SEARCH · Search NASA

Results for “Angular”

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

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Measurements of the groomed and ungroomed jet angularities in pp collisions at $ \sqrt{s}$ = 5.02 TeV

The jet angularities are a class of jet substructure observables which characterize the angular and momentum distribution of particles within jets. These observables are sensitive to momentum scales ranging from perturbative hard scatterings to nonperturbative fragmentation into final-state hadrons. We report measurements of several groomed and ungroomed jet angularities in pp collisions at $\sqrt{s}$ = 5.02 TeV with the ALICE detector. Jets are reconstructed using charged particle tracks at midrapidity (|η| < 0.9). The anti-$k_T$ algorithm is used with jet resolution parameters R = 0.2 and R = 0.4 for several transverse momentum $p^{ch jet}_{T}$ intervals in the 20–100 GeV/c range. Using the jet grooming algorithm Soft Drop, the sensitivity to softer, wide-angle processes, as well as the underlying event, can be reduced in a way which is well-controlled in theoretical calculations. We report the ungroomed jet angularities, λ α , and groomed jet angularities, λ α,g , to investigate the interplay between perturbative and nonperturbative effects at low jet momenta. Various angular exponent parameters α = 1, 1.5, 2, and 3 are used to systematically vary the sensitivity of the observable to collinear and soft radiation. Results are compared to analytical predictions at next-to-leading-logarithmic accuracy, which provide a generally good description of the data in the perturbative regime but exhibit discrepancies in the nonperturbative regime. Moreover, these measurements serve as a baseline for future ones in heavy-ion collisions by providing new insight into the interplay between perturbative and nonperturbative effects in the angular and momentum substructure of jets. They supply crucial guidance on the selection of jet resolution parameter, jet transverse momentum, and angular scaling variable for jet quenching studies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Orbital angular momentum constraints in the variational optimization of the two-electron reduced-density matrix

The direct variational determination of the two-electron reduced-density matrix (2-RDM) corresponding to an atomic or molecular system is usually carried out in a basis of real-valued atom-centered Gaussian basis functions, under the assumption that the 2-RDM is a real-valued quantity. Furthermore, for systems that possess orbital angular momentum symmetry, the description of states with a well-defined, nonzero z projection of the orbital angular momentum requires a computational framework generalized to include either complex basis functions or a complex-valued 2-RDM. We consider a semidefinite program suitable for the direct optimization of a complex-valued 2-RDM and explore the role of orbital angular momentum constraints in systems that possess the relevant symmetries. For atomic systems, constraints on the expectation values of the square and z projection of the orbital angular momentum operator allow one to optimize 2-RDMs for multiple orbital angular momentum states. Similarly, in linear molecules, orbital angular momentum projection constraints enable the description of multiple electronic states and, moreover, the application of such constraints is essential for a qualitatively correct description of the electronic structure. For example, in the case of molecular oxygen, we demonstrate that orbital angular momentum constraints are necessary to recover the correct energy ordering of the lowest-energy singlet and triplet states near the equilibrium geometry. However, care must still be taken in the description of the dissociation limit, because the 2-RDM-based approach is not size consistent, and the size-consistency error varies dramatically, depending on the z projections of the spin and orbital angular momenta.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1998

Angular-Rate Estimation Using Quaternion Measurements

In most spacecraft (SC) there is a need to know the SC angular rate. Precise angular rate is required for attitude determination, and a coarse rate is needed for attitude control damping. Classically, angular rate information is obtained from gyro measurements. These days, there is a tendency to build smaller, lighter and cheaper SC, therefore the inclination now is to do away with gyros and use other means and methods to determine the angular rate. The latter is also needed even in gyro equipped satellites when performing high rate maneuvers whose angular-rate is out of range of the on board gyros or in case of gyro failure. There are several ways to obtain the angular rate in a gyro-less SC. When the attitude is known, one can differentiate the attitude in whatever parameters it is given and use the kinematics equation that connects the derivative of the attitude with the satellite angular-rate and compute the latter. Since SC usually utilize vector measurements for attitude determination, the differentiation of the attitude introduces a considerable noise component in the computed angular-rate vector.

