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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.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Constraining the nuclear spin distribution using improved 197 Au neutron resonance parameters

New neutron transmission data at resonance energies using a 197 Au sample were measured using an early version of the Device for Indirect Capture Experiments on Radionuclides (DICER), which is under development at the Los Alamos Neutron Science Center (LANSCE). These data were combined with previous neutron transmission and capture data in a simultaneous R-matrix analysis to extract improved neutron resonance parameters for this nuclide. As a result, total radiation widths, Γ γ , were obtained for 33 J=1 and 44 J=2 197 Au+n resonances. Γ γ distributions for these two spins states were compared to distributions calculated according to the nuclear statistical model using published nuclear level density (NLD) and photon strength functions (PSF) measured using the Oslo technique. The calculated distributions were found to be narrower and the average values for the two spins states closer together than the data. The calculation can be brought into agreement with the data by substantial modifications to the spin distribution in 198 Au as a function of excitation energy. As far as we know, the spin distribution currently is otherwise poorly constrained. The modified spin distribution changes the shapes of the NLD and PSF extracted using the Oslo technique and so could have broad implications.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Aerosol–climate interactions in the Norwegian Earth System Model – NorESM1-M

The objective of this study is to document and evaluate recent changes and updates to the module for aerosols and aerosol–cloud–radiation interactions in the atmospheric module CAM4-Oslo of the core version of the Norwegian Earth System Model (NorESM), NorESM1-M. Particular attention is paid to the role of natural organics, sea salt, and mineral dust in determining the gross aerosol properties as well as the anthropogenic contribution to these properties and the associated direct and indirect radiative forcing. The aerosol module is extended from earlier versions that have been published, and includes life-cycling of sea salt, mineral dust, particulate sulphate, black carbon, and primary and secondary organics. The impacts of most of the numerous changes since previous versions are thoroughly explored by sensitivity experiments. The most important changes are: modified prognostic sea salt emissions; updated treatment of precipitation scavenging and gravitational settling; inclusion of biogenic primary organics and methane sulphonic acid (MSA) from oceans; almost doubled production of land-based biogenic secondary organic aerosols (SOA); and increased ratio of organic matter to organic carbon (OM/OC) for biomass burning aerosols from 1.4 to 2.6. Compared with in situ measurements and remotely sensed data, the new treatments of sea salt and dust aerosols give smaller biases in near-surface mass concentrations and aerosol optical depth than in the earlier model version. The model biases for mass concentrations are approximately unchanged for sulphate and BC. The enhanced levels of modeled OM yield improved overall statistics, even though OM is still underestimated in Europe and overestimated in North America. The global anthropogenic aerosol direct radiative forcing (DRF) at the top of the atmosphere has changed from a small positive value to -0.08 W m-2 in CAM4-Oslo. The sensitivity tests suggest that this change can be attributed to the new treatment of biomass burning aerosols and gravitational settling. Although it has not been a goal in this study, the new DRF estimate is closer both to the median model estimate from the AeroCom intercomparison and the best estimate in IPCC AR4. Estimated DRF at the ground surface has increased by ca. 60%, to -1.89 W m-2. We show that this can be explained by new emission data and omitted mixing of constituents between updrafts and downdrafts in convective clouds. The increased abundance of natural OM and the introduction of a cloud droplet spectral dispersion formulation are the most important contributions to a considerably decreased estimate of the indirect radiative forcing (IndRF). The IndRF is also found to be sensitive to assumptions about the coating of insoluble aerosols by sulphate and OM. The IndRF of -1.2 W m-2, which is closer to the IPCC AR4 estimates than the previous estimate of -1.9 W m-2, has thus been obtained without imposing unrealistic artificial lower bounds on cloud droplet number concentrations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Experimentally Constrained (\(n,\gamma \)) Reaction Rates Relevant to r- and i-Process Nucleosynthesis

