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DOE OSTI2021

Auxiliary function approach for determining symmetry energy at suprasaturation densities

Nuclear symmetry energy E sym (ρ) at density ρ is normally expanded or simply parameterized as a function of χ = (ρ – ρ 0 )/3ρ 0 in the form of Esym(ρ) ≈ S + Lχ + 2 –1 K sym χ 2 + 6 –1 J sym χ 3 + … using its magnitude S, slope L, curvature K sym and skewness J sym at the saturation density ρ0 of nuclear matter. Much progress has been made in recent years in constraining especially the S and L parameters using various terrestrial experiments and astrophysical observations. Furthermore, such kind of expansions/parameterizations do not converge at supra-saturation densities where χ is not small enough, hindering an accurate determination of high-density E sym (ρ) even if its characteristic parameters at ρ0 are all well determined by experiments/observations. By expanding the E sym (ρ) in terms of a properly chosen auxiliary function Π sym (χ,Θ sym ) with a parameter Θsym fixed accurately by an experimental E sym (ρ r ) value at a reference density ρr, we show that the shortcomings of the χ-expansion can be completely removed or significantly reduced in determining the high-density behavior of E sym (ρ). In particular, using two significantly different auxiliary functions, we show that the new approach effectively incorporates higher χ-order contributions and converges to the same E sym (ρ) much faster than the conventional χ-expansion at densities ≲3ρ 0 . Several quantitative demonstrations using Monte Carlo simulations are given.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Determination of β -decay feeding patterns of 88 Rb and 88 Kr using the Modular Total Absorption Spectrometer at ORNL HRIBF

We report precise determination of ground-state feeding in the β decay of fission products is an important but challenging component in modeling reactor antineutrino flux and reactor decay heat. The Modular Total Absorption Spectrometer (MTAS) is a versatile NaI(Tl) detector array that determines the true β-decay pattern free from the pandemonium effect, including precise ground-state feeding intensities. In this paper, we report MTAS results of the β feeding intensities of 88 Rb and 88 Kr, fission products with large cumulative yields in nuclear reactors. By comparing MTAS results with previous measurements, 88 Rb provides a validation of MTAS's ability to determine ground-state feedings in β decays, while the precision of 88 Kr ground-state feeding is improved when compared with the Evaluated Nuclear Structure Data File (ENSDF). The investigation of sources that contribute to β feeding branching uncertainties in MTAS experiments is discussed in detail. Lastly, the deconvolution of 88 Rb decay spectra suggests that MTAS can distinguish an allowed β spectral shape from a first forbidden unique β spectral shape.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Model-independent determination of the dipole response of 66 Zn using quasimonoenergetic and linearly polarized photon beams

Background: Photon strength functions are an important ingredient in calculations relevant for the nucleosynthesis of heavy elements. The relation to the photoabsorption cross section allows to experimentally constrain photon strength functions by investigating the photoresponse of atomic nuclei. Purpose: Here, we determine the photoresponse of 66 Zn in the energy region of 5.6 MeV to 9.9 MeV and analyze the contribution of the 'elastic' decay channel back to the ground state. In addition, for the elastic channel electric and magnetic dipole transitions were separated. Methods: Nuclear resonance fluorescence experiments were performed using a linearly polarized quasi-monoenergetic photon beam at the High Intensity γ-ray Source. Photon beam energies from 5.6 to 9.9 MeV with an energy spread of about 3% were selected in steps of 200–300 keV. Two high purity germanium detectors were used for the subsequent γ-ray spectroscopy. Results: Full photoabsorption cross sections are extracted from the data making use of the monoenergetic character of the photon beam. For the ground-state decay channel, the average contribution of electric and magnetic dipole strengths is disentangled. The average branching ratio back to the ground state is determined as well. Conclusions: The new results indicate lower cross sections when compared to the values extracted from a former experiment using bremsstrahlung on 66 Zn. In the latter, the average branching ratio to the ground state is estimated from statistical-model calculations in order to analyze the data. Corresponding estimates from statistical-model calculations underestimate this branching ratio compared to the values extracted from the present analysis, which would partly explain the high cross sections determined from the bremsstrahlung data.

