter over antimatter, requires TRIV (the impossibility of going from the past to the future). However, the source of TRIV in the Standard model is not strong enough to explain why our universe exists. Thus, the observation of large TRIV effects will be a clear signal of new physics. The proposed research topics include calculations of Parity Violating (PV) and TRIV effects in neutron nuclei scattering on different targets, and the study of the possible manifestations of new physics in neutron-decays, neutron-antineutron oscillations, and in interactions of ultra-cold neutrons with nuclei. This research will provide theoretical support to the ongoing experimental programs related to the search for TRIV in neutron scattering at Los Alamos National Laboratory and J-PARC (Japan), and will contribute in the efforts in searching for new physics in fundamental neutron physics experiments at the Oak Ridge National Laboratory, and at other national and international neutron research centers.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Examination of Digital-Delay Rossi-$\alpha$ for 252 Cf-Driven Highly Enriched Uranium Using Organic Scintillators

Neutron noise techniques constitute several analysis methods applicable to non-destructive assay. One technique is the Rossi-α method to calculate the prompt neutron decay constant (α) or its inverse, the prompt neutron period (1/α), for assemblies of fissionable material. This work evaluates a high-data-throughput measurement at the National Criticality Experiments Research Center (NCERC) with organic scintillators measuring a subcritical assembly of highly enriched uranium (HEU) metal (93% 235 U). The assembly comprises hemi shells stacked together to form fully closed shells and is driven by a Cf source at the center. The assembly is a total of 59.85 kg HEU and a k eff of 0.99, according to MCNP6.2 KCODE simulations. Measurements were acquired with a three-by-four array of 5.08-cm-diameter by 5.08-cm-length trans-stilbene crystals 166 cm from the assembly center. Two types of coincident binning methods are used to build the Rossi-α distribution of coincident neutron detections: A) type 1 binning, also known as any-and-all forward time differences, and B) type 1 binning with a digital-delay technique that is analogous to Orndoff’s use of delay cabling in early Rossi-alpha measurements. Method B) disregards same-detector coincidences and once all nearest time coincidences are collected between all detectors after a trigger, a time delay of 0.75 µs is implemented. The measured prompt neutron decay constants for both techniques are calculated from single exponential fits and the two methods are compared. Method A) shows an apparent timing discontinuity near 500 ns time differences. This timing discontinuity interferes with the fitting method used to calculate the prompt neutron decay constant. Method B) mitigates the artificial timing discontinuity and removes the disagreement of the fit. Future work will model the time-dependent detector response to discern why this timing discontinuity occurs, discern how Method B) reduces the amplitude of this timing discontinuity, and apply this method to critical assembly measurements to ultimately confirm the recommendation to use Method B) for high-data-throughput measurements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Data Assimilation using Non-invasive Monte Carlo Sensitivity Analysis of Reactor Kinetics Parameters [Slides]

Sensitivity coefficients of prompt neutron decay constant (α) and effective delayed neutron fraction (β eff ) to Pu-239 nuclear data were calculated using a newly available tool (ACEtk). Uncertainty calculations showed the following trends: (1) The prompt neutron decay constant can be used to reduce nuclear data-induced uncertainty in Pu-239(n,f) and (2) the effective delayed neutron fraction can be used to effectively reduce nuclear data-induced uncertainty in Pu-239 total fission $\tilde{v}$. Sensitivity/uncertainty analysis can be used to determine optimal experiment/detector setup to identify compensating errors in nuclear data. Upcoming work includes investigating other nuclide-reaction pairs and response sensitivities, such as Δ$\rho$, neutron leakage spectra, and reaction rate measurements to constrain nuclear data of interest.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Initial Delayed Critical Configuration of SHEBA I and Subcritical Measurements by Californium Source-Driven Noise Analysis