The element distribution that we observe in the Universe today, tells a fascinating story of nucleosynthesis events that have taken place throughout the 13.7-billion-years-long history starting with the Big Bang. It is known for a long time that radiative neutron-capture reactions play a major role in synthesizing elements heavier than iron. However, many questions remain when it comes to our understanding of neutron-capture processes in extreme stellar environments. In particular, the intermediate and rapid neutron-capture processes are very challenging to describe, as there exist little or no data on the much-needed neutron-capture rates. In this work we discuss possibilities to obtain indirect, experimental constrains on these rates by means of the Oslo and the β-Oslo methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1973

Evaluation of data utility for earth sciences from methodical point of view

The author has identified the following signficant results. A very distinct line representing the Ra-substage of the last deglaciation period is observable around the outer parts of the Oslo fjord. The moraine line is also traceable in some parts of the forest district on the Swedish side of the border forming part of the Central Swedish End Moraines. In the area of Lake Vanern to the southeast, the line is then again more distinct, partly due to the cultivation pattern. Outside the Central Swedish Moraine Line and nearer to the coast another not so distinct moraine line could be observed running NNW-SSE. This line crosses the coastline before reaching the Oslo fjord. Probably the moraine deposits on some outer islands in the fjord constitute part of this older moraine line. The study will be extended to districts of southern Sweden, where old moraine lines of the last deglaciation period are incompletely mapped.

Svensson, H.↗
NASA NTRS1990

An aircraft noise study in Norway

An extensive study of aircraft noise is currently being conducted in Oslo, Norway. The traffic at Oslo Airport Fornebu that includes both national and international flights, totals approximately 350 movements per day: 250 of these are regular scheduled flights with intermediate and large size aircraft, the bulk being DC9 and Boeing 737. The total traffic during the summer of 1989 was expected to resemble the maximum level to which the regular traffic will increase before the new airport can be put into operation. The situation therefore represented a possibility to study the noise impact on the communities around Fornebu. A comprehensive social survey was designed, including questions on both aircraft and road traffic noise. A random sample of 1650 respondents in 15 study areas were contacted for an interview. These areas represent different noise levels and different locations relative to the flight paths. The interviews were conducted in a 2 week period just prior to the transfer of charter traffic from Gardemoen to Fornebu. In the same period the aircraft noise was monitored in all 15 areas. In addition the airport is equipped with a permanent flight track and noise monitoring system. The noise situation both in the study period and on an average basis can therefore be accurately described. In August a group of 1800 new respondents were subjected to identical interviews in the same 15 areas, and the noise measurement program was repeated. Results of the study are discussed.

Gjestland, Truls T.↗
NASA NTRS1994

TOMS total ozone data compared with northern latitude Dobson ground stations

Ozone measurements from the Total Ozone Mapping Spectrometer on the Nimbus 7 satellite are compared with ground-based measurements from five Dobson stations at northern latitudes to evaluate the accuracy of the TOMS data, particularly in regions north of 50 deg N. The measurements from the individual stations show mean differences from -2.5 percent up to plus 8.3 percent relative to TOMS measurements and two of the ground stations, Oslo and Longyearbyen, show a significant drift of plus 1.2 percent and plus 3.7 percent per year, respectively. It can be shown from nearly simultaneous measurements in two different wavelength double pairs at Oslo that at least 2 percent of the differences result from the use of the CC' wavelength double pair instead of the standard AD wavelength double pair. Since all Norwegian stations used the CC' wavelength double pair exclusively a similar error can be assumed for Tromso and Longyearbyren. A comparison between the tropospheric ozone content in TOMS data and from ECC ozonesonde measurements at Ny-Alesund and Bear Island shows that the amount of tropospheric ozone in the standard profiles used in the TOMS algorithm is too low, which leads to an error of about 2 percent in total ozone. Particularly at high solar zenith angles (greater than 80 deg), Dobson measurements become unreliable. They are up to 20 percent lower than TOMS measurements averaged over solar zenith angles of 88 deg to 89 deg.

