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All sources NASA NTRS DOE OSTI

DOE OSTI2020

MULTI-DIMENSIONAL MODELING OF THE CFR ENGINE FOR THE INVESTIGATION OF SI NATURAL GAS COMBUSTION AND CONTROLLED END-GAS AUTOIGNITION

Engine knock and misfire are barriers to pathways leading to high-efficiency Spark-Ignited (SI) Natural Gas engines. The general tendency to knock is highly dependent on engine operating conditions and the fuel reactivity. The problem is further complicated by low emission limits and the wide range of chemical reactivity in pipeline quality natural gas. Depending on the region and the source of the natural gas, its reactivity, described by its methane number (analogous to the octane number for liquid SI fuels) can span from 65 - 95. In order to realize diesel-like efficiencies, SI natural gas engines must be designed to operate at high BMEP near knock limits over a wide range of fuel reactivity. This requires a deep understanding regarding the combustion-engine interactions pertaining to flame propagation and end-gas autoignition (EGAI). However, EGAI, if controlled, provides an opportunity to increase SI natural gas engine efficiency by increasing combustion rate and the total burned fuel, mitigating the effects of the slow flame speeds of natural gas fuels which generally reduce BMEP and increase unburned hydrocarbon emissions. For this reason, in order to study EGAI phenomenon, the present work highlights multi-dimensional computational fluid dynamics (CFD) models of the Cooperative Fuel Research (CFR) engine. The CFR engine models are used to investigate fuel-engine interactions that lead to EGAI with natural gas, including effects of fuel reactivity, engine operating parameters, and exhaust gas recirculation (EGR). A Three-Pressure Analysis, performed with GT-Power, was used to estimate initial and boundary conditions for the three-dimensional CFD model. CONVERGE CFD v2.4 was used for the three-dimensional CFD modeling where the level set G-Equation model and SAGE detailed chemical kinetics solver were used. An assessment of the different modeling approaches is also provided to evaluate their limitations, advantages and disadvantages, and for which situations they are most applicable. Model validation was performed with experimental data taken with a CFR engine over varying compression ratio, CA50, EGR fraction, and IMEP and shows good agreement in Peak Cylinder Pressure (PCP), PCP crank angle, and the location of the 10%, 50%, and 90% mass fraction burned (CA10, CA50, and CA90, respectively). The models can predict the onset crank angle and pressure rise rate for light, medium, and heavy EGAI under a variety of fuel reactivities and engine operating conditions.

Bestel, Diego↗

DOE OSTI2020

Electron transport in gaseous detectors with a Python-based Monte Carlo simulation code

Understanding electron drift and diffusion in gases and gas mixtures is a topic of central importance for the development of modern particle detection instrumentation. The industry-standard MagBoltz code has become an invaluable tool during its 20 years of development, providing capability to solve for electron transport (‘swarm’) properties based on a growing encyclopedia of built-in collision cross sections. We have made a refactorization of this code from FORTRAN into Cython, and studied a range of gas mixtures of interest in high energy and nuclear physics. The results from the new open source PyBoltz package match the outputs from the original MagBoltz code, with comparable simulation speed. An extension to the capabilities of the original code is demonstrated, in implementation of a new Modified Effective Range Theory interface. We hope that the versatility afforded by the new Python code-base will encourage continued use and development of the MagBoltz tools by the particle physics community.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Extraction and Separation of Rare-Earth Elements from Coal Fly Ash and Leachate using a Recyclable Ionic Liquid

