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DOE OSTI2023

Multiple-core-hole resonance spectroscopy with ultraintense X-ray pulses

Understanding the interaction of intense, femtosecond X-ray pulses with heavy atoms is crucial for gaining insights into the structure and dynamics of matter. One key aspect of nonlinear light–matter interaction was, so far, not studied systematically at free-electron lasers—its dependence on the photon energy. Here, we use resonant ion spectroscopy to map out the transient electronic structures occurring during the complex charge-up pathways of xenon. Massively hollow atoms featuring up to six simultaneous core holes determine the spectra at specific photon energies and charge states. We also illustrate how different X-ray pulse parameters, which are usually intertwined, can be partially disentangled. The extraction of resonance spectra is facilitated by the possibility of working with a constant number of photons per X-ray pulse at all photon energies and the fact that the ion yields become independent of the peak fluence beyond a saturation point. Our study lays the groundwork for spectroscopic investigations of transient atomic species in exotic, multiple-core-hole states that have not been explored previously.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2026

Understanding spectral dependance of laser-induced damage precursors in dielectric materials (Abbreviated report_23-ERD-006)

High peak and average power laser systems are typically limited by the handling fluence of the optical components. In particular, the multilayer dielectric coatings are known to be much lower operational fluence than the more ideal bulk materials. In this project we proposed and succeeded in probing different established classes of damage prone precursors at different wavelengths to understand their fundamental laser damage response as a function of wavelength. This study helped to shed light on the fundamental physics of the non-linear precursors that govern laser damage phenomena for ns-regime pulsed laser damage. In this study, we utilized the onsite coating capabilities (VPL, IBS coating lab) to purposefully generate laser damage-prone precursors in hafnia-based coatings (both single and multi-layer coatings). Specifically, we engineered coatings with craze lines initiated by nodules, generated coatings with our xenon-based coating process to suppress nanobubble formation and generated hafnia coatings under controlled oxygen flow conditions to study hafnia sub-oxides and oxygen flow dependance. In these studies we found that craze lines are rife with precursors that are sensitive to ultra-violet light but not to infrared light; we found that the removal of nanobubbles helps with all wavelengths tested, but is most impactful for ultra-violet light; we also found that ultra-violet laser damage performance of hafnia is closely matched to oxygen flow rate, while the infrared performance may be slightly better at lower flow rates. During this LDRD we also successfully stood up a new laser damage testing capability, namely a wavelength agile damage test station to study the spectral response of known laser-induced damage precursors. This is a unique and important capability for Lawrence Livermore National Lab, allowing us to understand the spectral response of materials under high intensity irradiation and damage. This is a vital tool to understand non-linear optical response at wavelengths that we have previously been unable to test at.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Measurement of the liquid argon scintillation pulse shape using differentiable simulation in the coherent CAPTAIN-Mills experiment

The coherent CAPTAIN-Mills (CCM) experiment is a liquid argon (LAr) light collection detector searching for MeV-scale neutrino and beyond Standard Model physics signatures. Two hundred eight-inch photomultiplier tubes instrument the seven-ton fiducial volume with 50% photocathode coverage to detect light produced by charged particles. CCM’s light-based approach reduces requirements of LAr purity, compared to other detection technologies, such that sub-MeV particles can be reliably detected without additional LAr filtration and with 𝒪⁡(1) parts per million of common contaminants. We present a measurement of LAr light production and propagation parameters, with uncertainties, obtained from a sample of MeV-scale electromagnetic events. The optimization of this high-dimensional parameter space was facilitated by a differentiable optical photon Monte Carlo simulation and detailed photomultiplier tube response characterization. This result accurately predicts the timing and spatial distribution of light due to scintillation and Cherenkov emission in the detector. This is the first description of photon propagation in LAr to include several effects, including anomalous dispersion of the index of refraction near the ultraviolet resonance, Mie scattering from impurities, and Cherenkov light production.