Azor, Ruth↗

DOE OSTI2024

Angular Distribution of Dimuons from Drell-Yan Production in p+Fe Interactions at 120 GeV Beam Energy

In the E906/SeaQuest Fermilab experiment, we report a measurement of the angular distributions by measuring the angular parameters $\lambda$, $\mu$, and $\nu$ of Drell-Yan dimuons produced using a 120 GeV proton beam incident on an iron target. The angular distribution in the naive Drell-Yan model does not show any $\cos2\phi$ dependency, where $\phi$ denotes the azimuthal angle of dimuons in the Collins-Soper frame. However, pion-induced Drell-Yan experiments, such as NA10 and E615, have observed a significant dependence on $\cos2\phi$. The Boer–Mulders function, a transverse momentum-dependent distribution function, represents the correlation between the transverse spin and the transverse momentum of the quark. A non-zero Boer-Mulders function or an improved higher-order Drell-Yan model considering QCD effects can produce a $\cos 2\phi$ modulation in the Drell-Yan angular distribution. To measure the angular distributions, we have used an event mixing method to construct the combin atorial background, which was then subtracted from the data to isolate the Drell-Yan signal. Following this, we corrected the detector, trigger, and reconstruction efficiencies using a doubly-iterative Bayesian Unfolding method. This iterative unfolding technique improves the response matrix based on the results of the previous unfolding step, ensuring robust convergence without exaggeration of uncertainties. The angular distributions of the dimuons were measured over the invariant mass range $5.0 < M_{\mu^+ \mu^-} < 8.0$ $GeV/c^2$, with dimuon transverse momentum $P_T < 2$ GeV/c and Feynman-x $-0.18 < x_F < 0.9$. The measured angular distributions are then compared with the QCD calculations for $p + \text{Fe}$ interactions, and proton-induced angular distribution measurements from other experiments. We have observed weak $\cos 2\phi$ modulations as a function of $P_T$. For $P_T > 1.0 \, \text{GeV}/c$, the predicted NNLO perturbative QCD value of $\nu$ is larger than what we have me asured at E906/SeaQuest. Moreover, we have not observed a strong dependence of $\nu$ on the kinematic variables, such as dimuon mass $M_{\mu^+ \mu^-}$ and Bjorken-$x$. The spin alignment of the virtual photon, $\lambda$, measured from the SeaQuest Drell-Yan $p+\text{Fe}$ data, is found to be strongly dependent on $P_T$, decreasing as $P_T$ increases. $\lambda$ also holds to the upper bound condition $\lambda < 1.0$ within the statistical uncertainty, showing a trend similar to that predicted by NNLO perturbative QCD. However, for $1.0 < P_T < 2.0 \, \text{GeV}/c$, the extracted $\lambda$ value from SeaQuest is smaller than that predicted by perturbative QCD at NNLO.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Asymptotic convergence of the angular discretization error in the scalar flux computed from the particle transport equation with the method of discrete ordinates

The asymptotic convergence of the angular discretization error in the scalar flux solution of the particle transport equation computed with the Discrete Ordinates (S N ) method with increasing quadrature order is examined. Five selected angular quadrature types are considered: Level Symmetric (LS), Legendre-Chebyshev Quadrangular (LCQ), Legendre-Chebyshev Triangular(LCT), Quadruple Range (QR) and Quadruple Range Spence-type (QRS) quadrature sets. We relate the S N angular discretization error to the quadrature error, and split the total flux into the uncollided flux and the fully collided flux, and then we verify the uncollided scalar flux error and the fully collided scalar flux error separately. After developing the theoretical basis for the relationship between true solution regularity and quadrature rule error, we employ a two-dimensional problem to verify the observed and theoretical convergence orders for the region-averaged uncollided and fully collided scalar flux errors. Numerical results show that the angular discretization errors in the region-averaged scalar flux obtained by different quadrature types converge with different rates, that are commensurate with the regularity order of the exact angular flux within the quadrature-designed integration interval. The angular discretization error in the uncollided region-averaged scalar flux obtained by LC class quadratures converges linearly, and the error obtained by QR class quadrature sets converges quadratically. The angular discretization error in the fully collided region-averaged scalar flux converges linearly for LC class quadratures, and faster-than-second order for QR class quadrature sets.

