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At least 127 records · Page 7

The convergence of quadrupole rotational invariants from the nuclear shell model

Nuclei exhibit both single-particle and collective degrees of freedom, with the latter often subdivided into vibrational and rotational motions. Experimentally identifying the relative roles of these collective modes is extremely challenging, particularly in the face of possible shape coexistence. Model-independent, invariant quantities describing the deformation of a nucleus in the intrinsic frame have long been known but their determination potentially requires a large quantity of experimental data to achieve convergence. Through comparison with the nuclear shell model, the question of convergence is addressed. Shell-model calculations performed in the sd- and pf-shell model spaces are used to determine electric-quadrupole matrix elements for a multitude of low-lying states using the first 40 states of the relevant spins. Relative contributions to the rotationally invariant quantities from multiple states can therefore be determined. It is found that, on average, the inclusion of four intermediate states results in the leading-order invariant, $\langle\hat{Q^2}\rangle$, converging to within 10% of its true value and the triaxiality term, cos (3δ), converging to its true value, though some variance remains. Higher-order quantities relating to the softness of the nuclear shape are found to converge more slowly. The convergence of quadrupole rotationally invariant sum rules was quantified in the sd- and pf-shell model spaces and indicates the challenge inherent in a full determination of nuclear shape. The present study is limited to relatively small valence spaces. Finally, larger spaces, such as the rare-earth region, potentially offer faster convergence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Measurements and computational analysis of the natural decay of 176 Lu

Background: Mainly because of its long half-life and despite its scientific relevance, spectroscopic measurements of 176 Lu forbidden β decays are very limited and lack formulation of shape factors. A direct precise measurement of its Q value is also presently unreported. In addition, the description of forbidden decays provides interesting challenges for nuclear theory. The comparison of precise experimental results with theoretical calculations for these decays can help to test underlying models and can aid the interpretation of data from other experiments. Purpose: Perform the first precision measurements of 176 Lu β-decay spectra and attempt the observation of its electron capture decays, as well as perform the first precision direct measurement of the 176 Lu β-decay Q value. Compare the shape of the precisely determined experimental β spectra to theoretical calculations, and compare the end point energy to that obtained from an independent Q value measurement. Method: Here, the 176 Lu β-decay spectra measurements and the search for electron capture decays were performed with an experimental setup that employed lutetium-containing scintillator crystals and a NaI(Tl) spectrometer for coincidence counting. The β decay Q value was determined via high-precision Penning trap mass spectrometry (PTMS) with the LEBIT facility at the National Superconducting Cyclotron Laboratory. The β-spectrum calculations were performed within the Fermi theory formalism with nuclear structure effects calculated using a shell model approach. Results: Both β transitions of 176 Lu were experimentally observed and corresponding shape factors formulated in their entire energy ranges. The search for electron capture decay branches led to an experimental upper limit of 6.3×10 –6 relative to its β decays. The 176 Lu β-decay and electron capture Q values were measured using PTMS to be 1193.0(6) and 108.9(8) keV, respectively. This enabled precise β end point energies of 596.2(6) and 195.3(6) keV to be determined for the primary and secondary β decays, respectively. The conserved vector current hypothesis was applied to calculate the relativistic vector matrix elements. The β-spectrum shape was shown to significantly depend on the Coulomb displacement energy and on the value of the axial vector coupling constant gA, which was extracted according to different assumptions. Conclusion: The implemented self-scintillation method has provided unmatched observations of 176 Lu, independently validated by the first direct measurements of its β-decay Q value by Penning trap mass spectrometry. Theoretical study of the main β transition led to the extraction of very different effective gA and log10f values, showing that a high-precision description of this transition would require a realistic nuclear structure with nucleus deformation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Summary of Development for Structural Component Modeling in Fiscal Year 2022

This report summarizes efforts performed during Fiscal Year 2022 to develop capabilities for modeling structural component degradation in support of the U.S. Department of Energy's Nuclear Energy Advanced Modeling and Simulation Program. These efforts were centered around development of capabilities for the Grizzly code. Efforts focused both on foundational engineering-scale analysis capabilities for damage and shell formulations and on material-scale tools for accounting for irradiation effects in Grade 91 steel. A major outcome of this effort was the development of a general-purpose tool for nonlocal averaging of material properties, which enabled nonlocal damage models. In addition, the applicability of the shell elements in MOOSE has been expanded to allow modeling a wider range of component geometries and using a wide variety of material models. For irradiation effects on materials, a previously developed cluster dynamics model for light water reactor pressure vessel steels has been adapted for application to Grade 91 alloy. This work builds on prior efforts to build a flexible, capable code for addressing a variety of aging and component performance issues in nuclear power plant structural components.

