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DOE OSTI2023

Measurement of the $\textit{B}(\textit{E}2 ↑)$ strengths of 36 Ca and 38 Ca

In this work, the $B(E2, 0^+_1 → 2^+_1)$ strengths of 36 Ca and 38 Ca are measured to be 131(20) $e^2\text{fm}^4$ and 101(11) $e^2\text{fm}^4$, respectively. The $\textit{B}(\textit{E}2)$ value for 36 Ca required a measurement of the p/γ branching ratio because the 2 + state is proton unbound. This branching ratio is $B_p$=0.087(8). These $\textit{B}(\textit{E}2)$ and branching-ratio values can be reproduced in the shell-model with the ZMB2 interaction, an interaction that predicts the $\textit{Z} = 20 \textit{sd}$-shell closure is incomplete with large proton pf-shell occupancies in the ground state. These occupancies are at odds with other shell-model and energy-density-functional calculations of 36 Ca. New data are used to provide an update on constraints of the density dependence of the symmetry energy through mirror charge-radii differences as well as to help reduce uncertainties of the astrophysical important 35 K(p,γ) reaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

In-beam γ -ray spectroscopy of negative-parity states of 37 K populated in dissipative reactions

In-beam γ-ray spectroscopy was used to study excited states of the neutron-deficient nucleus 37 K populated in fast-beam inelastic-scattering and proton-removal reactions at high-momentum loss. New γ-ray transitions and γγ coincidence relationships were established using the γ-ray tracking array GRETINA. The extension of the level scheme up to the first (13/2 – ) state highlights the potential of this recently demonstrated population pathway for studies of isospin symmetry involving mirror-energy differences. Furthermore, the nature of the newly identified states is discussed in comparison to shell-model calculations with the FSU cross-shell effective interaction. The calculated occupation numbers of individual orbitals are shown to offer a consistent explanation of the measured mirror-energy differences between 37 K and 37 Ar.

20 ≤ A ≤ 38↗

DOE OSTI2023

The Jefferson Lab tritium program of nucleon and nuclear structure measurements

In this work a series of experiments were performed in Hall A of Jefferson Lab in 2018 that used a novel tritium and helium-3 target system. These experiments took advantage of the isospin symmetry of these mirror nuclei to make precise measurements of isospin dependence in both nucleon and nuclear structure. We summarize here the design and properties of these cells, the physics measurements that have been published, and results currently under analysis from this program.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Strain engineering a persistent spin helix with infinite spin lifetime

Persistent spin textures (PSTs) in solid-state materials arise from a unidirectional spin-orbit field in momentum space and offer a route to deliver long carrier spin lifetimes sought for future quantum microelectronic devices. Nonetheless, few three-dimensional materials are known to host PSTs owing to crystal symmetry and chemical requirements. There are even fewer examples demonstrated experimentally. Here we report that high-quality persistent spin textures can be obtained in the polar point groups containing an odd number of mirror operations. We use representation theory analysis and electronic structure calculations to formulate general discovery principles to identify PSTs hidden in known complex ternary layered and perovskite structures with large electric polarizations. We then show some of these materials exhibit PSTs without requiring any special crystalline symmetries. This finding removes the limitation imposed by mirror-symmetry protected PSTs that has limited compound discovery. Our general design approach enables the pursuit of persistent spin helices in materials exhibiting the C 3 v crystal class adopted by many quantum materials exhibiting large Rashba coefficients.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Propagator Zeros and Lattice Chiral Gauge Theories

