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At least 667 records · Page 37

Radiative transfer in cometary dust atmospheres: Critique of recent developments

The gas and dust production rates of comets near the sun are intimately linked to the fate of the solar radiation as it is scattered and partially absorbed by the cometary dust envelope or halo surrounding the comet's nucleus. The radiation of nuclear matter (mostly water ice) and the release of dust particles embedded in the ice which are entrained by the escaping gas and subsequently form a dust atmosphere or halo. On the other hand, the interaction of the dust cloud with the solar radiation is in turn responsible for the amount of radiative energy received by the nucleus and thus determines the evaporation rate. It is shown that recent attempts to formulate this problem quantitatively are in error. The correct formulation is given and it is pointed out that negative extinction (enhancement of the primary radiation received by the nucleus due to multiple scattering) may not be as large as predicted.

Vonroos, O.↗

Critical fluid light scattering

The objective is to measure the decay rates of critical density fluctuations in a simple fluid (xenon) very near its liquid-vapor critical point using laser light scattering and photon correlation spectroscopy. Such experiments were severely limited on Earth by the presence of gravity which causes large density gradients in the sample when the compressibility diverges approaching the critical point. The goal is to measure fluctuation decay rates at least two decades closer to the critical point than is possible on earth, with a resolution of 3 microK. This will require loading the sample to 0.1 percent of the critical density and taking data as close as 100 microK to the critical temperature. The minimum mission time of 100 hours will allow a complete range of temperature points to be covered, limited by the thermal response of the sample. Other technical problems have to be addressed such as multiple scattering and the effect of wetting layers. The experiment entails measurement of the scattering intensity fluctuation decay rate at two angles for each temperature and simultaneously recording the scattering intensities and sample turbidity (from the transmission). The analyzed intensity and turbidity data gives the correlation length at each temperature and locates the critical temperature. The fluctuation decay rate data from these measurements will provide a severe test of the generalized hydrodynamic theories of transport coefficients in the critical regions. When compared to equivalent data from binary liquid critical mixtures they will test the universality of critical dynamics.

Gammon, Robert W.↗

The axisymmetric stellar wind of AG Carinae

We present optical linear spectropolarimetry of the Luminous Blue Variable AG Carinae obtained after a recent visual brightness increase. The absence of He II lambda 4686 emission, together with the weakening of the He I spectrum and the appearance of Fe lines in the region around 5300 A, confirm that AG Car has started a new excursion across the HR diagram. The H alpha line profile exhibits very extended line wings that are polarized differently in both amount and position angle from either the continuum or the line core. The polarization changes across H alpha, together with variable continuum polarization, indicate the presence of intrinsic polarization. Coexistence of the line-wing polarization with extended flux-line wings evidences that both are formed by electron scattering in a dense wind. The position angle rotates across the line profiles, in a way that presently available models suggest is due to rotation and expansion of the scattering material. AG Car displays very large variations of its linear polarization with time, Delta P approximately 1.2%, indicating significant variations in envelope opacity. We find that the polarization varies along a preferred position angle of approximately 145 deg (with a scatter of +/- 10 deg) which we interpret as a symmetry axis of the stellar wind (with an ambiguity of 90 deg). This position angle is co-aligned with the major axis of the AG Car ring nebula and perpendicular to the AG Car jet. Our observations thus suggest that the axisymmetric geometry seen in the resolved circumstellar environment at various distances already exists within a few stellar radii of AG Car. From the H alpha polarization profile we deduce an interstellar polarization of Q = 0.31%, U = -1.15% at H alpha. The inferred interstellar polarization implies that the intrinsic polarization is not always of the same sign. This indicates either significant temporal changes in the envelope geometry, or it may arise from effects of multiple scattering in conjunction with density variations.

