Search NASA⌕ Search

SEARCH · Search NASA

Results for “thermal separations”

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.

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

At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

An Instrumented Capsule Design to Measure Thermal Conductivity in Miniature UO2 Specimens

Numerous separate effects irradiations of miniature nuclear fuel specimens have been conducted in the High Flux Isotope Reactor (HFIR) under the experimental platform designated as MiniFuel. MiniFuel is a static irradiation capability in which microstructural evolution and fuel performance phenomena are observed during postirradiation examination thereby offering a snapshot of the terminal fuel characteristics. This approach inherently requires fielding an irradiation where the experimental conditions are determined using predictive models and the pertinent outcomes are measured at the end of the test. Static irradiations can provide useful insights to the relationships between fuel performance and the pivotal irradiation conditions, namely temperature and burnup, but the ability to monitor fuel performance in situ would further support fuel development and qualification. To this end, an instrumented experiment design is being developed at Oak Ridge National Laboratory to capture thermal conductivity degradation and fission gas release during HFIR irradiation. These phenomena will be monitored using unique capsule designs that each target a different phenomenon. This paper details the thermal conductivity capsule (TCC) design and its expected performance envelope as determined using computer models. Each TCC will contain a miniature UO2 disc specimen (~0.5 mm thick × 5 mm diameter) sandwiched between metallic slugs with embedded thermocouples. The coupling of in situ temperature measurements, known thermal conductivity of the metallic components, and heat generation rates computed using high-fidelity neutronics models make the thermal conductivity measurement possible. This paper describes the reactor physics and heat transfer models used to predict the capsule’s performance and the methodology for calculating the fuel specimen’s thermal conductivity from the thermocouple measurements.

Gorton, Jacob [ORNL] (ORCID:0000000269806083)↗
DOE OSTI2023

Coarse-grained methods for heterogeneous vesicles with phase-separated domains: Elastic mechanics of shape fluctuations, plate compression, and channel insertion

We develop coarse-grained particle approaches for studying the elastic mechanics of vesicles with heterogeneous membranes having phase-separated domains. We perform simulations both of passive shape fluctuations and of active systems where vesicles are subjected to compression between two plates or subjected to insertion into narrow channels. Analysis methods are developed for mapping particle configurations to continuum fields with spherical harmonics representations. Heterogeneous vesicles are found to exhibit rich behaviors where the heterogeneity can amplify surface two-point correlations, reduce resistance during compression, and augment vesicle transport times in channels. The developed methods provide general approaches for characterizing the mechanics of coarse-grained heterogeneous systems taking into account the roles of thermal fluctuations, geometry, and phase separation.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Calorimetric thermal-vacuum performance characterization of the BAe 80 K space cryocooler

A comprehensive characterization program is underway at JPL to generate test data on long-life, miniature Stirling-cycle cryocoolers for space application. The key focus of this paper is on the thermal performance of the British Aerospace (BAe) 80 K split-Stirling-cycle cryocooler as measured in a unique calorimetric thermal-vacuum test chamber that accurately simulates the heat-transfer interfaces of space. Two separate cooling fluid loops provide precise individual control of the compressor and displacer heatsink temperatures. In addition, heatflow transducers enable calorimetric measurements of the heat rejected separately by the compressor and displacer. Cooler thermal performance has been mapped for coldtip temperatures ranging from below 45 K to above 150 K, for heatsink temperatures ranging from 280 K to 320 K, and for a wide variety of operational variables including compressor-displacer phase, compressor-displacer stroke, drive frequency, and piston-displacer dc offset.

Kotsubo, V. Y.↗
DOE OSTI2022

Thin film combinatorial sputtering of Al-Ce alloys: Investigating the phase separation of as-deposited solid solutions and determining the coefficient of thermal expansion

Al x Ce 100–x thin films with a composition range of ~75.0 < x < 99.5 at% (36.5 < x < 97.5 wt%) were synthesized via combinatorial co-sputtering from an Al and an Al 50 Ce 50 target. The crystal structure, phase fraction, film morphology, electrical resistivity, and temperature-dependent coefficients of thermal expansion (CTE) are all correlated to the Al x Ce 100–x composition. The as-deposited films form a metastable solid-solution, and annealing leads to the formation of the thermodynamically stable two-phase system of Al and the α-Al 11 Ce 3 intermetallic. Temperature dependent x-ray diffraction (XRD) reveals that the two phases expand independently of one another, and the thin film Al temperature-dependent CTE is similar to bulk Al. The thin film Al 11 Ce 3 intermetallic phase has a nearly constant CTE of ~1.5 × 10 –5 /°C within the temperature range studied (25–550 °C). To confirm the thin film Al 11 Ce 3 results, bulk stoichiometric Al 11 Ce 3 and +/- 1 wt% Ce samples were prepared and the CTE of each was measured with the same conditions. A Rietveld analysis of the bulk data enabled an estimation of the CTE in each of the 3 orthorhombic lattice parameters, which displayed anisotropic behavior. The thin film and bulk CTE measurements were in very good agreement. Estimations of the temperature dependent CTE of the two-phase alloys are made via the Reuss and Voigt models. Finally, by demonstrating the efficacy of the approach, more complex multi-component rapid materials discovery of low CTE Al-alloys can be pursued via the combinatorial thin film synthesis and XRD measurement.