Symmetric mass generation (SMG) has been advocated as a mechanism to render mirror fermions massive without symmetry breaking, ultimately aiming for the construction of lattice chiral gauge theories. It has been argued that in an SMG phase, the poles in the mirror fermion propagators are replaced by zeros. Using an effective Lagrangian approach, we investigate the role of propagator zeros when the gauge field is turned on, finding that they act as coupled ghost states. In four dimensions, a propagator zero makes an opposite-sign contribution to the one-loop beta function as compared to a normal fermion. In two dimensional Abelian theories, a propagator zero makes a negative contribution to the photon mass squared. In addition, propagator zeros generate the same anomaly as propagator poles. Thus, gauge invariance will always be maintained in an SMG phase, in fact, even if the target chiral gauge theory is anomalous, but unitarity of the gauge theory is lost. Published by the American Physical Society 2024

Physics↗

DOE OSTI2022

Derivation of closed-form ellipsoidal X-ray mirror shapes from Fermat's principle

Ellipsoidal and plane-elliptical surfaces are widely used as reflective, point-to-point focusing elements in many optical systems, including X-ray optics. Here the classical optical path function approach of Fermat is applied to derive a closed-form expression for these surfaces that are uniquely described by the object and image distances and the angle of incidence at a point on a mirror surface. A compact description facilitates design, modeling, fabrication, and testing to arbitrary accuracy. Congruent surfaces in two useful coordinate systems — a system centered on the ellipsoid's axes of symmetry and a mirror-centered or `vertex' system with the surface tangent to the xy plane at the mirror's center — are presented. Expressions for the local slope and radii of curvature are derived from the result, and the first several terms of the Maclauren series expansion are provided about the mirror center.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1972

Research study to determine critical optical/mechanical properties of materials considered for selection as substrates for the primary mirror on a large telescope

An investigation was conducted to evaluate the stability of a specific low expansion glass-ceramic material relative to its use as a large, lightweight mirror substrate for diffraction-limited spaceborne optical applications. These evaluations were made on a segment (0.44 meter diameter by 0.31 meter thick) of a 2 to 3 meter diameter mirror blank. The dimensional stability of this mirror was measured interferometrically before and after lightweighting, as a function of rough machining, etching, thermal environment, and support configuration. A special computer analysis program was used to plot the coefficients corresponding to aberrations with sixfold symmetry (caused by the mirror's self-weight deflection on a three point support). The objective was to enhance the test sensitivity. Results indicate that any such effects due to self-weight deflection are of the order of 0.015 lambda rms. The rms and peak-to-peak figure changes associated with each processing operation are summarized.

Slomba, A. F.↗

DOE OSTI2020

Gapless Criterion for Crystals from Effective Axion Field

Gapless criteria that can efficiently determine whether a crystal is gapless or not are particularly useful for identifying topological semimetals. In this work, we propose a sufficient gapless criterion for three-dimensional noninteracting crystals, based on the simplified expressions for the bulk average value of the static axion field. The brief logic is that two different simplified expressions give the same value in an insulator, and thus the gapless phase can be detected by the mismatch of them. We demonstrate the effectiveness of the gapless criterion in the magnetic systems with space groups 26 and 13, where mirror, glide, and inversion symmetries provide the simplified expressions. In particular, the gapless criterion can identify gapless phases that are missed by the symmetry-representation approach, as illustrated by space group 26. Our proposal serves as a guiding principle for future discovery of topological semimetals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Electronic structure and exchange interactions in altermagnetic MnGeP 2 in the quasiparticle self-consistent G W approach