59 ≤ A ≤ 89↗

DOE OSTI2015

Determination of the direct double- β -decay Q value of Zr 96 and atomic masses of Zr 90 - 92 , 94 , 96 and Mo 92 , 94 - 98 , 100

Experimental searches for neutrinoless double-β decay offer one of the best opportunities to look for physics beyond the standard model. Detecting this decay would confirm the Majorana nature of the neutrino, and a measurement of its half-life can be used to determine the absolute neutrino mass scale. Important to both tasks is an accurate knowledge of the Q value of the double-β decay. The LEBIT Penning trap mass spectrometer was used for the first direct experimental determination of the ⁹⁶Zr double-β decay Q value: Q ββ =3355.85(15) keV. This value is nearly 7 keV larger than the 2012 Atomic Mass Evaluation [M. Wang et al., Chin. Phys. C 36, 1603 (2012)] value and one order of magnitude more precise. The 3-σ shift is primarily due to a more accurate measurement of the ⁹⁶Zr atomic mass: m(⁹⁶Zr)=95.90827735(17) u. Using the new Q value, the 2νββ-decay matrix element, |M 2ν |, is calculated. Improved determinations of the atomic masses of all other zirconium ( 90-92,94,96 Zr) and molybdenum ( 92,94-98,100 Mo) isotopes using both ¹²C₈ and ⁸⁷Rb as references are also reported.

Gulyuz, K.↗

DOE OSTI2018

Mass measurement of 51 Fe for the determination of the 51 Fe($p, γ$) 52 Co reaction rate

Background: The 51 Fe(p, γ) 52 Co reaction lies along the main rp-process path leading up to the 56 Ni waiting point. The uncertainty in the reaction Q value, which determines the equilibrium between the forward protoncapture and reverse photodisintegration 52 Co(γ,p) 51 Fe reaction, contributes to considerable uncertainty in the reaction rate in the temperature range of interest for Type I x-ray bursts and thus to an ≈10% uncertainty in burst ashes lighter than A = 56. Purpose: With a recent Penning trap mass measurement of 52 Co reducing the uncertainty on its mass to 6.6 keV [Nesterenko et al., J. Phys. G 44, 065103 (2017)], the dominant source of uncertainty in the reaction Q value is now the mass of 51 Fe, reported in the 2016 atomic mass evaluation to a precision of 9 keV [Wang et al., Chin.Phys. C 41, 030003 (2017)]. A new, high-precision Penning trap mass measurement of 51 Fe was performed to allow the determination of an improved precision Q value and thus new reaction rates. Method: 51 Fe was produced using projectile fragmentation at the Coupled Cyclotron Facility at the National Superconducting Cyclotron Laboratory, and separated using the A1900 fragment separator. The resulting secondary beam was then thermalized in the beam stopping area before a mass measurement was performed using the LEBIT 9.4T Penning trap mass spectrometer. Results: The new mass excess, ME = -40189.2(1.6) keV, is sixfold more precise than the current AME value, and 1.6σ less negative. This value was used to calculate a new proton separation energy for 52 Co of 1431(7) keV. New excitation levels were then calculated for 52 Co using the NUSHELLX code with the GXPF1A interaction, and a new reaction rate and burst ash composition was calculated. Conclusions:With a new measured Q value, the uncertainty on the 51 Fe(p, γ ) reaction rate is dominated by the poorly measured 52 Co level structure. Finally, reducing this uncertainty would allow a more precise rate calculation and a better determination of the mass abundances in the burst ashes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Lattice determination of 𝐼=0 and 2 𝜋⁢𝜋 scattering phase shifts with a physical pion mass