In September 1980, the initial delayed critical configuration of the Solution High-Energy Burst Assembly (SHEBA I) was assembled, and the US Department of Energy’s Oak Ridge National Laboratory (ORNL) staff performed near critical and subcritical measurements using the californium source-driven noise analysis (CSDNA) method at the Los Alamos National Laboratory (LANL) Critical Experiments Facility. An unreflected 56 cm outside diameter stainless-steel cylindrical tank was partially filled with uranyl fluoride solution (235U enrichment was 4.95 wt %) until delayed criticality was achieved. Then, measurements were performed for various fuel solution heights from delayed critical to 60% of the height required for delayed criticality. The stainless-steel tank had an inside diameter of 54.6 cm and a height of 105 cm and was partially (20–36.5 cm) filled with an aqueous solution of uranyl fluoride (with a density of 2.162 g/cm 3 ). The density of the uranium in solution was 1.042 g/cm 3 , and the solution had a H/U atomic ratio of 20.43. The tank had a 6.35 mm wall thickness and an axial reentrant tube with an inside diameter of 6.02 cm and wall thickness of 0.165 cm. The tank was essentially unreflected on the top and sides because it was in a thin metal shed. The reactivity of the near–delayed critical configuration was −10.4 cents, which corresponds to a k eff value of 0.99922. In addition to the CSDNA measurements, the prompt neutron decay constants were determined from break frequency noise analysis (BNFA) measurements. The subcritical neutron multiplication factors from CSDNA and BFNA compared extremely well. These data can be used as the basis of International Nuclear Criticality Safety Evaluation benchmark for the near-critical configuration, and the k eff values at various subcritical configurations can be used as subcritical benchmarks. Furthermore, the measured prompt neutron decay constants can be used as reactor physics benchmarks. This report documents the experimental information for the measurements performed so that, at a later date, researchers could perform the required uncertainty and calculational analyses and documentation to use these data for an International Criticality Safety Benchmark Evaluation Program (ICSBEP) or Nuclear Energy Agency benchmarks. The measured prompt neutron decay constants can be used as the basis of a benchmark for the International Reactor Physics Evaluation Program (IRPhEP). The data from these measurements are available from the ORNL Records Management Services Department, and the logbook is available from ICSBEP at Idaho National Laboratory.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Feynman-α analysis using BGO gamma-ray detector in UTR-KINKI reactor

In conventional reactor noise measurement based on neutron detection, a neutron detector must be placed as close to a core as possible, to observe a largest possible correlation amplitude. For most of reactors other than critical assemblies, however, the placement is hardly possible. We focused on an alternative reactor noise measurement using prompt gamma-rays having a long flight range, to overcome the above constraint. A Feynman-α analysis using a NaI(Tl) scintillation detector was previously performed in UTR-KINKI, however, white noise originating from radioactivation of the scintillator significantly degraded the correlation amplitude. In this study, another Feynman-α analysis using a BGO gamma-ray detector, which never suffers from any radioactivation, is performed. A series of Feynman-α analyses for a critical state and several subcritical states of UTR-KINKI reactor has been carried out using two BGO detectors and a BF{sub 3} neutron detector to determine prompt-neutron decay constant. In the present analysis, the dead-time effect of these detectors and the delayed-neutron effect are considered. The prompt-neutron decay constant determined from Feynman-α analysis based on gamma-ray detection agrees with that from the analysis based on neutron detection. The Feynman-α analysis based on detecting gamma rays appears to be able to determine prompt-neutron decay constant at least as efficiently as the conventional analysis detecting neutrons.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Lattice QCD Calculation of Electroweak Box Contributions to Superallowed Nuclear and Neutron Beta Decays

We present the first lattice QCD calculation of the universal axial γ W -box contribution □ γ W V A to both superallowed nuclear and neutron beta decays. This contribution emerges as a significant component within the theoretical uncertainties surrounding the extraction of | V u d | from superallowed decays. Our calculation is conducted using two domain wall fermion ensembles at the physical pion mass. To construct the nucleon four-point correlation functions, we employ the random sparsening field technique. Furthermore, we incorporate long-distance contributions to the hadronic function using the infinite-volume reconstruction method. Upon performing the continuum extrapolation, we arrive at □ γ W V A = 3.65 ( 7 ) lat ( 1 ) PT × 10 − 3 . Consequently, this yields a slightly higher value of | V u d | = 0.973 86 ( 11 ) exp ( 9 ) RC ( 27 ) NS , reducing the previous 2.1 σ tension with the CKM unitarity to 1.8 σ . Additionally, we calculate the vector γ W -box contribution to the axial charge g A , denoted as □ γ W V V , and explore its potential implications. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Fill and dump measurement of the neutron lifetime using an asymmetric magneto-gravitational trap