Cherenkov detectors↗

DOE OSTI2020

A phenomenological rate of injection model for predicting fuel injection with application to mixture formation in light-duty diesel engines

Fuel injection rate laws are one of the most important pieces of information needed when modeling engine combustion with computational fluid dynamics. In this study, a simple phenomenological model of a common-rail injector was developed and calibrated for the Bosch CRI2.2 platform. The model requires three tunable parameter fits, making it relatively easy to calibrate and suitable for injector modeling when high-fidelity information about the internal injector’s geometry and electrical circuit details are not available. Each injection pulse is modeled as a sequence of up to four stages: an injection needle mechanical opening transient, a full-lift viscous flow inertial transient, a Bernoulli steady-state stage, and a needle descent transient. Parameters for each stage are obtained as polynomial fits from measured injection rate properties. The model enforces total injected mass, and the intermediate stages are only introduced if the injection pulse duration is long enough. Experimental rates of injection from two separate campaigns on the same injector were used to calibrate the model. The model was first validated against measured injection rate laws featuring pilot injections, short partially premixed combustion pulses, and conventional diesel combustion injection strategies. Then, it was employed as an input to engine computational fluid dynamics simulations, which were run to simulate experiments of mixture formation in an optically accessible light-duty diesel engine. It was found that, though simple, this model is capable of predicting both pilot and main injection pulse mass flow rates well: the simulations yielded accurate predictions of in-cylinder equivalence ratio distributions from injection strategies for both partially premixed combustion and pilot injections. Also, once calibrated, the model produced appropriate results for a wide range of injected mass and rail pressure values. Finally, it was observed that usage of such a relatively simple model can be a good choice when high-fidelity injection rate input and highly detailed information of the injector’s geometry and operation are not available, particularly as noticeable discrepancies can be present also among different experimental campaigns on similar hardware.

42 ENGINEERING↗

DOE OSTI2024

Filament-induced breakdown spectroscopy of solids through highly scattering media

Ultrafast laser pulse filamentation in the air can be used for remote sensing by exciting a characteristic optical emission, which is usually referred to as filamentation-induced breakdown spectroscopy. In environments that impede light propagation, such as fog, haze, or clouds, scattering makes it challenging to propagate laser beams and retrieve generated optical signatures. We demonstrate the effectiveness of laser filamentation for simultaneously clearing the path for intense femtosecond pulse propagation in a highly scattering medium, generation of luminous plasma on a solid target, and counter-propagation of a characteristic spectroscopic signal over a cleared channel along the filament path. In a dense cloud, the counter-propagating signal predominantly transits the cleared on-axis path but is highly affected by the negative thermal lensing of a Gaussian beam. Furthermore, these insights enhance our understanding of laser filamentation in atmospheric sensing and could substantially improve remote detection capabilities in poor visibility conditions.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Uranium Single Particle Analysis for Simultaneous Fluorine and Uranium Isotopic Determinations via Laser-Induced Breakdown Spectroscopy/Laser Ablation–Multicollector–Inductively Coupled Plasma–Mass Spectrometry

Uranyl fluoride (UO 2 F 2 ) particles (<20 μm) were subjected to first-of-its-kind analysis via simultaneous laser-induced breakdown spectroscopy (LIBS) and laser ablation multi-collector inductively coupled plasma–mass spectrometry (LA–MC–ICP–MS). Briefly, a nanosecond pulsed high-energy laser was focused onto the sample (particle) surface. In a single laser pulse, the UO 2 F 2 particle was excited/ionized within the microplasma volume, and the emission of light was collected via fiber optics such that emission spectroscopy could be employed for the detection of uranium (U) and fluorine (F). The ablated particle was simultaneously transported into the MC–ICP–MS for high precision isotopic (i.e., 234 U, 235 U, and 238 U) analysis. This method, LIBS/LA–MC–ICP–MS was optimized and employed to rapidly measure 80+ UO 2 F 2 particles, which were subjected to different calcination processes, which results in varying degrees of F loss from the individual particles. In measuring the particles, the average F/U ratios for the populations treated at 100 and 500 °C were 2.78 ± 1.28 and 1.01 ± 0.50, respectively, confirming loss of F through the calcination process. The average 235 U/ 238 U on the particle populations for the 100 and 500 °C were 0.007262 (22) and 0.007231 (23), which was determined to be <0.2% from the expected value. The 234 U/ 238 U ratios on the same particles were 0.000053 (11) and 0.000050 (10) for the 100 and 500 °C, respectively, <10% from the expected value. Notably, each population was analyzed in under 5 min, demonstrating the truly rapid analysis technique presented here in this paper.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2021