36 MATERIALS SCIENCE↗
NASA NTRS2012

Development of a Deep-Penetrating, Compact Geothermal Heat Flow System for Robotic Lunar Geophysical Missions

Geothermal heat flow measurements are a high priority for the future lunar geophysical network missions recommended by the latest Decadal Survey of the National Academy. Geothermal heat flow is obtained as a product of two separate measurements of geothermal gradient and thermal conductivity of the regolith/soil interval penetrated by the instrument. The Apollo 15 and 17 astronauts deployed their heat flow probes down to 1.4-m and 2.3-m depths, respectively, using a rotary-percussive drill. However, recent studies show that the heat flow instrument for a lunar mission should be capable of excavating a ~3-m deep hole to avoid the effect of potential long-term changes of the surface thermal environment. For a future robotic geophysical mission, a system that utilizes a rotary/percussive drill would far exceed the limited payload and power capacities of the lander/rover. Therefore, we are currently developing a more compact heat flow system that is capable of 3-m penetration. Because the grains of lunar regolith are cohesive and densely packed, the previously proposed lightweight, internal hammering systems (the so-called moles ) are not likely to achieve the desired deep penetration. The excavation system for our new heat flow instrumentation utilizes a stem which winds out of a pneumatically driven reel and pushes its conical tip into the regolith. Simultaneously, gas jets, emitted from the cone tip, loosen and blow away the soil. Lab tests have demonstrated that this proboscis system has much greater excavation capability than a mole-based heat flow system, while it weighs about the same. Thermal sensors are attached along the stem and at the tip of the penetrating cone. Thermal conductivity is measured at the cone tip with a short (1- to 1.5-cm long) needle sensor containing a resistance temperature detector (RTD) and a heater wire. When it is inserted into the soil, the heater is activated. Thermal conductivity of the soil is obtained from the rate of temperature increase during the heating. By stopping during the excavation, it is possible to measure thermal conductivities at different depths. The gas jets are turned off when the penetrating cone reaches the target depth. Then, the stem pushes the needle sensor into the undisturbed soil at the bottom of the hole and carries out a thermal conductivity measurement. When the measurement is complete, the system resumes excavation. RTDs, placed along the stem at short (approx 30 cm) intervals, will monitor long-term temperature stability of the subsurface. Temperature in the shallow subsurface would fluctuate with the diurnal, annual, and precession cycles of the Moon. These thermal waves penetrate to different depths into the regolith. Longterm monitoring of the subsurface temperature would allow us to accurately delineate these cyclic signals and separate them from the signal associated with the outward flow of the Moon s endogenic heat. Further, temperature toward bottom of the 3-m hole should be fairly stable after the heat generated during the excavation dissipates into the surrounding soil. The geothermal gradient may be determined reliably from temperature measurements at the RTDs near the bottom. In order to minimize the heat conduction along the stem from affecting the geothermal gradient measurements, we plan to use low-conductive materials for the stem and develop a mechanism to achieve close coupling between the RTDs and the wall of the excavated hole.

Nagihara, Seiichi↗
NASA NTRS1997

Cluster Observations for Combined X-Ray and Sunyaev-Zel'dovich Estimates of Peculiar Velocities and Distances