Schulte-Ladbeck, Regina E.↗

Universal features of 2 → N scattering in QCD and gravity from shockwave collisions

A remarkable double-copy relation of Einstein gravity to QCD in Regge asymptotics is Γ μ ν = 1 2 C μ C ν − 1 2 N μ N ν , where Γ μ ν is the gravitational Lipatov vertex in the 2 → 3 graviton scattering amplitude, C μ its Yang-Mills counterpart, and N μ the QED bremsstrahlung vertex. In QCD, the Lipatov vertex is a fundamental building block of the BFKL equation describing the 2 → N scattering of gluons at high energies. Likewise, the gravitational Lipatov vertex is a key ingredient in a 2D effective field theory framework describing trans-Planckian 2 → N graviton scattering. We construct a quantitative correspondence between a semiclassical Yang-Mills framework for radiation in gluon shockwave collisions and its counterpart in general relativity. In particular, we demonstrate the Lipatov double copy in a dilute-dilute approximation corresponding to R S , L , R S , H ≪ b , where R S , L , R S , H are the respective emergent Schwarzchild radii generated in shockwave collisions and b is the impact parameter. We outline extensions of the correspondence developed here to the dilute-dense computation of gravitational wave radiation in the close vicinity of one of the black holes, the construction of graviton propagators in the shockwave background, and a renormalization group approach to compute 2 → N amplitudes that incorporates graviton Reggeization and coherent graviton multiple scattering. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Ocean observations with EOS/MODIS: Algorithm development and post launch studies

An investigation of the influence of stratospheric aerosol on the performance of the atmospheric correction algorithm was carried out. The results indicate how the performance of the algorithm is degraded if the stratospheric aerosol is ignored. Use of the MODIS 1380 nm band to effect a correction for stratospheric aerosols was also studied. The development of a multi-layer Monte Carlo radiative transfer code that includes polarization by molecular and aerosol scattering and wind-induced sea surface roughness has been completed. Comparison tests with an existing two-layer successive order of scattering code suggests that both codes are capable of producing top-of-atmosphere radiances with errors usually less than 0.1 percent. An initial set of simulations to study the effects of ignoring the polarization of the the ocean-atmosphere light field, in both the development of the atmospheric correction algorithm and the generation of the lookup tables used for operation of the algorithm, have been completed. An algorithm was developed that can be used to invert the radiance exiting the top and bottom of the atmosphere to yield the columnar optical properties of the atmospheric aerosol under clear sky conditions over the ocean, for aerosol optical thicknesses as large as 2. The algorithm is capable of retrievals with such large optical thicknesses because all significant orders of multiple scattering are included.

Gordon, Howard R.↗

Electronic and nuclear contributions to time-resolved optical and X-ray absorption spectra of hematite and insights into photoelectrochemical performance

Ultrafast time-resolved studies of photocatalytic thin films can provide a wealth of information crucial for understanding and thereby improving the performance of these materials by directly probing electronic structure, reaction intermediates, and charge carrier dynamics. The interpretation of transient spectra, however, can be complicated by thermally induced structural distortions, which appear within the first few picoseconds following excitation due to carrier–phonon scattering. Here we present a comparison of ex situ steady-state thermal difference spectra and transient absorption spectra spanning from NIR to hard X-ray energies of hematite thin films grown by atomic layer deposition. We find that beyond the first 100 picoseconds, the transient spectra measured for all excitation wavelengths and probe energies are almost entirely due to thermal effects as the lattice expands in response to the ultrafast temperature jump and then cools to room temperature on the microsecond timescale. At earlier times, a broad excited state absorption band that is assigned to free carriers appears at 675 nm, and the lifetime and shape of this feature also appear to be mostly independent of excitation wavelength. The combined spectroscopic data, which are modeled with density functional theory and full multiple scattering calculations, support an assignment of the optical absorption spectrum of hematite that involves two LMCT bands that nearly span the visible spectrum. Lastly, our results also suggest a framework for shifting the ligand-to-metal charge transfer absorption bands of ferric oxide films from the near-UV further into the visible part of the solar spectrum to improve solar conversion efficiency.