The past two decades have yielded several new measurements and reanalysis of older measurements of the neutron lifetime. These have led to a 4.4 standard deviation discrepancy between the most precise measurements of the neutron decay rate producing protons in cold neutron beams and the most precise lifetime measured in neutron storage experiments. Measurements using different techniques are important for investigating whether there are unidentified systematic effects in any of the measurements. In this paper we report a new measurement using the Los Alamos asymmetric magneto-gravitational trap where the surviving neutrons are counted external to the trap using the fill and dump method. In this work, the new measurement gives a free neutron lifetime of $τ_n$ = 876.3(2.4) stat (0.8) syst . Although this measurement is not as precise, it is in statistical agreement with previous results using in situ counting in the same apparatus.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Evolution of the two-neutron configuration from 11 Li to 13 Li

In this work we investigate the two-neutron decay of 13 Li and of the excited states of 11 Li populated via one-proton removal from 14 Be and 12 Be, respectively. A phenomenological model is used to describe the decay of 11 Li and 13 Li. While the first one displays important sequential components, the second one appears dominated by the direct two-neutron decay. A microscopic three-body model is used to extract information on the spatial configuration of the emitted neutrons before the decay and shows that the average distance between the neutrons increases going from 11 Li to 13 Li.

Dineutron decay↗

Measurement uncertainty of rossi-alpha neutron experiments

Rossi-alpha neutron experiments are used to estimate the prompt neutron decay constant of a fissile assembly, a quantity of widespread interest in applications including in nuclear nonproliferation and criticality safety. This work develops a mathematical model to efficiently estimate measurement uncertainty of Rossi-alpha neutron experiments inferred from a two-exponential fit model with histogram binning. The derived uncertainty estimates were validated using repeated Rossi-alpha measurements of a subcritical, 4.5-kg sphere of weapons-grade, alpha-phase plutonium with nickel, copper, tungsten, and polyethylene reflectors. The estimates of uncertainty for the histogram data produced by the model were conservative and agree with the reference uncertainties within noise. The estimates of the prompt neutron decay constant uncertainty agreed with the reference uncertainties within one standard deviation. In conclusion, the proposed model will reduce total measurement times, ultimately reducing operational and procedural costs in application.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Rossi-alpha Analysis of Thermal/Epithermal eXperiments Optimized for Polyethylene Thermal Neutron Scattering

Accurate nuclear data is the foundation for predictive simulations and design of new experimental in the nuclear community. The criticality safety community has particular interest in benchmarking assemblies with thermal neutron data. To address such needs the Nuclear Criticality Safety Program (NCSP) funded the Thermal/Epithermal eXperiments (TEX) campaigns that were to be completed between Lawrence Livermore National Laboratory (LLNL) and Los Alamos National Laboratory (LANL). Specifically, analysis of plutonium with a thermal neutron spectrum expands on previous work to help validate thermal scattering law data, which can have larger impacts in thermal applications. The first of these experiments were successfully conducted in 2018, but this paper will focus on the 2021 measurement focused on investigating the the thermal scattering law (TSL) for polyethylene. These experiments were successfully conducted at the National Criticality Experiments Research Center (NCERC) using the Planet vertical lift critical assembly machine. Polethylene plates were layered with trays of Zero Power Physics Reactor (ZPPR) 24 plates in a 12" by 12" square. The ZPPR plates were 2" by 3" by 0.125" bearing weapons grade plutonium. The polyethylene moderator was either 2" or 1.6875" thick. This work builds on the Rossi-alpha calculations done by McKenzie et al. for the same detector-assembly system and will only focus on the Rossi-alpha neutron noise method. This work will aim to further validate the results of the experiment through a novel neutron noise python package. Following similar methodology to the previous analysis, analysis of TEX evaluated the prompt neutron decay constant at delayed critical, $α_{DC}$ using Rossi-alpha for different polyethylene moderator thicknesses. These results will help improve understanding of TSL in critical experiments. Alpha (α), is the prompt neutron decay constant of the measured system and allows for the evaluation of a systems propensity to sustain fission chains via prompt neutrons. The single value description of the assemblies allow for comparison between experiments regardless of composition, geometry, and reflectors/moderators. Rossi-alpha measurements were performed on the polyethylene moderated TEX experiments to estimate $α_{DC}$.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