Coal fly ash (CFA) can be a promising source for recovering rare-earth elements (REEs), as it contains a broad range of REEs with average concentrations frequently exceeding those in traditional rare earth mines. Recent research from our group has demonstrated that REEs can be preferentially extracted from CFA solids using a recyclable ionic liquid (IL), betainium bis-(trifluoromethylsulfonyl)imide ([Hbet][Tf2N]). When CFA was heated with the mixture of IL and an aqueous solution above 65°C, most leached REEs partitioned into the IL phase and were separated from the bulk elements. Subsequent acid stripping of the REE-loaded IL removed the REEs and regenerated the IL for reuse in multiple extraction cycles. This IL-based REE-CFA recovery method has been applied to ten CFA samples derived from different coal sources, including ash recovered from disposal ponds. Analysis of 34 elements confirmed the process consistently achieved high REE recovery efficiency, with strong selectivity over bulk and trace elements across diverse CFA types. In addition to the IL-solid extraction, the performance of [Hbet][Tf2N] in extracting REEs from fly-ash leachates have been evaluated by four commonly used leaching reagents, including HCl, HNO3, H2SO4, and citrate. During the IL-leachate extraction, [Hbet][Tf2N] was mixed and heated with a Class C fly ash leachate generated from each leaching reagent, followed by an acid stripping. It was observed that the partitioning and recovery of REEs increased as the leachate pH increased from 3 to 11. Among the investigated leachates, HCl and citrate proved to be the most compatible with IL extraction, exhibiting a slightly higher REE recovery and a lower non-REE co-extraction compared to the IL-solid extraction. Sc, Y, Nd, Sm, Gd, Dy, and Yb consistently showed a high recovery rate from both CFA solids and leachates. Notably, Pr, Tb, and Ho, which were not previously leached from the CFA solids, were partially recovered from the leachates. Overall, our studies revealed the strong potential of [Hbet][Tf2N] for effectively recovering REEs from leachates, highlighting its applicability as a sustainable strategy for other aqueous REE feedstocks. Furthermore, a techno-economic analysis will be performed to quantify the economic viability of the IL-based REE recovery method and guide future process improvement.

42 ENGINEERING↗

DOE OSTI2021

Measuring a Low Horizontal Hydraulic Gradient in a High Transmissivity Aquifer

Abstract High transmissivity aquifers typically have low hydraulic gradients (i.e., a flat water table). Measuring low gradients using water levels can be problematic because measurement error may be greater than the true difference in water levels (i.e., a low signal‐to‐noise ratio). In this study, the feasibility of measuring a hydraulic gradient in the range of 10 −6 to 10 −5 m/m was demonstrated. The study was performed at a site where the depth to water from land surface ranged from 40.1 to 94.2 m and the aquifer transmissivity was estimated at 41,300 m 2 /d (hydraulic conductivity of 18,800 m/d). The goals of the study were to reduce measurement error as much as practicable and assess the importance of factors affecting water level measurement accuracy. Well verticality was the largest source of error (0.000 to 0.168 m; median of 0.014 m), and geodetic survey of casing elevations was the next most important source of error (0.002 to 0.013 m; median of 0.005 m). Variability due to barometric pressure fluctuations was not an important factor at the site. Hydraulic heads were measured to an accuracy of ±0.0065 m, and the average hydraulic gradient was estimated to be 8.0 × 10 −6 (±0.9 × 10 −6 ) m/m. The improvement in accuracy allowed for two reversals in the groundwater flow direction to be identified, after which the gradient averaged 2.5 × 10 −5 (±0.4 × 10 −5 ) m/m. This study showed it is possible to sufficiently control sources of error to measure hydraulic gradients in the 10 −6 to 10 −5 m/m range.

McDonald, John P.↗

DOE OSTI2022

Boron isotopes in blue diamond record seawater-derived fluids in the lower mantle

Boron is a quintessential crustal element but its conspicuous presence in diamond – a mantle mineral – raises questions about potential subduction pathways for boron and other volatiles. It has been a long-standing goal to characterize the isotopic composition of boron in blue, boron-bearing (Type IIb) diamonds to reveal its origin. Mineral inclusions indicate that Type IIb diamonds crystallize at transition zone to lower mantle depths, meaning that if the boron is subducted it would trace a pathway of volatile elements into the deep mantle. Here, using off-line laser ablation sampling, we present the first boron isotope compositions, along with trace element contents and carbon isotope compositions, of a suite of blue diamonds mainly sourced from the Cullinan diamond mine in South Africa. The ten analyzed blue diamonds have a wide range in δ 11 B, between -9.2 ± 2‰ and -0.5 ± 2‰, compared to the more restricted range for mid-ocean ridge basalts (-7.1 ± 0.9‰). Carbon isotope values for the blue diamonds range between -20.6 and -1.8‰, with a mode at -17‰, significantly more negative than the main mantle mode at -5‰. Combined, the boron and carbon isotope compositions require fluid input from subducted oceanic lithosphere down into deep mantle source regions of blue diamonds. This finding highlights a deep subduction pathway for volatiles to stoke the source regions of deeply-derived magmas.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