Heese, B.↗
DOE OSTI2024

DICER: A new instrument at LANSCE to constrain neutron capture rates on radionuclides

. With very few exceptions, direct measurements of neutron capture rates on radionuclides have not been possible. A number of indirect methods have been pursued such as the surrogate method, the γ-ray strength function method, the Oslo method and the β-Oslo method. Substantial effort has been devoted to quantify the usually large systematic errors that accompany the results from these techniques. A new instrument has been developed at the Los Alamos Neutron Science Center (LANSCE) to provide more accu rate data on several radionuclides relevant to nuclear criticality safety, radiochemical diagnostics, astrophysics, nuclear forensics and nuclear security, by measuring the transmission of neutrons through radioactive samples and studying resonance properties. The Device for Indirect Capture on Radionuclides (DICER) and as sociated radionuclide production at the Isotope Production Facility (IPF), both at LANSCE, as well radioactive sample fabrication, have been under development the last few years. A description of the new apparatus, data on a few mid-weight stable isotopes and efforts on radionuclide measurements will be presented.

Nuclear Criticality Safety Program (NCSP)↗
DOE OSTI2025

Influence of Phase-Change Materials and Operating Periods on Load Shifting for Thermal Storage Heat Pumps in European Climate Zones

As the reliance on heat pumps (HPs) for space conditioning increases worldwide, ex-tensive grid strains during utility peak hours are expected. Significant research efforts focus on investigating the use of integrated thermal energy storage (TES) systems to reduce peak energy demands. Conventionally, TES systems are often integrated to store and provide either cooling or heating, but not both. In this work, a single room-temperature phase-change material (PCM)-TES was integrated for dual-mode opera-tion with an R290 air-to-water 10.5 kW (3-Ton) HP. Two PCM melting temperatures (17°C, 22°C) were assessed to investigate their impact on system performance and cost reductions for Milan, Italy (4A); Barcelona, Spain (3A); and Oslo, Norway (6A). HP and HP-TES performance maps were generated using Modelica-based transient models and co-simulated with a prototype residential building using the Spawn of En-ergyPlusTM with simple rule-based controls. Our simulations indicate that PCM-17°C provided annual cost savings at higher peak-to-off-peak cost ratios, as the demand re-duction dominated the savings potential. The recharge energy costs and requirements became more dominant at lower cost ratios, making PCM-22°C more beneficial at lower cost ratios. Finally, despite Oslo's heating-dominated climate, the utility peak hours favor cooling demand reductions, making PCM-17°C more appealing. In all cases, the cost savings potential stabilized between 4 – 10% regardless of cost ratio, suggesting that system-level component and operation control optimization is required to maximize cost savings further.

25 ENERGY STORAGE↗
DOE OSTI2025

Probing the limits of statistical neutron capture for the r process: Experimental constraints on 141 Cs nuclear level densities

The r-process abundance peaks, particularly near mass number A ∼ 130, reflect underlying nuclear structure effects such as closed neutron shells, yet modeling the nucleosynthesis in this region remains hindered by uncertain neutron-capture rates. These rates are especially sensitive to nuclear level densities (NLDs) and γ-ray strength functions of neutron-rich nuclei, where experimental data are scarce. We present the first experimental constraint on the NLD of 141 Cs using the β-Oslo method, extending sensitivity to the neutron-rich regime near the N = 82 closed shell. Our data allow for critical calibration of microscopic NLD models and reveal that 141 Cs lies near the limit of statistical model applicability. Using this experimental input, we evaluate radiative neutron-capture rates across neighboring isotones using both Hauser–Feshbach (HF) and High Fidelity Resonance (HFR) models. Our results show order-of-magnitude rate increases for nuclei along the N = 86 line, signaling a transition to resonance-dominated capture in this region. These findings underscore the importance of constraining NLDs to improve r-process reaction network predictions, particularly in environments where the validity of statistical models breaks down.