Phase shifts for 𝑠-wave 𝜋⁢𝜋 scattering in both the 𝐼 =0 and 𝐼 =2 channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of 32 3 ×64. These results support our recent 2021 study of direct 𝐶⁢𝑃 violation in 𝐾 → 𝜋⁢𝜋 decay, improving our earlier 2015 calculation. The phase shifts are determined for both stationary and moving 𝜋⁢𝜋 systems, at three (𝐼 = 0) and four (𝐼 = 2) different total momenta. We implement several 𝜋⁢𝜋 interpolating operators including a scalar bilinear “𝜎” operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Bootstrap-determined p values in lattice QCD

We present a general method to determine the probability that stochastic Monte Carlo data, in particular those generated in a lattice QCD calculation, would have been obtained were that data drawn from the distribution predicted by a given theoretical hypothesis. Such a probability, or p -value, is often used as an important heuristic measure of the validity of that hypothesis. The proposed method offers the benefit that it remains usable in cases where the standard Hotelling T 2 methods based on the conventional χ 2 statistic do not apply, such as for uncorrelated fits. Specifically, we analyze q 2 , defined as the correlated χ 2 statistic obtained using an arbitrary covariance matrix estimator, and show how to use the bootstrap as a data-driven method to determine the expected distribution of q 2 for a given hypothesis with minimal assumptions. This distribution can then be used to determine the p -value for a fit to the data. We also describe a bootstrap approach for quantifying the impact upon this p -value of estimating population parameters from a single ensemble of N samples. The overall method is accurate up to a 1 / N bias which we do not attempt to quantify. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2012

Study of B̄→X u lν̄ decays in BB̄ events tagged by a fully reconstructed B-meson decay and determination of |V ub |

We report measurements of partial branching fractions for inclusive charmless semileptonic B decays B¯¯¯→X u lν¯ and the determination of the Cabibbo–Kobayashi–Maskawa (CKM) matrix element |V ub |. The analysis is based on a sample of 467×10⁶ Υ(4S)→BB¯¯¯ decays recorded with the BABAR detector at the PEP-II e⁺e⁻ storage rings. We select events in which the decay of one of the B mesons is fully reconstructed and an electron or a muon signals the semileptonic decay of the other B meson. We measure partial branching fractions ΔB in several restricted regions of phase space and determine the CKM element |V ub | based on different QCD predictions. For decays with a charged lepton momentum p * l >1.0 GeV in the B meson rest frame, we obtain ΔB=(1.80±0.13stat±0.15sys±0.02theo)×10⁻³ from a fit to the two-dimensional M X -q² distribution. Here, M X refers to the invariant mass of the final state hadron X and q² is the invariant mass squared of the charged lepton and neutrino. From this measurement we extract |V ub |=(4.33±0.24 exp ±0.15 theo )×10⁻³ as the arithmetic average of four results obtained from four different QCD predictions of the partial rate. We separately determine partial branching fractions for B¯¯¯0 and B⁻ decays and derive a limit on the isospin breaking in B¯¯¯→X u lν¯ decays.

Lees, J. P.↗

DOE OSTI2017

Determination of the Spin and Parity of the Z c ( 3900 )

In this paper, the spin and parity of the Z c (3900) ± state are determined to be J P = 1 + with a statistical significance larger than 7σ over other quantum numbers in a partial wave analysis of the process e + e - → π + π - J/Ψ. We use a data sample of 1.92 fb -1 accumulated at $ \sqrt{s}=4.23 $ and 4.26 GeV with the BESIII experiment. When parametrizing the Z c (3900) ± with a Flatté-like formula, we determine its pole mass M pole = (3881.2±4.2 stat ±52.7 syst ) MeV/c 2 and pole width Γ pole = (51.8± 4.6 stat ± 36.0 syst ) MeV. Finally, we also measure cross sections for the process e + e - → Z c (3900) + π - + c.c. → J/Ψπ + π - and determine an upper limit at the 90% confidence level for the process e + e - → Z c (4020) + π - + c.c. → J/Ψ π + π - .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2012