Measurements of the peculiar velocities of galaxy clusters with respect to the Hubble flow allow the determination of the gravitational field from all matter in the universe, not just the visible component. The Sunyaev-Zel'dovich (SZ) effect (the inverse-Compton scattering of cosmic microwave background photons by the hot gas in clusters of galaxies) allows these velocities to be measured without the use of empirical distance indicators. Additionally, because the magnitude of the SZ effect is independent of redshift, the technique can be used to measure velocities out to the epoch of cluster formation. The SZ technique requires a determination of the temperature of the hot cluster gas from X-ray observations, and measurements of the SZ effect at millimeter wavelengths to separate the contribution from the thermal motions within the gas from that of the cluster peculiax velocity. We have constructed a bolometric receiver, the Sunyaev-Zel'dovich Infrared Experiment, specifically to make measurements of the SZ effect at millimeter wavelengths in order to apply the SZ technique to peculiar velocity measurements. This receiver has already been used to set limits to the peculiar velocities of two galaxy clusters at z approx. 0.2. As a test of the SZ technique, the double cluster pair Abell 222 and 223 was selected for observation. Measurements of the redshifts of the two components suggest that, if the clusters are gravitationally bound, they should exhibit a relative velocity of 10OO km/ s, well above the expected precision of 200 km/ s (set by astrophysical confusion) that is expected from the SZ method. The temperature can be measured from ASCA data which we obtained for this cluster pair. However, in order to ensure that the temperature estimate from the ASCA data was not dominated by cooling flows within the cluster, we requested ROSAT HRI observations of this cluster pair. Analysis of the X-ray properties of the cluster pair is continuing by combining the ROSAT observations funded under this proposal, archival PSPC data and our own PI ASCA data. The imaging data shows that neither cluster has a strong cooling flow, although A223 is the more compact of the two components. A223 also has a sub-cluster projected 1 Mpc to the North. The observed properties of this cluster pair are strikingly similar to those of the well-studied pair of A399 and A401 which are widely believed to be interacting and are in the initial stages of merging. This strengthens our selection of this cluster pair as a test for cluster peculiar motions. Combining these X-ray observations with SUZIE measurements of the SZ effect will provide important constraints on cluster merger models. This part of the program has been heavily delayed by bad weather at Mauna Kea, however SZ observations were obtained in November 1997 as part of a separately funded effort. These data are currently being analyzed.

Lange, A. E.↗
NASA NTRS1984

Radiative tearing - Magnetic reconnection on a fast thermal-instability time scale

Two energy modification mechanisms which are known to occur in sheared magnetic fields are the tearing and thermal instabilities. These processes can be studied separately with formalisms incorporating just the effective driving mechanism of interest (finite resistivity for the tearing mode and unstable radiation for the thermal mode). A model which includes both effects, and a temperature-dependent resistivity, indicates that modified forms of these two instabilities may coexist for identical physical conditions. When they are isolated computationally, one can show that their limiting growth rates are approximately those of the uncoupled instabilities. The spatial structure and energy content of these two new hybrid processes are then individually examined and are found to differ considerably from those obtained from separate treatments of the driving mechanisms. The faster radiative instability, which has a hydromagnetically scaled growth rate like the condensation mode of the thermal instability, is shown to involve a substantial amount of magnetic field reconnection. This can be partially explained by a large temperature drop (or resistivity rise) at the X-point. The island width of the Coulomb-coupled radiative mode is 30 percent of that produced by a comparable level of the slower tearing instability. In addition, the perturbed magnetic energy in the radiative instability is 5 times that of the perturbed thermal energy, indicating an appreciable modification of the initial magnetic structure.

Steinolfson, R. S.↗
NASA NTRS1989

Hydrogen-oxygen proton-exchange membrane fuel cells and electrolyzers

Hydrogen-oxygen SPE fuel cells and SPE electrolyzers (products of Hamilton Standard) both use a Proton-Exchange Membrane (PEM) as the sole electrolyte. The SPE cells have demonstrated a ten year life capability under load conditions. Ultimate life of PEM fuel cells and electrolyzers is primarily related to the chemical stability of the membrane. For perfluorocarbon proton-exchange membranes an accurate measure of the membrane stability is the fluoride loss rate. Millions of cell hours have contributed to establishing a relationship between fluroride loss rates and average expected ultimate cell life. Several features were introduced into SPE fuel cells and SPE electrolyzers such that applications requiring greater than or equal to 100,000 hours of life can be considered. Equally important as the ultimate life is the voltage stability of hydrogen-oxygen fuel cells and electrolyzers. Here again the features of SPE fuel cells and SPE electrolyzers have shown a cell voltage stability in the order of 1 microvolt per hour. That level of stability were demonstrated for tens of thousands of hours in SPE fuel cells at up to 500 amps per square foot (ASF) current density. The SPE electrolyzers have demonstrated the same at 1000 ASF. Many future extraterrestrial applications for fuel cells require that they be self recharged. To translate the proven SPE cell life and stability into a highly reliable extraterrestrial electrical energy storage system, a simplification of supporting equipment is required. Static phase separation, static fluid transport and static thermal control will be most useful in producting required system reliability. Although some 200,000 SPE fuel cell hours were recorded in earth orbit with static fluid phase separation, no SPE electrolyzer has, as yet, operated in space.