36 MATERIALS SCIENCE↗

Reinvestigation of the level structures of the even-even nuclei 90 Zr and 92 Zr

Excited states of 90 Zr and 92 Zr were investigated using the fusion reactions 6 Li + 89 Y and 14 N + 82 Se , respectively. Based on the experimental data, 5 and 18 new 𝛾 rays have been added to the level schemes of 90 Zr and 92 Zr , respectively. The level structures of 90 Zr and 92 Zr have been interpreted with shell-model calculations using the GWBXG and SNET effective interactions. The neutron core-breaking and the importance of the 1⁢𝑔 7/2 and 1⁢ℎ 11/2 orbits for high-spin states of 92 Zr were discussed. Finally, the excitation energy of the neutron core-breaking of nuclei in the 𝐴=90 region was compared.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Coexistence of single-particle and collective excitation in Ni 61

Here, the high-spin states in 61 Ni have been studied using the fusion evaporation reaction, 50 Ti( 14 C, 3n) 61 Ni at an incident beam energy of 40 MeV. A Compton suppressed multi-HPGe detector setup, consisting of six clover detectors and three single-crystal HPGe detectors, was used to detect the de-exciting $\gamma$ rays from the excited states. The level scheme has been extended up to an excitation energy of 12.8 MeV and a tentative J π =35/2 + . The low-lying negative parity levels are found to be generated by single-particle excitation within the fp shell and also excitations to the g 9/2 orbitals as explained well with shell model calculations using the GXPF1Br+V MU (modified) interaction. Two rotational structures of regular E2 sequences with small to moderate axial deformation have been established at higher excitation energy. Most interestingly, two sequences of M1 transitions are reported for the first time and described as magnetic rotational bands. The shears mechanism for both the bands can be described satisfactorily by the geometrical model. The shell model calculation involving the cross shell excitation beyond the fp shell well reproduce the M1 and E2 sequences. The shell model predicted B(M1) values for the magnetic rotational band B1 show the decreasing trend with spin as expected with closing of the shears.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

BASS XXXII: Studying the Nuclear Millimeter-wave Continuum Emission of AGNs with ALMA at Scales ≲100–200 pc

To understand the origin of nuclear (≲100 pc) millimeter-wave (mm-wave) continuum emission in active galactic nuclei (AGNs), we systematically analyzed subarcsecond resolution Band-6 (211–275 GHz) Atacama Large Millimeter/submillimeter Array data of 98 nearby AGNs (z < 0.05) from the 70 month Swift/BAT catalog. The sample, almost unbiased for obscured systems, provides the largest number of AGNs to date with high mm-wave spatial resolution sampling (~1–200 pc), and spans broad ranges of 14–150 keV luminosity {$40\lt \mathrm{log}[{L}_{14-150}/(\mathrm{erg}\,{{\rm{s}}}^{-1})]\lt 45$}, black hole mass $[5\lt \mathrm{log}({M}_{\mathrm{BH}}/{M}_{\odot })\lt 10$], and Eddington ratio ($-4\lt \mathrm{log}{\lambda }_{\mathrm{Edd}}\lt 2$). We find a significant correlation between 1.3 mm (230 GHz) and 14–150 keV luminosities. Its scatter is ≈0.36 dex, and the mm-wave emission may serve as a good proxy of the AGN luminosity, free of dust extinction up to N H ~ 10 26 cm –2 . While the mm-wave emission could be self-absorbed synchrotron radiation around the X-ray corona according to past works, we also discuss different possible origins of the mm-wave emission: AGN-related dust emission, outflow-driven shocks, and a small-scale (<200 pc) jet. The dust emission is unlikely to be dominant, as the mm-wave slope is generally flatter than expected. Also, due to no increase in the mm-wave luminosity with the Eddington ratio, a radiation-driven outflow model is possibly not the common mechanism. Furthermore, we find independence of the mm-wave luminosity on indicators of the inclination angle from the polar axis of the nuclear structure, which is inconsistent with a jet model whose luminosity depends only on the angle.