Analysis of phases in the structure determination of an icosahedral virus

The constraints imposed on structure-factor phases by noncrystallographic symmetry (NCS) allow phase improvement, phase extension to higher resolution and hence ab initio phase determination. The more numerous the NCS redundancy and the greater the volume used for solvent flattening, the greater the power for phase determination. In a case analyzed here the icosahedral NCS phasing appeared to have broken down, although later successful phase extension was possible when the envelope around the NCS region was tightened. The phases from the failed phase-determination attempt fell into four classes, all of which satisfied the NCS constraints. These four classes corresponded to the correct solution, opposite enantiomorph, Babinet inversion and opposite enantiomorph with Babinet inversion. These incorrect solutions can be seeded from structure factors belonging to reciprocal-space volumes that lie close to icosahedral NCS axes where the structure amplitudes tend to be large and the phases tend to be 0 or {pi}. Furthermore, the false solutions can spread more easily if there are large errors in defining the envelope designating the region in which NCS averaging is performed.

58 GEOSCIENCES↗

DOE OSTI2013

Structure determination of the functional domain interaction of a chimeric nonribosomal peptide synthetase from a challenging crystal with noncrystallographic translational symmetry

The structure of the functional interaction of NRPS adenylation and carrier protein domains, trapped with a mechanism-based inhibitor, is described. Crystals exhibit translational non-crystallographic symmetry, which challenged structure determination and refinement. The nonribosomal peptide synthetases (NRPSs) are a family of modular proteins that contain multiple catalytic domains joined in a single protein. Together, these domains work to produce chemically diverse peptides, including compounds with antibiotic activity or that play a role in iron acquisition. Understanding the structural mechanisms that govern the domain interactions has been a long-standing goal. During NRPS synthesis, amino-acid substrates are loaded onto integrated carrier protein domains through the activity of NRPS adenylation domains. The structures of two adenylation domain–carrier protein domain complexes have recently been determined in an effort that required the use of a mechanism-based inhibitor to trap the domain interaction. Here, the continued analysis of these proteins is presented, including a higher resolution structure of an engineered di-domain protein containing the EntE adenylation domain fused with the carrier protein domain of its partner EntB. The protein crystallized in a novel space group in which molecular replacement and refinement were challenged by noncrystallographic pseudo-translational symmetry. The structure determination and how the molecular packing impacted the diffraction intensities are reported. Importantly, the structure illustrates that in this new crystal form the functional interface between the adenylation domain and the carrier protein domain remains the same as that observed previously. At a resolution that allows inclusion of water molecules, additional interactions are observed between the two protein domains and between the protein and its ligands. In particular, a highly solvated region that surrounds the carrier protein cofactor is described.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2014

In cellulo structure determination of a novel cypovirus polyhedrin

The crystal structure of a previously unsolved type of cypovirus polyhedrin has been determined from data collected directly from frozen live insect cells. This work demonstrates that with the use of a microfocus synchrotron beam the structure of a novel viral polyhedrin could be successfully determined from microcrystals within cells, removing the preparatory step of sample isolation and maintaining a favourable biological environment. The data obtained are of high quality, comparable to that obtained from isolated crystals, and enabled a facile structure determination. A small but significant difference is observed between the unit-cell parameters and the mosaic spread of in cellulo and isolated crystals, suggesting that even these robust crystals are adversely affected by removal from the cell.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2014

Direct phase selection of initial phases from single-wavelength anomalous dispersion (SAD) for the improvement of electron density and ab initio structure determination