The quasiparticle self-consistent 𝐺⁡𝑊 method is used to study the electronic band structure, optical dielectric function, and exchange interactions in chalcopyrite, 𝐼⁢ ‾ 4 ⁢2⁢𝑑, structure MnGeP 2 . The material is found to be an antiferromagnetic semiconductor with a lowest direct gap of 2.44 eV at the Γ point and a lower indirect gap of 1.87 eV from Γ to 𝑀. The material is an altermagnet because the two magnetic atoms of opposite spin are related by a twofold rotation operation perpendicular to the main fourfold rotation inversion axis. The spin splittings along a low symmetry line like 𝑃⁢𝑁 is sizable while at k points on the diagonal mirror planes or on the twofold symmetry axes the spin splitting is zero. The exchange interactions are calculated using a linear response approach. The antiferromagnetic exchange interaction between nearest neighbors in the primitive unit cell is dominating and found to be slightly decreasing upon carrier doping but not sufficiently to change the interaction to become ferromagnetic. The bare (noninteracting) and interacting transverse spin susceptibilities, which provide interatomic site exchange interactions after averaging over the muffin-tin spheres, are calculated from the 𝐺⁡𝑊 band structure and wave functions. From these exchange interactions, the spin wave spectra are obtained along the high symmetry lines and the Néel temperature is calculated using the mean-field and Tyablikov estimations. The dielectric function and the optical absorption spectra are calculated including excitonic effects using the Bethe Salpeter equation. The exchange interactions around Mn Ge defect sites is also studied. While we find it can generate ferromagnetic interactions with neighboring spins, we did not find direct evidence of producing an overall ferromagnetic phase. First, if Mn antisites are introduced by exchanging Mn with a nearby Ge, the interactions stay largely antiferromagnetic. Second, when we add additional Mn, in other words in Mn-rich stoichiometry, the Mn Ge antisites produce a strong ferromagnetic interaction primarily with the Mn in the same basal plane but weaker ferromagnetic interaction with adjacent plane Mn. The interactions between regular lattice Mn stay antiferromagnetic as before and thus favor keeping the antiferromagnetic order along the [001] direction. Adding Mn antisites, however, does lead to a metallic band structure.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Fermiology and transport properties of the candidate topological crystalline insulator SrAg 4 ⁢Sb 2

Compared to time-reversal symmetry-protected ℤ 2 topological insulators and Dirac/Weyl semimetals, there are significantly fewer candidates for topological crystalline insulators. SrAg 4 ⁢Sb 2 is predicted to exhibit topological crystalline insulator behavior when considering spin-orbit coupling. In this study, we systematically investigate single crystals of SrAg 4 ⁢Sb 2 using electrical transport and magnetic torque measurements, along with first-principles calculations. Our transport data reveals its compensated semimetal nature with a magnetoresistance up to around 700% at 2 K and 9 T. Analysis of de Haas–van Alphen oscillations uncovers a Fermi surface consisting of three distinct Fermi pockets with light effective masses. Comparison between the three-dimensional fermiology obtained from our oscillation data and the first-principles calculations demonstrates excellent agreement. This confirms the accuracy of the calculations, which indicate a band inversion centered at the 𝑇 point and identify the existence of nontrivial tube and needle hole Fermi pockets at Γ, alongside one trivial diamond electron pocket at the 𝐹 point in the Brillouin zone. Furthermore, symmetry and topology analysis results in two potential sets of topological invariants, suggesting the emergence of two-dimensional gapless Dirac surface states either on the 𝑎⁢𝑏 planes or on both the 𝑎⁢𝑏 planes and mirror planes, protected by crystal symmetries. Therefore, SrAg 4 ⁢Sb 2 emerges as a promising candidate topological crystalline insulator.