The Marginal Ice Zone as a dominant source region of atmospheric mercury during central Arctic summertime

Atmospheric gaseous elemental mercury (GEM) concentrations in the Arctic exhibit a clear summertime maximum, while the origin of this peak is still a matter of debate in the community. Based on summertime observations during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition and a modeling approach, we further investigate the sources of atmospheric Hg in the central Arctic. Simulations with a generalized additive model (GAM) show that long-range transport of anthropogenic and terrestrial Hg from lower latitudes is a minor contribution (~2%), and more than 50% of the explained GEM variability is caused by oceanic evasion. A potential source contribution function (PSCF) analysis further shows that oceanic evasion is not significant throughout the ice-covered central Arctic Ocean but mainly occurs in the Marginal Ice Zone (MIZ) due to the specific environmental conditions in that region. Our results suggest that this regional process could be the leading contributor to the observed summertime GEM maximum. In the context of rapid Arctic warming and the observed increase in width of the MIZ, oceanic Hg evasion may become more significant and strengthen the role of the central Arctic Ocean as a summertime source of atmospheric Hg.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Floodplain nitrifiers harbor the genetic potential for utilizing a wide range of organic nitrogen compounds

Organic compounds such as urea and cyanate can serve as nitrogen (N) sources for nitrifying microorganisms, including ammonia-oxidizing archaea (AOA) and bacteria (AOB), complete ammonia-oxidizing (comammox) bacteria, and nitrite-oxidizing bacteria (NOB). Here we investigated metagenome-assembled genomes (MAGs) for all four nitrifier guilds generated from hydrologically variable floodplain sediments of the Wind River Basin (WRB; Riverton, WY, USA) for their genetic potential to utilize organic N compounds. A vast majority of WRB nitrifier MAGs harbored urease (ure) and at least one urea transporter ( utp, urt, dur3 ). AOA were the most abundant and phylogenetically diverse nitrifiers in WRB floodplain sediments. Several AOA MAGs encoded cyanase ( cynS ), nitrilase ( nit1 ), omega-amidase ( nit2 ), nitrile hydratase ( nthA ), and genes related to purine degradation, including biuret hydrolase ( biuH ), oxamic transcarbamylase ( allFGH ), and catabolic carbamate kinase ( allK ). AOA often encoded an uncharacterized amidohydrolase collocated with biuH , rather than allophanate hydrolase ( atzF ). A small number of AOA encoded atzF , functioning in an unknown pathway. AOB and comammox were of relatively low abundance and taxonomic diversity and were present only at certain depths in WRB; however, they encoded triuret/biuret degradation genes ( trtA, biuH , and atzH ), and in comammox, these genes were also collocated with allFGHK . The genetic potential of ammonia oxidizers in the WRB floodplain suggests that organic N may support nitrification in this system. The proposed pathways for utilizing purine degradation products other than urea potentially expand the known metabolic capabilities of AOA, AOB, and comammox bacteria and reveal the possibility for cryptic N cycling between microbial community members.

floodplain↗

DOE OSTI2023

Design Considerations for Compact High-Average Power Free-Electron Lasers/Masers at Terahertz Frequencies

Interest is increasing in high-power terahertz (THz) sources of radiation. The terminology is fluid, but researchers in the field typically refer to frequencies ranging from about 300 GHz to 10 THz as THz radiation. In this article, we present a description of design considerations for a compact, high-average power free-electron laser. At present, THz radiation is generated by a variety of mechanisms, including laser-based sources and electron-beam-based sources. Here, we provide a short description of current THz source technology to give background against which to compare the present concept; however, this should not be considered a comprehensive discussion of such technologies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Current status of anaerobic digestion of food waste in the United States