79 ASTRONOMY AND ASTROPHYSICS↗

Analysis of spent nuclear fuel multipurpose canister dynamics during rail transportation

The primary mode of spent nuclear fuel transportation within the United States will be by railcar. One such system is the Atlas railcar, which is designed to transport 17 different spent nuclear fuel cask systems, including bare fuel systems and canister fuel systems. In the latter configuration, multipurpose canisters containing spent nuclear fuel may be placed within an overpack for storage, or within a cask for transportation. Compared to bare fuel systems, canister fuel systems have additional degrees of freedom for motion during transportation, because clearance between the cask and canister allows for some motion of the canister to occur relative to the cask. This work investigates the effect of canister motion on the shock and vibration imparted to the spent nuclear fuel within. Structural dynamic analyses have been conducted to identify the effects of canister to cask clearance, presence and type of dunnage, and loading direction and frequency. This modeling study calculates anticipated cask motion, canister motion, and spent nuclear fuel structural dynamic response to normal conditions of transportation railcar motion using finite element analysis methods that were developed to model the rail segment of the ENSA/DOE (Equipos Nucleares S.A., U.S. Department of Energy) multimodal transportation test of 2017.

SNF, UNF, LS-DYNA, dynamics, kinematics, shock, vi↗

High-Sensitivity Nuclear-Structure Studies of Rare Isotopes and Few-Electron Systems

This final technical report presents the work that was completed during the award period for DE-SC0017649 related to the structure of nuclei for both astrophysics and tests of the Standard Model, namely: Using trapped bare (and few-electron) radioactive ions to probe the nature of elec- troweak decay modes under extreme conditions for structure and astrophysics, Providing experimental nuclear structure guidance to nuclear theory in systems relevant for testing the Standard Model, and Working with the HPGe sub-group of the FRIB decay station collaboration, which includes the technical development of a next-generation γ-ray spectrometer.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Mapping of fragmented νf 5/2 →πf 7/2 transitions in the 73 Co→ 73 Ni decay

Excited states in 73 , 75 Ni were investigated through the β decay of 73 , 75 Co in an experiment performed at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University (MSU). The experimental results extended the level scheme of Ni 73 to 3.2-MeV excitation energy and provided the experimental information on excited states in Ni 75 . The β -delayed neutron branching ratio for Co 73 was obtained. Furthermore, the experimental results are discussed in comparison with shell-model calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Onset of band structure in 70 Ga

Excited states in the odd-odd nucleus 70 Ga were studied using the 62 Ni( 14 C, αpn) fusion-evaporation reaction at the John D. Fox Superconducting Accelerator Laboratory at Florida State University with a 50 MeV beam. Depopulating γ rays were measured in coincidence with a Compton-suppressed Ge array consisting of three Clover detectors and seven single-crystal detectors. Analysis of γ–γ coincidences led to the addition of 16 new transitions to the 70 Ga level scheme, including transitions associated with the onset of a new positive-parity band structure likely based on the πg 9/2 ⊗ νg 9/2 configuration. Spins and parities were assigned using directional correlation of oriented nuclei (DCO) ratios and linear polarization measurements. Shell-model calculations with the JUN45 effective interaction reproduce the excitation energies of the positive-parity states reasonably well but predict negative-parity states that are typically 400–500 keV lower than observed. Furthermore, total Routhian surface calculations for the lowest positive-parity configuration with signature α = 0 indicate significant triaxiality (γ ≈ −20°) and the development of competing non-collective excitations at J = 8, corresponding to the experimentally observed onset of the positive-parity band. Similar features are found in the calculated surfaces for the lowest negative-parity states with α = 0.