Holes in Optical Lightning Flashes: Identifying Poorly Transmissive Clouds in Lightning Imager Data

Space-based optical lightning sensors including the lightning imaging sensor (LIS) and geostationary lightning mapper (GLM) are pixelated imagers that detect lightning as transient increases in cloud top illumination. Detection requires optical emissions to escape the cloud top to space with sufficient energy to trigger a pixel on the imaging array. Through scattering and absorption, certain clouds are able to block most light from reaching the instrument, causing a reduction in detection efficiency (DE) and possibly location accuracy (LA). Radiant lightning emissions that illuminate large cloud top areas are used to examine scenarios where clouds block light from reaching orbit. In some cases, these anomalies in the spatial radiance distribution from the lightning pulse lead to “holes” in the optical lightning flash where certain pixels fail to trigger. Such holes are identified algorithmically in the Tropical Rainfall Measuring Mission satellite LIS record and the microphysical properties of the coincident storm region are queried. We find that holes primarily occur in tall (IR T b < 235 K) convection (87%) and overhanging anvil clouds (10%). The remaining 3% of holes occur in moderate-to-weak convection or in clear air breaks between stormclouds. We further demonstrate how an algorithm that assesses the spatial radiance patterns from energetic lightning pulses might be used to construct an optical transmission gridded stoplight product for GLM that could help operators identify clouds with a potentially reduced DE and LA.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Octave-spanning mid-infrared femtosecond OPA in a ZnGeP 2 pumped by a 2.4 μm Cr:ZnSe chirped-pulse amplifier

We report on the highly efficient, octave-spanning mid-infrared (mid-IR) optical parametric amplification (OPA) in a ZnGeP 2 (ZGP) crystal, pumped by a 1 kHz, 2.4 μm, 250 fs Cr:ZnSe chirped-pulse amplifier. The full spectral coverage of 3−10 μm with the amplified signal and idler beams is demonstrated. The signal beam in the range of ∼3 − 5 μm is produced by either white light generation (WLG) in YAG or optical parametric generation (OPG) in ZGP using the common 2.4 μm pump laser. We demonstrate the pump to signal and idler combined conversion efficiency of 23% and the pulse energy of up to 130 μJ with ∼2 μJ OPG seeding, while we obtain the efficiency of 10% and the pulse energy of 55 μJ with ∼0.2 μJ WLG seeding. The OPA output energy is limited by the available pump pulse energy (0.55 mJ at ZGP crystal) and therefore further energy scaling is feasible with multi-stage OPA and higher pump pulse energy. The autocorrelation measurements based on random quasi-phase matching show that the signal pulse durations are ∼318 fs and ∼330 fs with WLG and OPG seeding, respectively. In addition, we show the spectrally filtered 30 μJ OPA output at 4.15 μm suitable for seeding a Fe:ZnSe amplifier. Our ultrabroadband femtosecond mid-IR source is attractive for various applications, such as strong-field interactions, dielectric laser electron acceleration, molecular spectroscopy, and medical surgery.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

HIGHER EFFICIENCY FISSION COUNTER FOR NEUTRON DETECTION

Fission chambers containing 235U have been used for detection of neutrons for many decades. In these chambers 235U is electroplated on a metal which is one plate of an ionization chamber. Since the range of fission products from induced fission in the chamber is extremely short, these deposits from electroplating are so thin that the amount of 235U results in low neutron detection efficiency and the chamber needs high internal 235U surface area to increase efficiency. A typical ~8 in. long, ~2 in. diameter fission counter only contains < 2 g of 235U total, resulting in very low detection efficiency per incident neutron impinging on the outer surface of the detector. However, because of their large electronic pulses from fission products compared to gamma rays it is very easy to discriminate against gamma rays impinging on the detector. These types of chambers are produced commercially and are used worldwide in nuclear research and nuclear power reactors. ORNL has made a higher efficiency fission ionization chamber by using many thin concentric annuli to increase the area. A higher efficiency fission counter would be useful and can be made by incorporating 235U into a glass or ceramic scintillator. For nearly 100 years the green color in antique glass was produced by incorporation of depleted uranium (up to 20 wt. %) into a glass. The concept for this scintillation-optical-based fission detector is to dope a scintillator (either ceramic or glass) with 235U. Glass scintillators are commercially available doped with as much as 8 wt. % 6Li for neutron detection. In the 235U doped scintillator the fission product pulses would be double the size of those in an ion chamber since all fission products produce light in the scintillator whereas in the ionization chamber half do not go into the ionizing gas volume. These higher efficiency fission chambers would be very useful for a wide variety of research, nuclear research, and nuclear power reactor applications. Because of their smaller size and weight, they should be useful for space application such as monitoring of space nuclear power reactors. This report reviews existing fission chamber technology and suggests the development of these small high-efficiency fission chambers. Other fission isotopes could be used for other research applications.