42 ENGINEERING↗

DOE OSTI2022

The MP{sub N} method: a new angular discretization method based on piecewise polynomial interfaces fluxes

In transport calculations, it is well known how S{sub N} method is extremely inefficient in problems where the particle physics is dominated by streaming. The ray-effect eventually produced by the insufficient angular discretization, appears to be extremely persistent with respect to the refinement of the angular quadrature. The MP{sub N} method, that relies on continuous angular representation, offers a robust remedy to such an issue. MP{sub N} is based on the decomposition of the unit sphere into solid angles and on a piecewise continuous definition of interface fluxes, which are expanded in polynomials in each solid angle. This allows propagating more than one angular degree of freedom simultaneously while maintaining unaltered the block-diagonal pattern of the displacement plus removal operator. The method is therefore well suited for the flux resolution by means of a conventional sweep algorithm. Furthermore, unlike the S{sub N} method, MP{sub N} does not rely on discrete directions and, thus, on an angular quadrature formula, but rather constructs a set of linear equations solving for the angular moments of the flux for all discrete solid angles within the sweep. MP{sub N} shows an error convergence rate higher than S{sub N} at the expense of an increased size of the coefficient matrices, so of the computational cost. Although MP{sub N} is not free from ray-effect, the latter is effectively mitigated and less persistent with respect to the increase of the angular refinement order. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Conservation of angular momentum in second harmonic generation from under-dense plasmas

Spin and orbital angular momentum of an optical beam are two independent parameters that exhibit distinct effects on mechanical objects. However, when laser beams with angular momentum interact with plasmas, one can observe the interplay between the spin and the orbital angular momentum. Here, by measuring the helical phase of the second harmonic 2ω radiation generated in an underdense plasma using a known spin and orbital angular momentum pump beam, we verify that the total angular momentum of photons is conserved and observe the conversion of spin to orbital angular momentum. We further determine the source of the 2ω photons by analyzing near field intensity distributions of the 2ω light. The 2ω images are consistent with these photons being generated near the largest intensity gradients of the pump beam in the plasma as predicted by the combined effect of spin and orbital angular momentum when Laguerre-Gaussian beams are used.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Constructing angular distributions of neutrinos in core-collapse supernovae from zeroth and first moments calibrated by full Boltzmann neutrino transport

Two-moment neutrino transport methods have been widely used for developing theoretical models of core-collapse supernovae (CCSN), since they substantially reduce the computational burden inherent in the multidimensional neutrino-radiation hydrodynamical simulations. The approximation, however, comes at a price; the detailed structure of angular distribution of neutrinos is sacrificed, that is the main drawback of this approach. In this paper, we develop a novel method by which to construct angular distributions of neutrinos from the zeroth and first angular moments. In our method, the angular distribution is expressed with two quadratic functions of the neutrino angle in a piecewise fashion. We determine the best parameters in the fitting function by comparing to the neutrino data in a spherically symmetric CCSN model with full Boltzmann neutrino transport. We demonstrate the capability of our method by using our recent 2D CCSN model. In this work, we find that the essential features of the angular distributions can be well reconstructed, whereas the angular distributions of incoming neutrinos tend to have large errors that increase with flux factor ($\textit{κ}$). This issue originates from the insensitiveness of incoming neutrinos to $\textit{κ}$, that is an intrinsic limitation in moment methods. Based on the results of the demonstration, we assess the reliability of electron- neutrinos lepton number (ELN)-crossing searches with the two-moment neutrino transport. This analysis is complementary to our [L. Johns and H. Nagakura arXiv:2104.04106] that scrutinizes the limitation of crossing searches with a few moments. We find that the systematic errors of angular distributions for incoming neutrinos lead to misjudgements of the crossing at $\textit{κ}$ ≳ 0.5. This casts doubt on the results of ELN-crossing searches based on two-moment methods in some previous studies.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Microscopic theory of angular momentum distributions across the full range of fission fragments

Modern nuclear theory provides qualitative insights into the fundamental mechanisms of nuclear fission and is increasingly capable of making reliable quantitative predictions. Most quantities of interest pertain to the primary fission fragments, whose subsequent decay is typically modeled using statistical reaction models. Consequently, a key objective of fission theory is to inform these models by predicting the initial conditions of the primary fragments. Here, in this work, we employ a framework that combines joint angular momentum and particle number projection with time-dependent configuration mixing to calculate the angular momentum distributions of primary fragments. Focusing on the benchmark cases of neutron-induced fission of 235 U and 239 Pu , we predict—for the first time—microscopic angular momentum distributions for all fragments observed in experiments. Our results reveal a pronounced sawtooth pattern in the average angular momentum as a function of fragment mass, consistent with recent measurements. Additionally, we observe substantial variations in angular momentum distributions along isobaric chains, indicating that commonly used empirical formulas lack sufficient accuracy. We also quantify a strong correlation between the angular momentum and the deformation of the fragments at scission, and a weak correlation in the magnitude of the angular momentum between fragment partners. The generated data will enable estimation of the impact of microscopic distributions on fission spectra, paving the way toward fission modeling based on microscopic inputs.