Nuclear level density↗
DOE OSTI2020

Covalent Graphene-MOF Hybrids for High-Performance Asymmetric Supercapacitors

In this work, the covalent attachment of an amine functionalized metal-organic framework (UiO-66-NH 2 = Zr 6 O 4 (OH) 4 (bdc-NH 2 ) 6 ; bdc-NH 2 = 2-amino-1,4-benzenedicarboxylate) (UiO-Universitetet i Oslo) to the basal-plane of carboxylate functionalized graphene (graphene acid = GA) via amide bonds is reported. The resultant GA@UiO-66-NH 2 hybrid displayed a large specific surface area, hierarchical pores and an interconnected conductive network. The electrochemical characterizations demonstrated that the hybrid GA@UiO-66-NH 2 acts as an effective charge storing material with a capacitance of up to 651 F g –1 , significantly higher than traditional graphene-based materials. The results suggest that the amide linkage plays a key role in the formation of a π-conjugated structure, which facilitates charge transfer and consequently offers good capacitance and cycling stability. Furthermore, to realize the practical feasibility, an asymmetric supercapacitor using a GA@UiO-66-NH 2 positive electrode with Ti 3 C 2 T X MXene as the opposing electrode has been constructed. The cell is able to deliver a power density of up to 16 kW kg –1 and an energy density of up to 73 Wh kg –1 , which are comparable to several commercial devices such as Pb-acid and Ni/MH batteries. Under an intermediate level of loading, the device retained 88% of its initial capacitance after 10 000 cycles.

2D materials↗
DOE OSTI2020

A Metal Organic Framework Derived Solid Electrolyte for Lithium–Sulfur Batteries

Lithium–sulfur batteries (LSBs) are currently considered as promising candidates for next-generation energy storage technologies. However, their practical application is hindered by the critical issue of the polysulfide-shuttle. Herein, a metal organic framework (MOF)-derived solid electrolyte is presented to address it. The MOF solid electrolyte is developed based on a Universitetet i Oslo (UIO) structure. By grafting a lithium sulfonate (-SO 3 Li) group to the UIO ligand, both the ionic conductivity and the polysulfide-suppression capability of the resulting -SO 3 Li grafted UIO (UIOSLi) solid electrolyte are greatly improved. After integrating a Li-based ionic liquid (Li-IL), lithium bis(trifluoromethanesulfonyl)imide in 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, the resulting Li-IL/UIOSLi solid electrolyte exhibits an ionic conductivity of 3.3 × 10 -4 S cm -1 at room temperature. Based on its unique structure, the Li-IL/UIOSLi solid electrolyte effectively restrains the polysulfide shuttle and suppresses lithium dendritic growth. Lithium–sulfur cells with the Li-IL/UIOSLi solid electrolyte and a Li 2 S 6 catholyte show stable cycling performance that preserves 84% of the initial capacity after 250 cycles with a capacity-fade rate of 0.06% per cycle.

25 ENERGY STORAGE↗
DOE OSTI2025

A new database website for nuclear level densities

We introduce a new open-access, web-based database (http://nld.ascsn.net), Current Archive of Nuclear Density of Levels (CANDL), that hosts experimental nuclear level density (NLD) datasets from a variety of techniques and energy ranges. Built using the Dash framework in Python, the database is designed to be interactive and user-friendly, allowing researchers to search, visualize, fit, and export NLD data with minimal effort. This resource includes data extracted from evaporation spectra, Oslo method variants, and other experimental techniques that cover excitation energies beyond the neutron resonance region. The database supports on-the-fly fitting with two widely-used phenomenological models—the Constant Temperature (CT) model and the Back-Shifted Fermi Gas (BSFG) model—selected for their simplicity and computational efficiency. Future versions aim to include additional datasets and model types, as well as easy-to-use interfaces to data science techniques. Here, this platform offers a vital tool for the nuclear physics, astrophysics, medicine, and reactor design communities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Ca-isotopes as a robust tracer of magmatic differentiation