Mihalczo, John [ORNL] (ORCID:0000000254292681)↗

DOE OSTI2022

Towards a Counting Point Detector for Nanosecond Coherent X-ray Science

We present the technical realization of a high-speed hard X-ray single-photon counting-detection scheme based on a commercial avalanche silicon photodiode and high-speed oscilloscope. The development is motivated by the need to perform pulse-resolved photon-correlation and pump-probe studies at synchrotron sources with densely packed pulse patterns that result in high repetition rate pulses on the order of hundreds of MHz. Commissioning experiments are performed at the 1C PAL-KRISS beamline at PLS-II of South Korea operating at a burst mode maximum repetition rate of 500 MHz. In such a high count-rate measurement, detector dead-time can lead to a distortion of counting statistics. We are able to model the counting behavior of our detector under these conditions with a detector dead-time comparable to time between X-ray pulses, implying that nanosecond X-ray photon correlation spectroscopy should be possible at diffraction-limited light sources.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Characterization of the upgraded single-line-of-sight time-resolved x-ray imager using short-pulse visible and UV lasers

The single-line-of-sight time-resolved x-ray imager (SLOS-TRXI), a fast-gated x-ray imager used for capturing x-ray self-emission in inertial confinement fusion experiments on OMEGA, has been upgraded and characterized. SLOS-TRXI combines an electron-dilation imager and a hybrid complementary metal–oxide–semiconductor (hCMOS) sensor to capture multiple gated frames on a single line of sight with a temporal resolution of ~40 ps and a spatial resolution of 10 µm. The original hCMOS sensor with four frames was replaced with a newer-generation hCMOS sensor having eight frames. Gate characterizations of both the sensor and the entire SLOS-TRXI diagnostic were performed using ~10-ps FWHM visible (2ω) and UV (4ω) short-pulse lasers, respectively. A stepped echelon was used to generate a train of five UV laser pulses having an interpulse separation of 30 ± 3 ps. Characterization results of the hCMOS gating (2.28 ± 0.02-ns FWHM on average) and a temporal resolution of the upgraded SLOS-TRXI (34 ± 4-ps FWHM on average) are presented. A temporal magnification for the electron-dilation imager between 40 and 60 was inferred from the characterization results. Furthermore, the spatial resolution of the upgraded SLOS-TRXI remains the same in light of this work.

47 OTHER INSTRUMENTATION↗

DOE OSTI2026

Pursuing Heteroleptic Ligand Design Principles for Photoactive Fe Complexes with Ultrafast X-ray Emission and Variable-Temperature Optical Spectroscopies