14 SOLAR ENERGY↗

Use of spectral analogy to evaluate canopy reflectance sensitivity to leaf optical property

The spectral variation of canopy reflectance is mostly governed by the absorption properties of the elements, hence the leaves, since their intrinsic scattering properties show very little spectral variation. The relationship between canopy reflectance and leaf reflectance measured at the red edge over sugar beet canopies was used to simulate canopy reflectance from leaf reflectance spectra measured over the whole spectral domain. The results show that the spectral analogies found allows accurate reconstruction of canopy reflectance spectra. Explicit assumptions about the very low spectral variation of leaf intrinsic scattering properties are thus indirectly justified. The sensitivity of canopy reflectance (rho(sub c)) to leaf optical properties can then be investigated from concurrent spectral variations of canopy (delta rho(sub c)/delta lambda) and leaf reflectance (delta rho(sub l)/delta lambda): (delta rho(sub c))/(delta rho(sub l)) = ((delta rho(sub c))/(delta lambda) ((delta rho( sub l))/(delta lambda))(sup -1)). This expression is strictly valid only when the optical properties of the soil background or the other vegetation elements such as bark are either spectrally flat or do not contribute significantly to canopy reflectance. Simulations using the SAIL and PROSPECT models demonstrate that the sensitivity of canopy reflectance to leaf reflectance is significant for large vegetation cover fractions in spectral domains where absorption is low. In these conditions, multiple, scattering enhances the leaf absorption features by a factor that can be greater than 2.0. To override the limitations of the SAIL model for the description of the canopy architecture, we tested the previous findings on experimental data. Concurrent canopy and leaf reflectance spectra were measured for a range of sugar beet canopies. The results show good agreement with the theoretical findings. Conclusions are drawn about the applicability of these findings, with particular attention to the potential detectability of leaf biochemical composition from canopy reflectance sensed from space.

Baret, Frederic↗

Polarized Radiative Transfer of a Cirrus Cloud Consisting of Randomly Oriented Hexagonal Ice Crystals: The 3 x 3 Approximation for Non-Spherical Particles

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 x 10(exp 3) so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling- adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5 for I and within 1.5 for Q for all viewing angles. In 1971 Hansen showed that for scattering by spherical particles the 3 x 3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3 x 3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3 x 3 approximation leads to an absolute error 2 x 10(exp -6) for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

Polarization↗

Laboratory scaled simulation of lidar cloud sounding experiments

The results of lidar measurements carried out on laboratory scale models of clouds are presented. Measurements on laboratory scale models are important since one has the knowledge of the relevant parameters of the diffusing medium, such as: scattering and absorption coefficients, phase function, homogeneity, shape, etc. Knowledge of these parameters enables one to use the results to test the reliability of theoretical and numerical investigations. To obtain a laboratory scaled model of a lidar system sounding a cloud, it is necessary to scale down all the geometrical quantities by the same factor to reduce distances of the order of kilometers to the order of meters, keeping the size and the optical depth of the diffusers unchanged. If a time resolution of the order of nanoseconds is necessary for a lidar sounding actual clouds, the corresponding time resolution for the laboratory model should be of the order of picoseconds. It is possible to obtain this resolution by using picosecond laser systems and fast electrooptical detectors like the streak camera. The results of the laboratory measurements showed that the multiple scattering effect strongly depends on the size of the diffusers, as well as on the concentration. The experimental results were compared with the numerical results of a Monte Carlo code. A generally good agreement was obtained.

Zaccanti, G.↗

Vertical Photon Transport in Cloud Remote Sensing Problems

Photon transport in plane-parallel, vertically inhomogeneous clouds is investigated and applied to cloud remote sensing techniques that use solar reflectance or transmittance measurements for retrieving droplet effective radius. Transport is couched in terms of weighting functions which approximate the relative contribution of individual layers to the overall retrieval. Two vertical weightings are investigated, including one based on the average number of scatterings encountered by reflected and transmitted photons in any given layer. A simpler vertical weighting based on the maximum penetration of reflected photons proves useful for solar reflectance measurements. These weighting functions are highly dependent on droplet absorption and solar/viewing geometry. A superposition technique, using adding/doubling radiative transfer procedures, is derived to accurately determine both weightings, avoiding time consuming Monte Carlo methods. Superposition calculations are made for a variety of geometries and cloud models, and selected results are compared with Monte Carlo calculations. Effective radius retrievals from modeled vertically inhomogeneous liquid water clouds are then made using the standard near-infrared bands, and compared with size estimates based on the proposed weighting functions. Agreement between the two methods is generally within several tenths of a micrometer, much better than expected retrieval accuracy. Though the emphasis is on photon transport in clouds, the derived weightings can be applied to any multiple scattering plane-parallel radiative transfer problem, including arbitrary combinations of cloud, aerosol, and gas layers.