59 ≤ A ≤ 89↗

Cross-shell excited configurations in the structure of 34 Si

The cross-shell excited states of 34 Si have been investigated via β decays of the 4 − ground state and the 1 + isomeric state of 34 Al. Since the valence protons and valence neutrons occupy different major shells in the ground state as well as the intruder 1 + isomeric state of 34 Al, intruder levels of 34 Si are populated via allowed β decays. Spin assignments to such intruder levels of 34 Si were established through γ-γ angular correlation analysis for the negative-parity states. The configurations of such intruder states play crucial roles in our understanding of the N = 20 shell gap evolution. A configuration interaction model derived from the FSU Hamiltonian was utilized in order to interpret the intruder states in 34 Si. Furthermore, shell model interaction derived from a more fundamental theory with the valence space in medium similarity renormalization group method was also employed to interpret the structure of 34 Si.

20 ≤ A ≤ 38↗

Evolution of low-lying M1 modes in germanium isotopes

Magnetic dipole strength functions are determined for the series of germanium isotopes from N=Z=32 to N = 48 on the basis of a large number of transition strengths calculated within the shell model. The evolution of the strength with increasing neutron number in the 1g 9/2 orbital is analyzed. A bimodal structure comprising an enhancement toward low transition energy and a resonance in the region of the scissors mode is identified. The low-energy enhancement is strongest near closed shells, in particular at the almost completely filled 1g 9/2 orbital, while the scissorslike resonance is most pronounced in the middle of the open shell, which correlates with the magnitude of the also deduced electric quadrupole transition strengths. The results are consistent with previous findings for the shorter series of iron isotopes and prove the occurrence and correlation of the two low-lying magnetic dipole modes as a global structural feature.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Puzzling 𝐵⁡(𝐸⁢2;0 + → 2 + ) strength in the proton dripline nucleus 36 Ca

Recent measurements of the 𝐸⁢2 transition rate from the ground state to the first 2 + excited state of the proton dripline nucleus 36 Ca show an unusual pattern when compared to its isotopic neighbor 38 Ca: despite having a higher 𝐸 𝑥 ⁡(2$^{+}_{1}$) excitation energy, the 𝐵⁡(𝐸⁢2;0$^{+}_{1}$ → 2$^{+}_{1}$) rate in 36 Ca is larger. The question that naturally arises is to what extent this observation can be attributed to the unbound character of the 2$^{+}_{1}$ state. To understand the influence of the continuum space on the low-energy properties of 36 Ca, we carried out Gamow shell model calculations that can account for the continuum coupling effects associated with the occupation of unbound 𝑓⁡𝑝 shells. We found that in the threshold 2 + state, 36 Ca is spatially diffused, which impacts the observed 𝐵⁡(𝐸⁢2) trend.

20 ≤ A ≤ 38↗

New level scheme and lifetime measurement of the 13/2 + state in 209 Po

The level structure of 209 Po has been studied by in-beam 𝛾-ray spectroscopy with the 209 Bi ⁢( 6 Li ,𝛼⁢2⁢𝑛) 209 Po reaction at beam energies of 28, 30, 34 MeV. The level scheme of 209 Po is expanded by the 𝛾−𝛾 coincidence measurement, where 27 new transitions and 23 new levels are observed. The lifetimes of 13/2 − , 17/2 − , and 23/2 + states are obtained and are consistent with the previous work, while the one of the 13/2 + state is measured for the first time. A configuration-interaction-shell-model calculation is performed, and its results are compared with the experimental results for 209 Po , with an emphasis on the coupling between the single valence neutron hole and the even-even core of 210 Po . A systematic comparison of the 13/2 + state in N = 125 chain is also studied in the current work.

190 ≤ A ≤ 219↗

Lifetimes of two- and four-neutron-hole states in 204 Pb and 206 Pb

The centroid-shift method was used to determine half-lives of excited levels in 204 Pb and 206 Pb. For the states with 𝐼 𝜋 = 12 + , 17 − , and 19 − in 204 Pb, values of 𝑇 1/2 = 4.9⁢(3), 3.9(3), and 0.9(3) ns, respectively, were determined. The half-life of the 𝐼 𝜋 = 9 − level in 206 Pb was measured to be 1.1(3) ns. In 204 Pb, the 12 + state arises from two neutron holes in the 𝑖 13/2 subshell, while the 17 − and 19 − levels are built on 𝜈⁡(𝑖$^{−3}_{13/2}$, 𝑝$^{−1}_{1/2}$) and 𝜈⁡(𝑖$^{−3}_{13/2}$, 𝑓$^{−1}_{5/2}$) four-neutron-hole configurations, respectively. The 9 − state in 206 Pb results from a 𝜈⁡(𝑖$^{−1}_{13/2}$, 𝑓${−1}_{5/2}$) excitation. As a result, the transition probabilities for the decay of these isomeric levels are reasonably consistent with the expected single-particle values, and these states are described well by shell-model calculations using the kshell code with the KHHE interaction.