Physics - Nuclear physics and radiation physics↗

NASA NTRS1977

Calculations of the effects of angular momentum on the early evolution of Jupiter

Early phases in the evolutionary development of a rotating cloud of gas and dust are investigated to determine whether physically reasonable initial conditions are likely to produce a planet-satellite system with the values of specific orbital angular momentum currently observed for Jupiter and its inner satellites. Spherically symmetric computations of Jupiter's evolutionary history are reviewed, and transport of angular momentum is considered along with evolutionary sequences of individual differentially rotating models with decreasing values of equatorial radius. The problem of accounting for the present specific orbital angular momenta of Jupiter and its regular satellites is examined qualitatively, and a range of possible angular-momentum distributions in an initially tidally unstable cloud is assessed. The results show that particular physically plausible angular-momentum distributions, which could either be established as initial conditions or be caused by angular-momentum transport, will lead to favorable situations for the formation of a central planet and a surrounding rotating cloud with specific angular momentum comparable to that of the regular satellites.

Bodenheimer, P.↗

NASA NTRS1997

Angular neutron transport investigation in the HZETRN free-space ion and nucleon transport and shielding computer program

Extension of the high charge and energy (HZE) transport computer program HZETRN for angular transport of neutrons is considered. For this paper, only light ion transport, He4 and lighter, will be analyzed using a pure solar proton source. The angular transport calculator is the ANISN/PC program which is being controlled by the HZETRN program. The neutron flux values are compared for straight-ahead transport and angular transport in one dimension. The shield material is aluminum and the target material is water. The thickness of these materials is varied; however, only the largest model calculated is reported which is 50 gm/sq cm of aluminum and 100 gm/sq cm of water. The flux from the ANISN/PC calculation is about two orders of magnitude lower than the flux from HZETRN for very low energy neutrons. It is only a magnitude lower for the neutrons in the 10 to 20 MeV range in the aluminum and two orders lower in the water. The major reason for this difference is in the transport modes: straight-ahead versus angular. The angular treatment allows a longer path length than the straight-ahead approximation. Another reason is the different cross section sets used by the ANISN/PC-BUGLE-80 mode and the HZETRN mode. The next step is to investigate further the differences between the two codes and isolate the differences to just the angular versus straight-ahead transport mode. Then, create a better coupling between the angular neutron transport and the charged particle transport.

Singleterry, R. C., Jr.↗

NASA NTRS2007

Simplified Generation of High-Angular-Momentum Light Beams

A simplified method of generating a beam of light having a relatively high value of angular momentum (see figure) involves the use of a compact apparatus consisting mainly of a laser, a whispering- gallery-mode (WGM) resonator, and optical fibers. The method also can be used to generate a Bessel beam. ( Bessel beam denotes a member of a class of non-diffracting beams, so named because their amplitudes are proportional to Bessel functions of the radii from their central axes. High-order Bessel beams can have high values of angular momentum.) High-angular-momentum light beams are used in some applications in biology and nanotechnology, wherein they are known for their ability to apply torque to make microscopic objects rotate. High-angular-momentum light beams could also be used to increase bandwidths of fiber-optic communication systems. The present simplified method of generating a high-angular-momentum light beam was conceived as an alternative to prior such methods, which are complicated and require optical setups that include, variously, holograms, modulating Fabry-Perot cavities, or special microstructures. The present simplified method exploits a combination of the complex structure of the electromagnetic field inside a WGM resonator, total internal reflection in the WGM resonator, and the electromagnetic modes supported by an optical fiber. The optical fiber used to extract light from the WGM resonator is made of fused quartz. The output end of this fiber is polished flat and perpendicular to the fiber axis. The input end of this fiber is cut on a slant and placed very close to the WGM resonator at an appropriate position and orientation. To excite the resonant whispering- gallery modes, light is introduced into the WGM resonator via another optical fiber that is part of a pigtailed fiber-optic coupler. Light extracted from the WGM resonator is transformed into a high-angular- momentum beam inside the extraction optical fiber and this beam is emitted from the polished flat output end. By adjusting the geometry of this apparatus, it is possible to generate a variety of optical beams characterized by a wide range of parameters. These beams generally have high angular momenta and can be of either Bessel or Bessel-related types.