Platnick, S.↗

Radar depolarization signatures of rain in cumulus clouds measured with a dual-frequency air-borne radar

Experimental data are presented on dual-wavelength scattering characteristics of subtropical rain observed during the convection and precipitation/electrification (CaPE) experiment. Linear depolarization ratios (LDRs) are calculated at both X-band and Ka-band channels. In stratiform rain, the cross-polarized return signal is generally below the noise level except within the melting layer where the maximum LDR at both frequencies is typically between -12 and -10 dB. In convective rain the range profiles of the LDR in X-band and those in Ka-band do not coincide. The X-band LDR values in convective rain typically remain smaller than -25 dB at high altitudes and take somewhat larger values of -25 to -15 dB at low altitudes. The Ka-band LDR values, in contrast, typically increase with radar range, sometimes reaching a level of -3 dB just before the cross-polarized signal falls below the noise level. Such high values of LDR in Ka-band are most likely attributable to multiple scattering effects.

Iguchi, Toshio↗

Active and Passive Radiative Transfer Modeling of the Olympic Mountains Experiment

Sensor forward models are an important tool for interpreting remote sensing observations of geophysical phenomena. By implementing a three-dimensional framework, we can simulate and analyze observations from various sensors on disparate platforms. To demonstrate our model framework, we simulate observations from the Olympic Mountains Experiment (OLYMPEX). The use of cloud model simulations allows us to understand sensor response to cloud ice, falling snow, and other processes and features, and the application of model tools to observations allows us to quantify precipitation.MIIST 3D Forward ModelThe Multi-Instrument Inverse Solver Testbed(MIIST) uses the Atmospheric Radiative TransferSimulator (ARTS) for solving the vector radiativetransfer (RT) equation in up to three spatialdimensions within a spherical geometry• Gas absorptiono Line-by-line calculationso Fast transmittance tables• Hydrometeor scattering solverso Discrete ordinateo RT4 (Evans, 1D)o Radar Single Scattering (1D or 3D)o Monte Carlo (3D)Scattering TablesHigh-fidelity hydrometeor scatteringtables are necessary for accurateand consistent forward modeling ofmulti-frequency observations• Requires full Stokes matriceso And absorption vector• Randomly oriented particleso Discrete Dipole Approximationo Characteristic Basis Function Method(coming soon)• Horizontally-oriented plateso Invariant Imbedding T-matrix MethodCloud Resolving SimulationsCloud resolving simulations (e.g.,NU-WRF) supply output consistentwith ARTS needs• Atmospheric Informationo Temperatureo Pressure / heighto Water vapor• Hydrometeor Profileso ARTS architecture ripe for explicit binmicrophysics• Examples use Morrison 2M schemeThe Olympic Mountains Experiment (OLYMPEX)Validation for GPM of mid-latitudefrontal systems approaching nearcoastalmountains from the ocean• Large collection of ground-based andairborne sensorso Radarso Radiometerso In situ• Contemporaneous with RADEXo Two sets of radar at same frequenciesRadiometer Simulation (3 km NUWRF, 20151203, 15:00)2018.12.14 7Simulate 166 GHz polarizationdifference• Corresponds to the presence of aligned icecrystals• Look at trends for both simulations andobservations• Simulations can tolerate lower resolutiono Larger domainSimulations from Observations: OLYMPEXSimulate sensor response usinggeophysical retrievals as input• Single frequency radar retrievals• Multiple scattering enhancementapparent at W band• Spatially dependent phenomenonModeling Application: 1D Retrievals03 December 2015• DC-8 and ER-2 flightso Focus on APR-3 (DC-8)• Citationo Stacked microphysics legso Qualitative comparisonso Range of frozen habitso Presence of supercooledliquid cloudsResults• Retrievals match probeso Good qualitative match• Bands of increasedreflectivity correspond tolarge Dm and highaggregate fraction• Significant amounts ofsupercooled liquid water

Adams, Ian S.↗

Energy production advantage of independent subcell connection for multijunction photovoltaics