Utilization of food waste (FW) and food processing waste streams in waste-to-energy technologies has increased over the years in United States (US). This review paper compiled information from published literature and open data sources to obtain a holistic view of the current state of FW availability and its management using anaerobic digestion (AD). The review examined the usage of FW as a feedstock for AD by considering the feedstock composition and availability of FW in the US as well as challenges and opportunities with implementing FW in mono- and co-digestion. Also presented are global trends in FW digestion and the current status of FW codigestion in the US. FW in the US was characterized with regard to volume and composition to show a need for waste management and an opportunity for valuable resource recovery. Challenges and opportunities of processing via AcoD were presented to review best practices for successful operations. Environmental standards, economic incentives, and governmental policies in the US and around the world regarding waste management and utilization were discussed to identify barriers and sources of opportunity for large-scale implementation of AcoD. Additionally, a range of facilities throughout the US was examined for information regarding digestion type, feedstock (s), biogas production and utilization, and energy self-sufficiency to better understand the current status of FW digestion. Several US facilities were outlined as case studies that co-digest FW and produce and utilize biogas for various applications. Future strategies, perspectives, and roadmaps were discussed to elucidate the shaping of future FW management practices.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2023

Evaluation of Uncertainties in the Anthropogenic SO 2 Emissions in the USA from the OMI Point Source Catalog

Satellite remote sensing is a promising method of monitoring emissions that may be missing in inventories, but the accuracy of these estimates is often not clear. We demonstrate here a comprehensive evaluation of errors in anthropogenic sulfur dioxide (SO 2 ) emission estimates from NASA’s OMI point source catalog for the contiguous US by comparing emissions from the catalog with high-quality emission inventory data over different dimensions including size of individual sources, aggregate vs individual source errors, and potential bias in individual source estimates over time. For sources that are included in the catalog, we find that errors in aggregate (sum of error for all included sources) are relatively low. Errors for individual sources in any given year can be substantial, however, with over- or underestimates in terms of total error ranging from –80 to 110 kt (roughly 10–90th percentile). In this study, we find that these errors are not necessarily random over time and that there can be consistently positive or negative biases for individual sources. We did not find any overall statistical relationship between the degree of isolation of a source and bias, either at a 40 or 70 km scales. For a sub-set of sources where inventory emissions over a radius of 70 km around an OMI detection are larger than twice the emissions within 40 km, the OMI value is consistently overestimated. We find, as expected, that emission sources not included in the catalog are the largest aggregate source of difference between the satellite estimates and inventories, especially in more recent years where source emission magnitudes have been decreasing and note that trends in satellite detections do not necessarily track trends in total emissions. We find that the OMI-based SO 2 emissions are accurate in aggregate, when summed over a number of sources, but must be interpreted more cautiously at the individual source level. Similar analyses would be valuable for other satellite emission estimates; however, in many cases, the appropriate high-quality reference data may need to be generated.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Milliwatt-level UV generation using sidewall poled lithium niobate

Integrated coherent sources of ultra-violet (UV) light are essential for a wide range of applications, from ion-based quantum computing and optical clocks to gas sensing and microscopy. Recently, approaches that use frequency upconversion have received considerable attention. Among these, the integrated thin-film lithium niobate (TFLN) photonic platform shows particular promise. However, to date, the high propagation losses and lack of reliable techniques for consistent poling of cm-long waveguides with small poling periods have impeded progress. Here, we present a sidewall poled lithium niobate (SPLN) waveguide approach that overcomes these obstacles and results in a two-orders-of-magnitude increase in generated UV power. We demonstrate SPLN waveguides featuring record-low propagation losses of 2.3 dB/cm, complete domain inversion across the waveguide cross-section, and an optimum 50% duty cycle, resulting in a record-high normalized conversion efficiency of 5050%W$^{−1}$cm$^{−2}$, and 4.2 mW of generated on-chip power at 390 nm wavelength. This advancement makes the TFLN platform a viable option for high-quality on-chip UV generation, benefiting emerging applications.