190 ≤ A ≤ 219↗

Availability of Critical Benchmark Experiments for the Pebble Tanker Transportation Model for Nuclear Criticality Safety Validation of TRISO Pebbles

This study addresses the need for comprehensive investigations into TRi-structural ISOtropic (TRISO) fuel pebble transportation validation. In this work, an exploratory model, the pebble tanker(PT), was developed with the aim of facilitating the validation of nuclear criticality safety calculations in the context of industrial-scale transportation of TRISO fuel. The PT model was designed to investigate the availability and applicability of critical benchmark experiments crucial for assessing the transportation of these pebbles. This work incorporated sensitivity/uncertainty (S/U) similarity studies to quantify the applicability of critical benchmark experiments and to address nuclear data uncertainties in the context of TRISO transportation. Two container models were investigated: one for the Hermes-type pebble and one for the Pebble Bed Modular Reactor (PBMR)–type pebble. The models were simplified, considering fuel, containment, and either water or air, to enable a focus on the underlying physics of applications involving TRISO fuel pebbles using the PT model. A crucial aspect under consideration was the capacity of the transport package to hold pebbles while ensuring subcriticality in the flooded state. An approach in the criticality validation process involves assessing the similarity between systems through an integral index parameter evaluation. This involves calculating a correlation coefficient (referred to as c k ) based on shared nuclear data–induced uncertainty between a benchmark experiment and the application of the PT model. To facilitate this analysis, the SCALE tools, particularly the CSAS6-Shift, TSUNAMI-3D-Shift, and TSUNAMI-IP sequences, were employed for comprehensive studies in neutronics and S/U analysis. Our findings showed that there are sufficient critical experimental benchmarks to perform this validation of the PT model in the most reactive state, i.e. when the tanker is flooded. This paper provides valuable insights into validating a transport package for Generation IV TRISO fuel pebbles.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Evidence for ground-state electron capture of K 40

Potassium-40 is a widespread, naturally occurring isotope whose radioactivity impacts estimated geological ages spanning billions of years, nuclear structure theory, and subatomic rare-event searches—including those for dark matter and neutrinoless double-beta decay. The decays of this long-lived isotope must be precisely known for its use as a geochronometer, and to account for its presence in low-background experiments. There are several known decay modes for potassium-40, but a predicted electron-capture decay directly to the ground state of argon-40 has never been observed. The existence of this decay mode impacts several fields, while theoretical predictions span an order of magnitude. Here we report on the first, successful observation of this rare decay mode, obtained by the KDK (potassium decay) Collaboration using a novel combination of a low-threshold x-ray detector surrounded by a tonne-scale, high-efficiency γ -ray tagger at Oak Ridge National Laboratory. A blinded analysis reveals a distinctly nonzero ratio of intensities of ground-state electron-captures ( I EC 0 ) over excited-state ones ( I EC * ) of I EC 0 / I EC * = 0.0095 ± stat 0.0022 ± sys 0.0010 (68% CL), with the null hypothesis rejected at 4 σ [Stukel et al. , Phys. Rev. Lett. 131 , 052503 (2023) ]. In terms of branching ratio, this unambiguous signal yields I EC 0 = 0.098 % ± stat 0.023 % ± sys 0.010 % , roughly half of the commonly used prediction. This first observation of a third-forbidden unique electron capture improves our understanding of low-energy backgrounds in dark-matter searches and has implications for nuclear-structure calculations. For example, a shell-model based theoretical estimate for the neutrinoless double-beta decay half-life of calcium-48 is increased by a factor of 7 - 2 + 3 . Our nonzero measurement shifts geochronological ages by up to a percent; implications are illustrated for Earth and solar system chronologies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