Baldwin, R.↗
NASA NTRS1974

First heated jettison test on the Centaur standard shroud

The first in a planned series of heated jettison tests on the Centaur Standard Shround was conducted at NASA Plum Brook Station's Space Power Facility on November 19, 1973. The first 250-second portion of the test sequence involved heating the shroud with a specially-built fixture designed to provide a simulation of the heating environment encountered by the shroud during its ascent through the earth's atmosphere. The two heater halves, which were mounted on a rail system, were then retracted. This was followed by the jettison of the two shroud halves into catch nets positioned at 90 deg to the heater rails. The condition which made this test unique compared to the planned subsequent tests was the location of the maximum thermal line at 32 deg from the shroud separation plane. Information on the test hardware, configuration, and sequence is presented. Shroud thermal and deflection data encountered during the heating portion of the test sequence is compared with free-skin design temperatures in various graphical formats.

Source record↗
NASA NTRS1986

The calibration of photographic and spectroscopic films. 1: Film batch variations of reciprocity failure in IIaO film. 2: Thermal and aging effects in relationship to reciprocity failure. 3: Shifting of reciprocity failure points as a function of thermal and aging effects

Reciprocity failure was examined for IIaO spectroscopic film. Three separate experiments were performed in order to study film batch variations, thermal and aging effects in relationship to reciprocity failure, and shifting of reciprocity failure points as a function of thermal and aging effects. The failure was examined over ranges of time between 5 and 60 seconds. The variation to illuminance was obtained by using thirty neutral density filters. A standard sensitometer device imprinted the wedge pattern on the film as exposure time was subjected to variation. The results indicate that film batch differences, temperature, and aging play an important role in reciprocity failure of IIaO spectroscopic film. A shifting of the failure points was also observed in various batches of film.

Peters, K. A.↗
NASA NTRS1987

The calibration of photographic and spectroscopic films. Part 1: Film batch variations of reciprocity failure in IIaO film. Part 2: Thermal and aging effects in relationship to reciprocity failure. P art 3: Shifting of reciprocity failure points as a function of thermal and aging effects

Reciprocity failure was examined for IIaO spectroscopic film. Three separate experiments were performed in order to study film batch variations, thermal and aging effects in relationship to reciprocity failure, and shifting of reciprocity failure points as a function of thermal and aging effects. The failure was examined over ranges of time between 5 and 60 seconds. The variation to illuminance was obtained by using thirty neutral density filters. A standard sensitometer device imprinted the wedge pattern on the film as exposure time was subjected to variation. Results indicate that film batch differences, temperature, and aging play an important role in reciprocity failure of IIaO spectroscopic film. A shifting of the failure points was also observed in various batches of film.

Peters, Kevin A.↗
DOE OSTI2021

Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction

We study quarkonium transport in the quark-gluon plasma by using the potential nonrelativistic QCD (pNRQCD) effective field theory and the framework of open quantum systems. We argue that the coupling between quarkonium and the thermal bath is weak using separation of scales, so the initial density matrix of the total system factorizes and the time evolution of the subsystem is Markovian. We derive the semiclassical Boltzmann equation for quarkonium by applying a Wigner transform to the Lindblad equation and carrying out a semiclassical expansion. We resum relevant interactions to all orders in the coupling constant at leading power of the nonrelativistic and multipole expansions. The derivation is valid for both weakly coupled and strongly coupled quark-gluon plasmas. We find reaction rates in the transport equation factorize into a quarkonium dipole transition function and a chromoelectric gluon distribution function. For the differential reaction rate, the definition of the momentum dependent chromoelectric gluon distribution function involves staple-shaped Wilson lines. For the inclusive reaction rate, the Wilson lines collapse into a straight line along the real time axis and the distribution becomes momentum independent. The relation between the two Wilson lines is analogous to the relation between the Wilson lines appearing in the gluon parton distribution function (PDF) and the gluon transverse momentum dependent parton distribution function (TMDPDF). The centrality dependence of the quarkonium nuclear modification factor measured by experiments probes the momentum independent distribution while the transverse momentum dependence and measurements of the azimuthal angular anisotropy may be able to probe the momentum dependent one. We discuss one way to indirectly constrain the quarkonium in-medium real potential by using the factorization formula and lattice calculations. The leading quantum correction to the semiclassical transport equation of quarkonium is also worked out. The study can be easily generalized to quarkonium transport in cold nuclear matter, which is relevant for quarkonium production in eA collisions in the future Electron-Ion Collider.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