36 MATERIALS SCIENCE↗

DOE OSTI2020

MEASUREMENT OF Fn 2 /Fp 2 FROM DEEP INELASTIC ELECTRON SCATTERING OFF A=3 MIRROR NUCLEI AT JEFFERSON LAB

This research is part of the Je?erson Lab MARATHON experiment (MeAsurement of the Fn 2 /Fp 2 , d/u RAtios and A = 3 EMC E?ect in Deep Inelastic Electron Scattering Off the Tritium and Helium MirrOr Nuclei). MARATHON is an experiment on electron deep inelastic scattering off the 3H, 3He mirror nuclei. It has extracted, from the measured deep inelastic scattering cross section ratio o? 3H and 3He, the ratio of the neutron to proton inelastic structure functions Fn 2 /Fp 2 . The extraction has taken advantage of the isospin symmetry of the A = 3 mirror nuclei within a novel technique, which avoids the theoretical uncertainties that are present in the SLAC experiments of the 1970s, which used hydrogen and deuterium targets. The experiment was performed using the upgraded 11 GeV beam of the Jefferson Lab electron accelerator, the Hall A Experimental Facility, and a newly designed cryogenic, high-pressure gas target system containing 3H and 3He cells. Electrons scattered o? the gas targets were detected in the two superconducting, high-resolution magnetic spectrometers of Hall A. The cross section data cover the four-momentum transfer squared range 2.0 < Q2 < 14.0 (GeV/c)2, and the Bjorken x scaling variable range 0.19 < x < 0.83. The experiment also measured, for calibration purposes, electron deep inelastic scattering off hydrogen and deuterium at selected kinematics.

Su, Tong↗

DOE OSTI2023

Extrinsic Nonlinear Kerr Rotation in Topological Materials under a Magnetic Field

Topological properties in quantum materials are often governed by symmetry and tuned by crystal structure and external fields, and hence, symmetry-sensitive nonlinear optical measurements in a magnetic field are a valuable probe. Here, we report nonlinear magneto-optical second harmonic generation (SHG) studies of nonmagnetic topological materials including bilayer WTe 2 , monolayer WSe 2 , and bulk TaAs. The polarization-resolved patterns of optical SHG under a magnetic field show nonlinear Kerr rotation in these time-reversal symmetric materials. For materials with 3-fold rotational symmetric lattice structure, the SHG polarization pattern rotates just slightly in a magnetic field, whereas in those with mirror or 2-fold rotational symmetry, the SHG polarization pattern rotates greatly and distorts. Further, these different magneto-SHG characters can be understood by considering the superposition of the magnetic field-induced time-noninvariant nonlinear optical tensor and the crystal-structure-based time-invariant counterpart. The situation is further clarified by scrutinizing the Faraday rotation, whose subtle interplay with crystal symmetry accounts for the diverse behavior of the extrinsic nonlinear Kerr rotation in different materials. Our work illustrates the application of magneto-SHG techniques to directly probe nontrivial topological properties, and underlines the importance of minimizing extrinsic nonlinear Kerr rotation in polarization-resolved magneto-optical studies.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Theoretical Constraints on Neutron-Mirror-Neutron Oscillation

Mirror models lead to the possibility that neutron (n) can oscillate into its mirror partner (n′), inspiring several experimental searches for this phenomenon. The condition for observability of this oscillation is a high degree of degeneracy between the n and n′ masses, which can be guaranteed if there is exact parity symmetry taking all particles to their mirror partners. However, consistency of these models with big-bang nucleosynthesis requires that this parity symmetry be broken in the early universe in a scenario called asymmetric inflation. In this paper, we study the consistency of an observable n−n′ oscillations signal with asymmetric inflation and derive various theoretical constraints. In particular, we find that the reheat temperature after inflation should lie below 2.5 TeV, and we predict a singlet fermion with a mass below 100 GeV. In simple models, where the right-handed neutrino is a mediator of baryon-number-violating interactions, we find that the light neutrinos are Dirac fermions with their masses arising radiatively through one-loop diagrams.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Search for Q ~0 Order near a Forbidden Bragg Position in Bi 2.1 Sr 1.9 CaCu 2 O 8+x with Resonant Soft X-ray Scattering