Savchenkov, Anatoliy↗

NASA NTRS2016

Polarbrdf: A General Purpose Python Package for Visualization Quantitative Analysis of Multi-Angular Remote Sensing Measurements

The Bidirectional Reflectance Distribution Function (BRDF) is a fundamental concept for characterizing the reflectance property of a surface, and helps in the analysis of remote sensing data from satellite, airborne and surface platforms. Multi-angular remote sensing measurements are required for the development and evaluation of BRDF models for improved characterization of surface properties. However, multi-angular data and the associated BRDF models are typically multidimensional involving multi-angular and multi-wavelength information. Effective visualization of such complex multidimensional measurements for different wavelength combinations is presently somewhat lacking in the literature, and could serve as a potentially useful research and teaching tool in aiding both interpretation and analysis of BRDF measurements. This article describes a newly developed software package in Python (PolarBRDF) to help visualize and analyze multi-angular data in polar and False Color Composite (FCC) forms. PolarBRDF also includes functionalities for computing important multi-angular reflectance/albedo parameters including spectral albedo, principal plane reflectance and spectral reflectance slope. Application of PolarBRDF is demonstrated using various case studies obtained from airborne multi-angular remote sensing measurements using NASA's Cloud Absorption Radiometer (CAR). Our visualization program also provides functionalities for untangling complex surface/atmosphere features embedded in pixel-based remote sensing measurements, such as the FCC imagery generation of BRDF measurements of grasslands in the presence of wild fire smoke and clouds. Furthermore, PolarBRDF also provides quantitative information of the angular distribution of scattered surface/atmosphere radiation, in the form of relevant BRDF variables such as sunglint, hotspot and scattering statistics.

CAR↗

NASA NTRSDate not supplied

Leveraging CPF Spectral Information for Effective Angular Corrections in Sensor Inter-calibration Studies

The Climate Absolute Radiance and Refractivity Observatory Pathfinder (CPF) mission will provide a high-accuracy (0.3% radiometric uncertainty at k=1) SI-traceable on-orbit calibration reference for sensor intercalibration in reflective solar spectral region. CPF inter-calibration algorithms have been developed to address various sampling differences between CPF and target sensors, particularly in spectral, angular, spatial and temporal domains. CPF provides unique hyper-spectral measurements that allow the utilization of rich spectral information for critical inter-calibration procedures including angular correction and spectral-gap filling. The angular correction scheme of CPF mission has been constructed based on the spectral correlation relationship between CPF observed spectra and the spectra to be measured at the viewing/sun geometry angles of target sensors. The angular correction relationship is both angular and scene dependent. The scene variability issue can impose undesired uncertainties that complicates the correction for those errors. We have demonstrated that hyper-spectral radiance information can be well utilized to identify different scene types associated with CPF observations. Using spectral radiances-based scene clustering analysis can greatly reduce the uncertainty associated with the angular correction algorithm. Additionally, a reliable quality control scheme has been established, utilizing spectral similarity and regression-prediction error analyses, to ensure the successful and efficient implementation of the angular correction method.