Abstract Increasing the number of subcells in a multijunction or “spectrum splitting” photovoltaic improves efficiency under the standard AM 1.5D design spectrum, but it can lower efficiency under spectra that differ from the standard if the subcells are connected electrically in series. Using atmospheric data and the SMARTS multiple scattering and absorption model, we simulated sunny day spectra over 1 year for five locations in the United States and determined the annual energy production of spectrum splitting ensembles with 2–20 subcells connected electrically in series or independently. While electrically independent subcells have a small efficiency advantage over series‐connected ensembles under the AM 1.5D design spectrum, they have a pronounced energy production advantage under realistic spectra over 1 year. Simulated energy production increased with subcell number for the electrically independent ensembles, but it peaked at 8–10 subcells for those connected in series. Electrically independent ensembles with 20 subcells produce up to 27% more energy annually than the series‐connected 20‐subcell ensemble. This energy production advantage persists when clouds are accounted for.

14 SOLAR ENERGY↗

Results of a Geant4 benchmarking study for bio‐medical applications, performed with the G4‐Med system

Geant4, a Monte Carlo Simulation Toolkit extensively used in bio-medical physics, is in continuous evolution to include newest research findings to improve its accuracy and to respond to the evolving needs of a very diverse user community. In 2014, the G4-Med benchmarking system was born from the effort of the Geant4 Medical Simulation Benchmarking Group, to benchmark and monitor the evolution of Geant4 for medical physics applications. The G4-Med system was first described in our Medical Physics Special Report published in 2021. Results of the tests were reported for Geant4 10.5. Purpose In this work, we describe the evolution of the G4-Med benchmarking system. Methods The G4-Med benchmarking suite currently includes 23 tests, which benchmark Geant4 from the calculation of basic physical quantities to the simulation of more clinically relevant set-ups. New tests concern the benchmarking of Geant4-DNA physics and chemistry components for regression testing purposes, dosimetry for brachytherapy with a 125 I source, dosimetry for external x-ray and electron FLASH radiotherapy, experimental microdosimetry for proton therapy, and in vivo PET for carbon and oxygen beams. Regression testing has been performed between Geant4 10.5 and 11.1. Finally, a simple Geant4 simulation has been developed and used to compare Geant4 EM physics constructors and physics lists in terms of execution times. Results In summary, our EM tests show that the parameters of the multiple scattering in the Geant4 EM constructor G4EmStandardPhysics_option3 in Geant4 11.1, while improving the modeling of the electron backscattering in high atomic number targets, are not adequate for dosimetry for clinical x-ray and electron beams. Therefore, these parameters have been reverted back to those of Geant4 10.5 in Geant4 11.2.1. The x-ray radiotherapy test shows significant differences in the modeling of the bremsstrahlung process, especially between G4EmPenelopePhysics and the other constructors under study (G4EmLivermorePhysics, G4EmStandardPhysics_option3, and G4EmStandardPhysics_option4). These differences will be studied in an in-depth investigation within our Group. Improvement in Geant4 11.1 has been observed for the modeling of the proton and carbon ion Bragg peak with energies of clinical interest, thanks to the adoption of ICRU90 to calculate the low energy proton stopping powers in water and of the Linhard–Sorensen ion model, available in Geant4 since version 11.0. Nuclear fragmentation tests of interest for carbon ion therapy show differences between Geant4 10.5 and 11.1 in terms of fragment yields. In particular, a higher production of boron fragments is observed with Geant4 11.1, leading to a better agreement with reference data for this fragment. Conclusions Based on the overall results of our tests, we recommend to use G4EmStandardPhysics_option4 as EM constructor and QGSP_BIC_HP with G4EmStandardPhysics_option4, for hadrontherapy applications. The Geant4-DNA physics lists report differences in modeling electron interactions in water, however, the tests have a pure regression testing purpose so no recommendation can be formulated.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Elucidating Structural Disorder in Ultra‐Thin Bi‐Rich Bismuth Oxyhalide Photocatalysts