Franken, C. A.A. [Harvard U.; Twente U., Enschede]↗

DOE OSTI2024

Controlling interactions between high-frequency phonons and single quantum systems using phononic crystals

The ability to control phonons in solids is key in many fields of quantum science, ranging from quantum information processing to sensing. Phonons often act as a source of noise and decoherence when solid-state quantum systems interact with the phonon bath of their host matrix. In this study, we demonstrate the ability to control the phononic local density of states of the host matrix using phononic crystals and measure its positive impact on single quantum systems. We design and fabricate diamond phononic crystals with features down to around 20 nm, resulting in a high-frequency complete phononic bandgap from 50 to 70 GHz. The engineered local density of states is probed using single silicon-vacancy colour centres embedded in the phononic crystals. We observe an 18-fold reduction in the phonon-induced orbital relaxation rate of the emitters compared to bulk, thereby demonstrating that the phononic crystal suppresses spontaneous single-phonon processes. Furthermore, we show that our approach can efficiently suppress single-phonon-emitter interactions up to 20 K, allowing the investigation of multi-phonon processes in the emitters. Our results represent an important step towards the realization of efficient phonon-emitter interfaces that can be used for quantum acoustodynamics and quantum phononic networks.

quantum information↗

DOE OSTI2025

18-membered macrocycle appended on resin for selective rare earth element extraction and separation

The rare earth elements are critically important for a wide range of modern technologies. However, obtaining them selectively and efficiently from natural sources and recycled materials is challenging and often requires harsh or wasteful conditions. Here we show that a macrocyclic chelator appended to a solid resin can overcome this challenge by acting as a robust platform for both the extraction and separation of these elements. This resin preferably captures the large rare earth elements in mixtures of these ions, giving rise to higher extraction efficiencies for them over the smaller ions. We further demonstrate that this resin can be used to separate rare earth elements. As a proof-of-principle validation, this resin was demonstrated to selectively extract rare earth elements in the presence of many different types of competing metal ions in a bioleachate solution obtained from autoslag waste, leading to their enrichment.

Coordination chemistry↗

DOE OSTI2023

Templates of expected measurement uncertainties

The covariance committee of CSEWG (Cross Section Evaluation Working Group) established templates of expected measurement uncertainties for neutron-induced total, (n,γ), neutron-induced charged-particle, and (n,xn) reaction cross sections as well as prompt fission neutron spectra, average prompt and total fission neutron multiplicities, and fission yields. Templates provide a list of what uncertainty sources are expected for each measurement type and observable, and suggest typical ranges of these uncertainties and correlations based on a survey of experimental data, associated literature, and feedback from experimenters. Information needed to faithfully include the experimental data in the nuclear-data evaluation process is also provided. These templates could assist (a) experimenters and EXFOR compilers in delivering more complete uncertainties and measurement information relevant for evaluations of new experimental data, and (b) evaluators in achieving a more comprehensive uncertainty quantification for evaluation purposes. This effort might ultimately lead to more realistic evaluated covariances for nuclear-data applications. In this topical issue, we cover the templates coming out of this CSEWG effort–typically, one observable per paper. This paper here prefaces this topical issue by introducing the concept and mathematical framework of templates, discussing potential use cases, and giving an example of how they can be applied (estimating missing experimental uncertainties of 235 U(n,f) average prompt fission neutron multiplicities), and their impact on nuclear-data evaluations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Protocols for x-ray transient grating pump/optical probe experiments at x-ray free electron lasers

Abstract Transient grating spectroscopy is a specialized application of the four-wave-mixing methodology and constitutes a versatile technique for investigating the dynamics of vibrational, magnetic and electronic degrees of freedom of matter in a background-free fashion. Recent developments in free-electron laser sources have enabled the extension of this technique into the extreme ultraviolet range. Ongoing efforts to expand transient grating spectroscopy into the x-ray regime promise numerous advantages: (1) substantial penetration depths that allow for probing bulk material properties, (2) element specificity via specific core-excited states, and (3) short wavelengths that allow for excitation gratings with higher momentum transfer and improved spatial resolution. In this study, we comprehensively outline the procedures for conducting x-ray transient grating pump/optical probe experiment. The process encompasses the design and alignment of the experimental setup, as well as the subsequent steps involved in data acquisition and analysis. This paper is intended as a comprehensive guide for researchers interested in implementing x-ray transient grating spectroscopy, providing valuable insights into the intricacies of the experimental workflow required for this novel technique. Furthermore, we discuss the potential for extending this methodology to an x-ray pump/x-ray probe scheme, envisioning a future direction that holds promise for enhancing the capabilities and scope of x-ray transient grating spectroscopy, opening new opportunities for studying ultrafast processes with unprecedented temporal and spatial resolutions.