Wan Wu↗

DOE OSTI2025

Angular Correlations of Gamma Rays from Fission Product Solution

Fission products from photon-induced fission are routinely used at Idaho National Laboratory as part of nuclear forensics activities. Typically, the focus is on fission products with relatively large fission yields (Ba-140, Mo-99, etc.). The nuclear data associated with the well-known isotopes have small uncertainties, and many have well-known angular correlations between emitted gamma-rays, if applicable. However, for isotopes with smaller fission yields or less intense gamma-ray emission intensities, the nuclear decay schemes and gamma-ray emission intensities may be less well-known. The Germanium Rotational Measurements for Angular Correlation (GeRMAC) system was designed to use two high-purity germanium (HPGe) detectors in a coincidence counting set-up but allows one of the HPGe detectors to rotate at a constant distance from a radioactive source, changing the relative angle between the two HPGe detectors. Angular correlations can then be determined from the relative photopeak areas between two gamma-rays emitted as part of the same nuclear decay. By recording the HPGe spectra in list mode, the angular correlations of gamma-rays emitted from complex sources, consisting of multiple isotopes, can be measured simultaneously and the individual isotope emissions can be isolated. Using the GeRMAC system, a multi-isotope fission product source, produced with photon-induced fission of U-238, was measured using a single rotational arc (180 degrees) to obtain the angular correlation between gamma-rays emitted by the large number of fission products contained in the solution with an angular accuracy of 1 degree. In particular, La-140 (38 gamma rays) and Nd-147 (26 gamma rays) are of interest to the nuclear forensics community.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗

DOE OSTI2024

Probing light quark Yukawa couplings through angularity distributions in Higgs boson decay

We propose to utilize angularity distributions in Higgs boson decay to probe light quark Yukawa couplings at e + e - colliders. Angularities $τ$ a are a class of 2-jet event shapes with variable and tunable sensitivity to the distribution of radiation in hadronic jets in the final state. Using soft-collinear effective theory (SCET), we present a prediction of angularity distributions from Higgs decaying to quark and gluon states at e + e - colliders to NNLL + $\mathcal{O}$(α s ) accuracy. Due to the different color structures in quark and gluon jets, the angularity distributions from H → $q\overline{q}$ and H → gg show different behaviors and can be used to constrain the light quark Yukawa couplings. We show that the upper limit of light quark Yukawa couplings could be probed to the level of ~ 15% of the bottom quark Yukawa coupling in the Standard Model in a conservative analysis window far away from nonperturbative effects and other uncertainties; the limit can be pushed to ≲ 7 – 9% with better control of the nonperturbative effects especially on gluon angularity distributions and/or with multiple angularities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Angular momentum of fission fragments from microscopic theory

During nuclear fission, a heavy nucleus splits into two rotating fragments. The associated angular momentum is large, yet the mechanism of its generation and its dependence on the mass of fragments remain poorly understood. In this Letter, we provide the first microscopic calculations of angular-momentum distributions in fission fragments for a wide range of fragment masses. For the benchmark case of 239 Pu(n th ,f), we find that the angular momentum of the fragments is largely determined by the nuclear shell structure and deformation, and that the heavy fragments therefore typically carry less angular momentum than their light partners. We use the fission model freya to simulate the emission of neutrons and photons from the fragments. The dependence of the angular momenta on fragment mass after the emission of neutrons and statistical photons is linear for the heavy fragments and either constant or weakly linear for the light fragments, consistent with the universal sawtooth pattern suggested by recent experimental data. Finally, we observe that using microscopic angular-momentum distributions modifies the number of emitted photons significantly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Angular correlations in the ${e^+}{e^-}$ decay of excited states in $\mathrm{^8Be}$

Motivated by the recent observation of anomalous electron-positron angular correlations in the decay of the 18.15-MeV $\mathrm{1^+}$ excited states in $\mathrm{^8Be}$, we reexamine in detail the standard model expectations for these angular correlations. The 18.15-MeV state is above particle threshold, and several multipoles can contribute to its ${e^+}{e^-}$ decay. Here, we present the general theoretical expressions for ${e^+}{e^-}$ angular distributions for nuclear decay by $C0, C1, C2, M1, E1,$ and $E2$ multipoles, and we examine their relative contribution to the ${e^+}{e^-}$ decay of $\mathrm{^8Be}$ at 18.15 MeV. We find that this resonance is dominated by $M1$ to $E1$ decay, and that the ratio of $M1$ to $E1$ strength is a strong function of energy. This is in contrast to the original analysis of the ${e^+}{e^-}$ angular distributions, where the $M1/E1$ ratio was assumed to be a constant over the energy region ${E_p} = 0.8 – 1.2$ MeV. We find that the existence of a “bump” in the measured angular distribution is strongly dependent on the assumed $M1/E1$ ratio, with the present analysis finding the measured large-angle contributions to the ${e^+}{e^-}$ angular distribution to be lower than expectation. Thus, in the current analysis we find no evidence for axion decay in the 18.15-MeV resonance region of $\mathrm{^8Be}$.

6 ≤ A ≤ 19↗