Abstract Advancing the field of photocatalysis requires the elucidation of structural properties that underpin the photocatalytic properties of promising materials. The focus of the present study is layered, Bi‐rich bismuth oxyhalides, which are widely studied for photocatalytic applications yet poorly structurally understood, due to high levels of disorder, nano‐sized domains, and the large number of structurally similar compounds. By connecting insights from multiple scattering techniques, utilizing electron‐, X‐ray‐ and neutron probes, the crystal phase of the synthesized materials is allocated as layered Bi 24 O 31 X 10 (X = Cl, Br), albeit with significant deviation from the reported 3D crystalline model. The materials comprise anisotropic platelet‐shaped crystalline domains, exhibiting significant in‐plane ordering in two dimensions but disorder and an ultra‐thin morphology in the layer stacking direction. Increased synthesis pH tailored larger, more ordered crystalline domains, leading to longer excited state lifetimes determined via femtosecond transient absorption spectroscopy (fs‐TAS). Although this likely contributes to improved photocatalytic properties, assessed via the photooxidation of benzylamine, increasing the overall surface area facilitated the most significant improvement in photocatalytic performance. This study, therefore, enabled both phase allocation and a nuanced discussion of the structure‐property relationship for complicated, ultra‐thin photocatalysts.

Chemistry↗

Fast and Accurate Predictions of Total Energy for Solid Solution Alloys with Graph Convolutional Neural Networks

We use graph convolutional neural networks (GCNNs) to produce fast and accurate predictions of the total energy of solid solution binary alloys. GCNNs allow us to abstract the lattice structure of a solid material as a graph, whereby atoms are modeled as nodes and metallic bonds as edges. This representation naturally incorporates information about the structure of the material, thereby eliminating the need for computationally expensive data pre-processing which would be required with standard neural network (NN) approaches. We train GCNNs on ab-initio density functional theory (DFT) for copper-gold (CuAu) and iron-platinum (FePt) data that has been generated by running the LSMS-3 code, which implements a locally self-consistent multiple scattering method, on OLCF supercomputers Titan and Summit. GCNN outperforms the ab-initio DFT simulation by orders of magnitude in terms of computational time to produce the estimate of the total energy for a given atomic configuration of the lattice structure. We compare the predictive performance of GCNN models against a standard NN such as dense feedforward multi-layer perceptron (MLP) by using the root-mean-squared errors to quantify the predictive quality of the deep learning (DL) models. We find that the attainable accuracy of GCNNs is at least an order of magnitude better than that of the MLP.

Lupo Pasini, Massimiliano↗

Power-Capping Metric Evaluation for Improving Energy Efficiency in HPC Applications

With high-performance computing systems now running at exascale, optimizing power-scaling management and resource utilization has become more critical than ever. This paper explores runtime power-capping optimizations that leverage integrated CPU-GPU power management on architectures like the NVIDIA GH200 superchip. We evaluate energy-performance metrics that account for simultaneous CPU and GPU power-capping effects by using two complementary approaches: speedup-energy-delay and a Euclidean distance-based multi-objective optimization method. By targeting a mostly compute-bound exascale science application, the Locally Self-Consistent Multiple Scattering (LSMS), we explore challenging scenarios to identify potential opportunities for energy savings in exascale applications, and we recognize that even modest reductions in energy consumption can have significant overall impacts. Our results highlight how GPU task-specific dynamic power-cap adjustments combined with integrated CPU-GPU power steering can improve the energy utilization of certain GPU tasks, thereby laying the groundwork for future adaptive optimization strategies.

Patrou, Maria [ORNL] (ORCID:0000000339754638)↗

The LPM effect in sequential bremsstrahlung

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We analyze the case when the coherence lengths of two consecutive splitting processes overlap, which is important for understanding corrections to standard treatments of the LPM effect in QCD. Previous authors have analyzed this problem in the case of overlapping double bremsstrahlung where at least one of the bremsstrahlung gluons is soft. Here we show how to generalize to include the case where both splittings are hard. A number of techniques must be developed, and so in this paper we simplify by (i) restricting attention to a subset of the interference effects, which we call the “crossed” diagrams, and (ii) working in the large-N c limit. We first develop some general formulas that could in principle be implemented numerically (with substantial difficulty). To make more analytic progress, we then focus on the case of a thick, homogeneous medium and make the multiple scattering approximation (also known as the $\hat{q}$ or harmonic approximation) appropriate at high energy. Lastly, we show that the differential rate dΓ/dx dy for overlapping double bremsstrahlung of gluons with momentum fractions x and y can then be reduced to the calculation of a 1-dimensional integral, which we perform numerically.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