Understanding the key parameters that govern the photophysical and photochemical properties of transition metal complexes is essential for the development of efficient photosensitizers for photocatalytic applications. Achieving this objective necessitates clear and detailed investigations of their electronic excited states, for which time-resolved metal Kβ X-ray emission spectroscopy (XES) has proven highly effective. Here, we present a time-resolved Fe Kβ XES study of a heteroleptic Fe(II) polypyridyl carbene complex, [Fe(phen) 2 (C 4 H 10 N 4 )] 2+ (1; phen = 1,10-phenanthroline), utilizing both the valence-to-core and Kβ mainline spectral regions, complemented by variable-temperature transient optical absorption (VT-TA) spectroscopy. Detailed analysis of the time-resolved Kβ XES data, supported by density functional theory (DFT) calculations and an Eyring analysis of the VT-TA data, reveals parallel excited state relaxation dynamics that support an assignment of the long-lived excited state to a triplet metal-centered state. Placing these results in the context of prior studies of heteroleptic Fe(II) polypyridyl cyanide complexes motivated a series of DFT calculations to investigate the effects of ligand structural flexibility and arrangement. These calculations reinforce the experimentally derived conclusion that constraining structural flexibility with multidentate ligands significantly impacts the excited state relaxation dynamics. Furthermore, our study emphasizes that the arrangement of strong field ligands in heteroleptic complexes substantially affects the energy of Jahn–Teller active triplet metal-centered states in low-spin d 6 metal complexes. Together, these findings provide synthetic design principles for extending metal-to-ligand charge transfer excited state lifetimes of heteroleptic Fe complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Machine-Learned Force Field for Molecular Dynamics Simulations of Nonequilibrium Ammonia Synthesis on Iron Catalysts

Ammonia (NH 3 ) is one of the most important industrial chemicals. The conventional NH 3 synthesis method-the Haber–Bosch process-converts atmospheric nitrogen (N 2 ) into NH 3 using H 2 with an iron (Fe) catalyst. However, this process requires high pressures (100–200 atm) and temperatures (700–800 K) near thermal equilibrium. Recently, Fe-based nanocatalysts have been reported to produce promising NH 3 yields under atmospheric pressures and temperature-modulated nonequilibrium conditions. Understanding the mechanism of nonequilibrium catalysis with programmed temperature variation could help to optimize this fully electrified and less energy-intensive process. Although reactive molecular dynamics (RMD) simulations can be a useful tool to model nonequilibrium catalytic processes, they require the development of accurate force fields (i.e., interatomic potentials). Here, we present a machine-learned (ML) force field within the Deep Potential MD (DPMD) framework, trained using periodic density functional theory (DFT) calculations, to model NH 3 synthesis on Fe catalysts with various surface adsorbates such as *N, *H, *N 2 , *H 2 , *NH, *NH 2 , and *NH 3 . Here, we generated the DFT data from static models of elementary reactions on the most stable (110) surface of body-centered cubic Fe, which then were augmented by data from constant number of particles–volume–temperature (NVT) DFT-MD trajectories at various temperatures. Finally, we utilized the fully optimized ML force field to investigate reaction dynamics at an Fe(110) surface at linearly increasing temperatures using NVT-DPMD simulations. Our simulations indicate that pulsed temperature ramping could prove favorable for NH3 synthesis. For example, we conducted ramping under multiple sets of conditions: (i) from 900 to 1200 K over periods of 0.1–0.3 ns for Fe surfaces precovered with N or NH along with H; and (ii) from 300 to 600 K over 0.1–0.3 ns for Fe surfaces precovered with NH 3 . While our simulations so far are limited to short time scales (very rapid heating), these observations shed light on the mechanism of the high NH 3 synthesis rate achieved in a novel temperature-modulated nonequilibrium catalytic reactor using pulsed heating and cooling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Sub-melt nanosecond pulsed-laser induced densification and strain-field relaxation in single-crystal diamond

Dislocations and polishing-induced defect networks in synthetic diamond introduce local strain fields and broaden Raman features, limiting performance in optical, thermal, and electronic applications. Laser annealing is emerging as a promising approach to repair surface and near-surface defects in diamond without entering the melt regime, yet surface densification, defect-state modification, and associated structural changes have not been well quantified. In this work, we show that sub-melt nanosecond pulsed-laser annealing (PLA) induces near-surface densification and defect-mediated strain relaxation in single-crystal Chemical Vapor Deposition (CVD) diamond. Single- and two-pulse PLA were applied, and structural evolution was quantified using co-registered ISO 25,178 white-light interferometry, depth-resolved Raman spectroscopy, and cross-sectional STEM with geometric phase analysis (GPA). Across a 5 × 6 grid (n = 30), responsive regions exhibit large reductions in local slope (Sdq 45–65%), developed area (Sdr 60–90%), height spread (Sp, Sz 30–65%), void volume (Vv 57–60%), and roughness amplitude (Sa, Sq 48–57%), consistent with densification of ∼4–6.5 nm. Raman profiling shows narrowing of the diamond line and improved spectral uniformity to depths of ∼2–3 μm. Given that the Raman probing depth significantly exceeds the densified layer thickness, this response is interpreted as consistent with long-range strain-field redistribution originating from the near-surface region. STEM-GPA strain maps further support this interpretation, showing smoother strain fields, suppressed hotspots, and redistribution of localized strain concentrations following PLA. These results are consistent with defect-mediated strain relaxation and densification-driven modification of the near-surface energy state. The approach provides a scalable pathway for improving near-surface structural quality in diamond relevant to electronic, photonic, and quantum applications.