A novel direct phase-selection method to select optimized phases from the ambiguous phases of a subset of reflections to replace the corresponding initial SAD phases has been developed. With the improved phases, the completeness of built residues of protein molecules is enhanced for efficient structure determination. Optimization of the initial phasing has been a decisive factor in the success of the subsequent electron-density modification, model building and structure determination of biological macromolecules using the single-wavelength anomalous dispersion (SAD) method. Two possible phase solutions (ϕ{sub 1} and ϕ{sub 2}) generated from two symmetric phase triangles in the Harker construction for the SAD method cause the well known phase ambiguity. A novel direct phase-selection method utilizing the θ{sub DS} list as a criterion to select optimized phases ϕ{sub am} from ϕ{sub 1} or ϕ{sub 2} of a subset of reflections with a high percentage of correct phases to replace the corresponding initial SAD phases ϕ{sub SAD} has been developed. Based on this work, reflections with an angle θ{sub DS} in the range 35–145° are selected for an optimized improvement, where θ{sub DS} is the angle between the initial phase ϕ{sub SAD} and a preliminary density-modification (DM) phase ϕ{sub DM}{sup NHL}. The results show that utilizing the additional direct phase-selection step prior to simple solvent flattening without phase combination using existing DM programs, such as RESOLVE or DM from CCP4, significantly improves the final phases in terms of increased correlation coefficients of electron-density maps and diminished mean phase errors. With the improved phases and density maps from the direct phase-selection method, the completeness of residues of protein molecules built with main chains and side chains is enhanced for efficient structure determination.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

From bacterial to human dihydrouridine synthase: automated structure determination

The crystal structure of a human dihydrouridine synthase, an enzyme associated with lung cancer, with 18% sequence identity to a T. maritima enzyme, has been determined at 1.9 Å resolution by molecular replacement after extensive molecular remodelling of the template. The reduction of uridine to dihydrouridine at specific positions in tRNA is catalysed by dihydrouridine synthase (Dus) enzymes. Increased expression of human dihydrouridine synthase 2 (hDus2) has been linked to pulmonary carcinogenesis, while its knockdown decreased cancer cell line viability, suggesting that it may serve as a valuable target for therapeutic intervention. Here, the X-ray crystal structure of a construct of hDus2 encompassing the catalytic and tRNA-recognition domains (residues 1–340) determined at 1.9 Å resolution is presented. It is shown that the structure can be determined automatically by phenix.mr-rosetta starting from a bacterial Dus enzyme with only 18% sequence identity and a significantly divergent structure. The overall fold of the human Dus2 is similar to that of bacterial enzymes, but has a larger recognition domain and a unique three-stranded antiparallel β-sheet insertion into the catalytic domain that packs next to the recognition domain, contributing to domain–domain interactions. The structure may inform the development of novel therapeutic approaches in the fight against lung cancer.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Precision lattice parameter determination from transmission diffraction of thick specimens with irregular cross sections

Accurate determination of lattice parameters from X-ray diffraction requires that the diffraction angles be measured very precisely, and significant errors result if the sample–detector separation differs from that assumed. Transmission diffraction from bones, which have a complex cross section and must be left intact, is a situation where this separation is difficult to measure and it may differ from position to position across the specimen. Here, this article describes a method for eliminating the effect of variable sample cross section. Diffraction patterns for each position on the specimen are collected before and after 180° rotation about an axis normal to the cross section of interest. This places the centroid of the diffracting mass at the center of rotation and provides the absolute lattice parameters from the average apparent lattice parameters at the two rotation angles. Diffraction patterns were collected across the cross section of three specimens: a 3D-printed elliptical cylinder of Hyperelastic Bone (HB), which is composed primarily of synthetic hydroxyapatite (hAp), a 3D-printed HB model of the second metacarpal bone (Mc2), and a modern human Mc2 containing nanocrystalline carbonated apatite (cAp). Rietveld refinement was used to determine precise unit-cell parameters a apparent and c apparent for each pattern of each scan, and these values determined the actual average < a > and < c > for each sample. In conclusion, the results indicate that the 0°/180° rotation method works well enough to uncover variations approaching 1 × 10 -3 Å in cAp unit-cell parameters in intact bones with irregular cross sections.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Determination of physically based pseudo-Voigt powder diffraction profile terms from the fundamental parameters approach