Identifying what broken symmetries are present in the cuprates has become a major area of research. Many authors have reported evidence for so-called “Q ~ 0” order that involves broken inversion, mirror, chiral, or time-reversal symmetry that is uniform in space. Not all these observations are well understood and new experimental probes are needed. Here we use resonant soft x-ray scattering (RSXS) to search for Q ~ 0 order in Bi 2.1 Sr 1.9 CaCu 2 O 8+x (Bi-2212) by measuring the region of a forbidden Bragg peak, (0,0,3), which is normally extinguished by symmetry but may become allowed on resonance if valence band order is present. Using circularly polarized light, we found that this reflection becomes allowed on the CuL 3 resonance for temperatures T c < T < T*, though remains absent in linear polarization and at other temperatures. This observation suggests the existence of spatially uniform valence band order near the pseudogap temperature. In addition, we observed periodic oscillations in the specular reflectivity from the sample surface that resemble thin film interference fringes, though no known film is present. These fringes are highly resonant, appear in all polarizations, and exhibit a period that depends on the location where the beam strikes the sample surface. We speculate that these fringes arise from interaction between some intrinsic valence band instability and extrinsic structural surface morphologies of the material. Our study supports the existence of some kind of Q ~ 0 broken symmetry state in Bi-2212 at intermediate temperatures. Further studies using a microfocused beam, which could disentangle microscopic effects from macroscopic heterogeneities, are needed to ascertain the universality of the effect.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1981

On the presence of electric currents in the solar atmosphere. I - A theoretical framework

The general magnetic field above the solar photosphere is divided by an elementary analysis based on Ampere's law into two parts: a potential field due to electric currents below the photosphere and a field produced by electric currents above the photosphere combined with the induced mirror currents. The latter, by symmetry, has a set of field lines lying in the plane taken to be the photosphere which may be constructed from given vector magnetograph measurements. These field lines also represent all the information on the electric currents above the photosphere that a magnetograph can provide. Theoretical illustrations are given, and implications for data analysis are discussed.

Hagyard, M.↗

NASA NTRS2018

Numerically Optimized Coronagraph Designs for the Habitable Exoplanet Imaging Mission (HabEx) Concept

The primary science goal of the Habitable Exoplanet Imaging Mission (HabEx), one of four candidate ﬂagship missions under investigation, is to image and spectrally characterize Earth-like exoplanets. It is well known that pupil obscurations degrade coronagraphic performance and complicate coronagraph design, so HabEx is planned to have an oﬀ-axis, unobscured primary mirror. We utilize the circular symmetry of the aperture to investigate 1D-radial coronagraph optimization methods that are prohibitively time-consuming or intractable in 2D, such as diﬀractive pupil remapping and concurrent, multi-plane optimization. We also directly constrain sensitivities to dynamic, low-order Zernike aberrations, which are separable in polar coordinates and can thus be propagated as 1D-radial integrals. The mask technologies in our designs claim heritage from the extensive modeling and testbed experiments performed by the Wide-Field Infrared Survey Telescope (WFIRST) Coronagraph Instrument (CGI) project. In this paper, we detail our optimization methods and outline future work to complete our design survey.

Balasubramaian, Kunjithapatham↗

DOE OSTI2023

Trends of Neutron Skins and Radii of Mirror Nuclei from First Principles

The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion Monte Carlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference between neutron and proton radii of mirror nuclei and quantify the effect of charge symmetry breaking terms in the nuclear Hamiltonian. In conclusion, our results for the mirror-difference charge radii and binding energies per nucleon agree with existing data.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Off-axis representation of hyperbolic mirror shapes for X-ray beamlines

Mirror-centered, closed-form expressions for hyperbolic surfaces used in X-ray beamlines have been derived. Hyperbolic mirrors create a virtual focus or source point and can be used to lengthen or shorten the effective focal distance of a compound optical system. The derivations here express off-axis segments of a hyperbolic surface in terms of the real and virtual focal distances and the incident glancing angle at the center of the mirror. Conventional mathematical expressions of hyperbolic shapes describe the surfaces in Cartesian or polar coordinates centered on an axis of symmetry, necessitating cumbersome rotation and translation to mirror-centered coordinates. The representation presented here, with zero slope and the origin at the central point, is most convenient for modeling, metrology, aberration correction, and general surface analysis of off-axis configurations. The direct derivation avoids the need for nested coordinate transforms. A series expansion provides a helpful approximation; the coefficients of the implicit equation are also provided.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