Areal surface metrology (ISO 25,178)↗

DOE OSTI2022

The time-resolved atomic, molecular and optical science instrument at the Linac Coherent Light Source

The newly constructed time-resolved atomic, molecular and optical science instrument (TMO) is configured to take full advantage of both linear accelerators at SLAC National Accelerator Laboratory, the copper accelerator operating at a repetition rate of 120 Hz providing high per-pulse energy as well as the superconducting accelerator operating at a repetition rate of about 1 MHz providing high average intensity. Both accelerators power a soft X-ray free-electron laser with the new variable-gap undulator section. With this flexible light source, TMO supports many experimental techniques not previously available at LCLS and will have two X-ray beam focus spots in line. Thereby, TMO supports atomic, molecular and optical, strong-field and nonlinear science and will also host a designated new dynamic reaction microscope with a sub-micrometer X-ray focus spot. The flexible instrument design is optimized for studying ultrafast electronic and molecular phenomena and can take full advantage of the sub-femtosecond soft X-ray pulse generation program.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Terawatt attosecond x-ray source driven by a plasma accelerator

Plasma accelerators can generate ultra-high-brightness electron beams that open the door to light sources with a smaller physical footprint and properties un-achievable with conventional accelerator technology. In this paper, we show that electron beams from Plasma WakeField Accelerators can generate few-cycle coherent tunable soft x-ray pulses with TW peak power and a duration of tens of attoseconds, an order of magnitude more powerful, shorter, and with better stability than state-of-the-art X-ray Free Electron Lasers (XFELs). Such a light source would significantly enhance the ability to experimentally investigate electron dynamics on ultrafast timescales, having a broad-ranging impact across multiple scientific fields. Rather than starting from noise as in typical XFELs, the x-ray emission in this approach is driven by coherent radiation from a pre-bunched, high peak current electron beam of attosecond duration. This relaxes the restrictive tolerances that have hindered progress toward utilizing plasma accelerators as coherent x-ray drivers thus far, presenting a new paradigm for advanced accelerator light source applications.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

Generation of a quasi-static magnetic field by a circularly polarised laser pulse due to tunnelling gas ionisation

We present a theoretical model of the quasi-static magnetic field generation in a laser channel, which is formed behind the front of a short laser pulse that ionises a gas. The generation of a magnetic field is caused by the appearance of the electron pressure anisotropy during tunnelling ionisation of atoms. In the considered case of subrelativistic laser light intensities, the generated magnetic field can reach ∼1 MG with an energy transformation ratio of about 1 %, which paves the way for identifying the proposed mechanism when use is made of a wide class of ultrashort pulse lasers. (interaction of laser radiation with matter. laser plasma)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Photon scattering by a 4π -spherically-focused ultrastrong electromagnetic wave

The scattering of high-power probe laser pulses by tightly focused ultrastrong laser pulses has been investigated through a semiclassical approach using a perturbative method based on the Born approximation. Under a 4π-spherically-focused ultrastrong light field, the electric permittivity and magnetic permeability tensors for vacuum are calculated from the Euler-Heisenberg Lagrangian to show the nonlinear birefringent property of vacuum. And, from permittivity and permeability tensors, the scattering potential is derived for the Born approximation. The first-order solution of the Born approximation is taken as an electric field scattered from the 4π-spherically-focused laser pulse when a probe laser pulse propagates through the focused laser field. The differential cross section of the nonlinear birefringent vacuum is derived, and the number of photons scattered from the nonlinear birefringent vacuum is analyzed in the laser power range of 10-1000 PW.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