In this study, a methodology is developed where a fundamental parameters approach (FPA) description of a laboratory powder diffraction instrument (configured in divergent-beam Bragg–Brentano geometry) is used to determine GSAS-II profile parameters for peak asymmetry and instrumental peak widths. This allows the instrumental contribution to peak shapes to be robustly determined directly from a physical description of the instrument, even though GSAS-II does not directly implement FPA for peak shape computation. The FPA-derived parameters can be used as the starting point for instrument characterization, or to characterize sample broadening without the use of a standard to determine the instrument profile function. This new method can facilitate generation of training sets for machine learning. A plot is generated that shows the differences between the two approaches, demonstrating upper bounds for the accuracy of the GSAS-II profile model for a particular instrumental configuration.

47 OTHER INSTRUMENTATION↗

DOE OSTI2019

Using powder XRD and pair distribution function to determine anisotropic atomic displacement parameters of orthorhombic tridymite and tetragonal cristobalite

Determination of the crystal structures of low-temperature tridymite and cristobalite using single-crystal XRD has been challenging because they generally occur as metastable fine-grained crystals in the geological environment. Therefore, using powder diffraction and scattering techniques is critical to study the low-temperature crystals. Synchrotron powder X-ray diffraction (XRD), pair distribution function (PDF) and transmission electron microscopy were used to investigate the structure of orthorhombic tridymite with C 222 1 symmetry and tetragonal cristobalite with P 4 1 2 1 2 symmetry, including their anisotropic atomic displacement parameters (ADPs). Rietveld refinement was used to determine the unit-cell parameters, fractional coordinates and isotropic atomic displacement parameters ( U iso ) of the tridymite and cristobalite. The PDF method was used to determine ADPs for each atom. The results suggest that the crystal structure with high quality ADP values can be obtained using the combined methods of XRD and PDF analyses. The method can be used for characterizing crystals that are not suitable for single-crystal XRD.

Lee, Seungyeol (ORCID:0000000201751389)↗

DOE OSTI2025

Fast event-based electron counting for small-molecule structure determination by MicroED

Electron counting helped realize the resolution revolution in single-particle cryoEM and is now accelerating the determination of MicroED structures. Its advantages are best demonstrated by new direct electron detectors capable of fast (kilohertz) event-based electron counting (EBEC). This strategy minimizes the inaccuracies introduced by coincidence loss (CL) and promises rapid determination of accurate structures. We used the Direct Electron Apollo camera to leverage EBEC technology for MicroED data collection. Given its ability to count single electrons, the Apollo collects high-quality MicroED data from organic small-molecule crystals illuminated with incident electron beam flux densities as low as 0.01–0.045 e − /Å 2 /s. Under even the lowest flux density (0.01 e − /Å 2 /s) condition, fast EBEC data produced ab initio structures of a salen ligand (268 Da) and biotin (244 Da). Each structure was determined from a 100° wedge of data collected from a single crystal in as few as 50 s, with a delivered fluence of only ∼0.5 e − /Å 2 . Fast EBEC data collected with a fluence of 2.25 or 3.33 e − /Å 2 also facilitated a 1.5 Å structure of thiostrepton (1665 Da). While refinement of these structures appeared unaffected by CL, a CL adjustment applied to EBEC data further improved the distribution of intensities measured from the salen ligand and biotin crystals. However, CL adjustment only marginally improved the refinement of their corresponding structures, signaling the already high counting accuracy of detectors with counting rates in the kilohertz range. Overall, by delivering low-dose structure-worthy data, fast EBEC collection strategies open new possibilities for high-throughput MicroED.

EBEC↗