Optics↗

DOE OSTI2024

Uncertainty in determining carbon dioxide removal potential of biochar

A quantitative and systematic assessment of uncertainty in life-cycle assessment is critical to informing sustainable development of carbon dioxide removal (CDR) technologies. Biochar is the most commonly sold form of CDR to date and it can be used in applications ranging from concrete to agricultural soil amendments. Previous analyses of biochar rely on modeled or estimated life-cycle data and suggest a cradle-to-gate range of 0.20–1.3 kg CO 2 net removal per kg of biomass feedstock, with the range reported driven by differences in energy consumption, pyrolysis temperature, and feedstock sourcing. Herein, we quantify the distribution of CDR possible for biochar production with a compositional life-cycle inventory model paired with scenario-aware Monte Carlo simulation in a 'best practice' (incorporating lower transportation distances, high pyrolysis temperatures, high energy efficiency, recapture of energy for drying and pyrolysis energy requirements, and co-generation of heat and electricity) and 'poor practice' (higher transportation distances, lower pyrolysis temperatures, low energy efficiency, natural gas for energy requirements, and no energy recovery) scenarios. In the best-practice scenario, cradle-to-gate CDR (which is representative of the upper limit of removal across the entire life cycle) is highly certain, with a median removal of 1.4 kg of CO 2 e/kg biomass and results in net removal across the entire distribution. In contrast, the poor-practice scenario results in median net emissions of 0.090 kg CO 2 e/kg biomass. Whether this scenario emits (66% likelihood) or removes (34% likelihood) carbon dioxide is highly uncertain. The emission intensity of energy inputs to the pyrolysis process and whether the bio-oil co-product is used as a chemical feedstock or combusted are critical factors impacting the net carbon dioxide emissions of biochar production, together responsible for 98% of the difference between the best- and poor-practice scenarios.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Heavy quark mass effects in charged-current deep-inelastic scattering at approximate NNLO in the Aivazis-Collins-Olness-Tung scheme

The approximate SACOT-𝜒 scheme for heavy quark production in deep-inelastic scattering was initially formulated for the neutral current structure functions 𝐹 2 and 𝐹 𝐿 . We extend this approach to the charged current case (also including 𝐹 3 ), and thereby complete the definitions for the most relevant inclusive structure functions. Furthermore, we implement these structure functions in the open-source code APFEL++ which provides fast numerical evaluations over a wide kinematic range; this addition to the APFEL++ code is publicly available, with details provided in the Appendix. This SACOT-𝜒 implementation enables detailed numerical insights on the mass dependence of the structure functions and cross sections in the (𝑥,𝑄 2 )-plane for both neutral and charged current processes. We consider kinematic regions relevant for the experimental measurements from fixed-target 𝜈⁢ DIS experiments (NuTeV, CCFR, and Chorus) and HERA, and also projections for the upcoming EIC. In particular, the 𝜈⁢ DIS experiments reveal a surprisingly strong dependence on the mass effects, offering valuable insights that may help resolve long-standing challenges in accurately describing these datasets.

Risse, P. [Westfälische Wilhelms-Universität Münst↗

DOE OSTI2021

Direct double ionization of the Ar + M shell by a single photon

Direct double ionization of the Ar + (3p –1 ) ion by a single photon is investigated both experimentally and theoretically. The photon-ion merged-beams technique was employed at the Advanced Light Source in Berkeley, USA, to measure absolute cross sections in the energy range from 60 to 150 eV. In this range, three contributions to the double ionization of Ar + are to be expected: the removal of two 3p electrons, of a 3s and a 3p electron, and of two 3s electrons. Among the possible mechanisms leading to double ionization, the TS1 (two-step one) process dominates in the near-threshold region. In TS1, a photoelectron is ejected and, on its way out, knocks out a secondary electron. Here, this two-step mechanism is treated theoretically by multiplying the calculated cross section for direct single photoionization of a given subshell with the calculated (e, 2e) ionization probability for the ejected photoelectron to knock off a secondary electron. The calculated cross section is in very good agreement with the experiment.

74 ATOMIC AND MOLECULAR PHYSICS↗