The large mass difference (~10%) between the two most abundant isotopes of calcium, 40 Ca and 44 Ca, gives Ca great potential in tracking mass-dependent fractionation during magmatic processes. Resolvable Ca-isotope fractionation during fractional crystallization of magma, particularly by feldspar in evolved melts, has been theoretically inferred but not robustly tested in nature. To further explore the effects of magmatic differentiation on Ca-isotope systematics, we studied the late-Permian alkaline igneous suite of the Øyangen Caldera, Oslo Rift, Norway, consisting of volcanic and intrusive units ranging from basanitic to rhyolitic compositions. Major and trace element variations and modeling demonstrate that the main series of samples (N = 21), including basanites, ring-dyke syenites, and central-dome syenites, likely documents a co-genetic and closed-system fractional crystallization sequence. Our data show minimal δ 44/40 Ca variation (< 0.05 ‰) in the intermediate magma and a marked increase in δ 44/40 Ca in the felsic magma of the Øyangen Caldera (from 0.62 ± 0.02 ‰ to 1.15 ± 0.03 ‰ relative to Ca standard, SRM915a). The systematic increase is best explained by equilibrium isotopic fractionation dominated by alkali feldspar in the fractionating mineral assemblage. This is further supported by strong correlations between δ 44/40 Ca, CaO, and Eu/Eu* in the main-series samples. Implementing a Monte Carlo approach, isotopic modeling of the liquid line of descent using Rayleigh fractionation is highly consistent with the observed Ca-isotope evolution. For the first time, we confirm prominent Ca stable isotope fractionation in felsic-stage differentiation of alkaline magma and constrain the isotope fractionation factors of plagioclase and K-feldspar. Integrated with extant estimations on mineral fractionation factors from the literature, our results suggest increasing fractionation effects of rock-forming minerals with decreasing Ca content. Finally, the affirmation of significant Ca-isotope fractionation in alkaline magma by feldspar empowers the application of Ca as a versatile tracer of crustal evolution, allowing further tests in other magmatic conditions across various planetary objects.

58 GEOSCIENCES↗
DOE OSTI2023

To what extent can decommissioning options for marine artificial structures move us toward environmental targets?

Switching from fossil fuels to renewable energy is key to international energy transition efforts and the move toward net zero. For many nations, this requires decommissioning of hundreds of oil and gas infrastructure in the marine environment. Current international, regional and national legislation largely dictates that structures must be completely removed at end-of-life although, increasingly, alternative decommissioning options are being promoted and implemented. Yet, a paucity of real-world case studies describing the impacts of decommissioning on the environment make decision-making with respect to which option(s) might be optimal for meeting international and regional strategic environmental targets challenging. To address this gap, we draw together international expertise and judgment from marine environmental scientists on marine artificial structures as an alternative source of evidence that explores how different decommissioning options might ameliorate pressures that drive environmental status toward (or away) from environmental objectives. Synthesis reveals that for 37 United Nations and Oslo-Paris Commissions (OSPAR) global and regional environmental targets, experts consider repurposing or abandoning individual structures, or abandoning multiple structures across a region, as the options that would most strongly contribute toward targets. This collective view suggests complete removal may not be best for the environment or society. However, different decommissioning options act in different ways and make variable contributions toward environmental targets, such that policy makers and managers would likely need to prioritise some targets over others considering political, social, economic, and ecological contexts. Current policy may not result in optimal outcomes for the environment or society.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Efficient alkene epoxidation catalyzed by molybdenyl acetylacetonate supported on aminated UiO-66 metal−organic framework

Metal–organic frameworks (MOFs) containing Mo Schiff base complexes were prepared by post-synthesis method and applied as efficient catalysts in the epoxidation of alkenes with tert-BuOOH. In this manner, UiO-66-NH{sub 2} (UiO=University of Oslo) MOF was reacted with salicylaldehyde and thiophene-2-carbaldehyde to produce bidentate Schiff bases. Then, the Schiff base ligands were used for immobilization of molybdenyl acetylacetonate. These new catalysts were characterized by FT-IR, UV–vis spectroscopic techniques, X-ray diffraction (XRD), BET, inductively coupled plasma atomic emission spectroscopy (ICP-AES) and field emission scanning electron microscopy (FE-SEM). These catalytic systems showed excellent activity in the epoxidation of alkenes such as cyclic and linear ones with tert-butyl hydroperoxide (TBHP) in 1,2-dichloroethane, and reused several times without any appreciable loss of their activity. - Graphical abstract: Efficient alkene epoxidation with TBHP catalyzed by heterogeneous and reusable molybdenum base catalysts is reported. - Highlights: • UiO-66-NH{sub 2} was modified with salicylaldehyde and thiophene-2-carbaldehyde. • The Schiff base groups were used for immobilization of MoO{sub 2}(acac){sub 2}. • The heterogeneous catalysts were prepared. • The prepared catalysts were used for epoxidation of alkenes. • Compared to other catalyst, our catalysts were more efficient and forceful.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Photon Strength Function at Low Energies in 95 Mo

A new and model-independent experimental method has been developed to determine the energy dependence of the photon strength function. It is designed to study statistical feeding from the quasi continuum to individual low-lying discrete levels. This new technique is presented and results for 95 Mo are compared to data from the University of Oslo. In particular, questions regarding the existence of the low-energy enhancement in the photon strength function are addressed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Mechanistic Insights into C–H Borylation of Arenes with Organoiridium Catalysts Embedded in a Microporous Metal–Organic Framework

Organometallic iridium catalysts can be used in conjunction with bispinacolatodiboron (B 2 Pin 2 ) to effect the borylation of a variety of substrates such as arenes, alkanes, heteroarenes, and oxygenates. Recently, efforts have also focused on integrating these catalysts into porous supports, such as metal–organic frameworks (MOFs). While the mechanism of homogeneous borylation systems has been thoroughly investigated experimentally and computationally, analogous studies in MOF-supported iridium catalysts have not been conducted. In this paper, we report the mechanistic investigation of a phenanthroline-iridium catalyst immobilized in the organic linker of Universitetet i Oslo (UiO)-67 (Zr 6 O 4 (OH) 4 (BPDC) 4 (PhenDC) 2 , BPDC = biphenyl-4,4'-dicarboxylate, PhenDC = 1,10-phenanthroline-4,4'-dicarboxylate). By using benzene as a model substrate, variable time normalization analysis (VTNA) of the kinetic data suggested a rate law consistent with zero-order in B 2 Pin 2 , and first-order in arene. A primary kinetic isotope effect (KIE) in the time course of benzene-d 6 borylation also provided complementary information about the role of the arene in the rate-determining step of the reaction. Characterization by techniques such as X-ray absorption spectroscopy (XAS) confirmed the presence of Ir(III), while pair distribution function (PDF) analysis suggested structures containing an Ir–Cl bond, further substantiated by X-ray photoelectron spectroscopy (XPS). Analysis of postcatalysis materials by inductively coupled plasma–optical emission spectroscopy (ICP-OES) revealed low boron accumulation, which may indicate an absence of boron in the resting state of the catalyst. Finally, in comparing borylation of benzene and toluene, a slight selectivity for benzene is observed, which is similar to the analogous homogeneous reaction, indicating the influence of substrate sterics on reactivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Local Coordination Environment of Lanthanides Adsorbed onto Cr- and Zr-based Metal–Organic Frameworks

Separating individual lanthanide (Ln) elements in aqueous mixtures is challenging. Ion-selective capture by porous materials, such as metal–organic frameworks (MOFs), is a promising approach. To design ion-selective MOFs, molecular details of the Ln adsorption complexes within the MOFs must be understood. We determine the local coordination environment of lanthanides Nd(III), Gd(III), and Lu(III) adsorbed onto Cr(III)-based terephthalate MOF (Cr-MIL-101) and Zr(IV)-based Universitet in Oslo MOFs (UiO-66 and UiO-68) and their derivatives. In the Cr(III)- and Zr(IV)-based MOFs, Ln adsorb as inner-sphere complexes at the metal oxo clusters, regardless of whether the organic linkers are decorated with amino groups. Missing linkers result in favorable Ln binding sites at oxo clusters; however, Ln can coordinate to metal sites even with linkers in place. Further, MOF functionalization with phosphonate groups led to Ln chemisorption onto these groups, which out-compete metal cluster sites. Ln form monodentate and bidentate and mononuclear and binuclear surface complexes. We conclude that MOFs for ion-selective Ln capture can be designed by a combination of (1) maximizing metal-lanthanide interactions via shared O atoms at the metal oxo cluster sites, where mixed oxo clusters can lead to ion-selective Ln adsorption, and (2) functionalizing MOFs with Ln-selective groups capable of out-completing the metal oxo cluster sites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