A structural and electrochemical study of perfluoropolyether-poly(ethylene oxide) solid polymer electrolytes

Solid polymer electrolytes offer attractive safety, processability, and interfacial adhesion for enabling high–energy solid-state lithium batteries, but they are often limited by narrow oxidative stability windows and low lithium-ion transference numbers. In an attempt to broaden the electrochemical stability window and increase lithium-ion transference number of poly(ethylene oxide) (PEO)-based solid polymer electrolytes, we produce an optically clear, crosslinked membrane of PEO and perfluoropolyether (PFPE) using a mixed solvent method and subsequently infuse the membrane with a lithium salt. Structural and thermal analyses reveal nanoscale phase separation between fluorocarbon and hydrocarbon domains with characteristic spacings of 7–8 nm and an elevated glass transition for the hydrocarbon phase. Consistent with this, PFPE-containing membranes exhibit substantially lower ionic conductivity than PEO analogs (dry and plasticized). The transference number and electrochemical stability are similar to pure PEO. These results demonstrate that fluorination implemented as segregated nanoscale domains does not deliver the anticipated transport or stability benefits; instead, phase separation increases tortuosity and suppresses hydrocarbon-phase dynamics. The work underscores the importance of fluorine placement and morphology control, guiding the design of partially fluorinated solid polymer electrolytes toward architectures that avoid detrimental nanoscale phase separation.

Carden, Peyton [ORNL] (ORCID:0000000162296538)↗
DOE OSTI2021

Spectroscopic, Magnetic, and Computational Investigations on a Series of Rhenium(III) Cyclopentadienide β-diketiminate Halide and Pseudohalide Complexes

Here the low-valent rhenium(I) salt Na[Re(η 5 -Cp)(BDI)] (BDI = N,N'-bis(2,6-diisopropylphenyl)-3,5-dimethyl-β-diketiminate) was shown to react with various halide and chalcogenolate reagents, leading to the isolation of a series of rhenium(III)-halide and -pseudohalide complexes: Re(X)(η 5 -Cp)(BDI) (1-X, X = F, Cl, Br, I; 2, X = OTf) and Re(ER)(η 5 -Cp)(BDI) (3-ER, ER = SBn, SeBn, TePh). The 1 H NMR spectra of these complexes displayed sharp resonances shifted several ppm from typical diamagnetic regions, as well as distinct chemical shift trends down both the halide (with the exception of F) and chalcogenolate series, with both Cp and BDI backbone peaks moving downfield with increasing atomic number. Subsequent magnetic susceptibility measurements of the rhenium(III) halides 1-Cl, 1-Br, and 1-I indicated that these complexes display temperature-independent paramagnetism (TIP), with χ TIP values of 7.41(44) × 10 -4 to 1.50(51) × 10 -3 cm 3 mol -1 . Multireference complete active space self-consistent field (CASSCF) computations incorporating spin-orbit state mixing revealed small energy separations (1.7-3.0 kcal/mol) between thermally isolated ground states and the first excited spin-orbit states for the rhenium halides, confirming that low-lying excited states are responsible for the observed TIP behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Crosslinked metallo-polyelectrolytes with enhanced flexibility and dimensional stability for anion-exchange membranes

High-performing anion-exchange membranes (AEMs) have attracted tremendous interest for applications in emerging energy storage and conversion devices. In this work, we present a strategy for the synthesis of crosslinked metallo-polyelectrolytes as mechanically flexible, dimensionally stable and ionically conductive AEMs. The water uptake and swelling ratio are suppressed remarkably by introducing a crosslinked polymeric network. The as-prepared membranes also exhibit excellent thermal stability. The phase-separated morphology allows rapid ion-transport with low water uptake at various temperatures. Specifically, a conductivity of 53.3 mS cm -1 at 80 °C was achieved with an ion exchange capacity of 1.07 mmol g -1 and a low swelling ratio of 13%.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

One-step fabrication of robust lithium ion battery separators by polymerization-induced phase separation

Conventional lithium ion battery separators are microporous polyolefin membranes that play a passive role in the electrochemical cell. Next generation separators should offer significant performance enhancements, while being fabricated through facile, low cost approaches with the ability to readily tune physicochemical properties. This study presents a single-step manufacturing technique based on UV-initiated polymerization-induced phase separation (PIPS), wherein microporous separators are fabricated from multifunctional monomers and ethylene carbonate (EC), which functions as both the pore-forming agent (porogen) and electrolyte component in the electrochemical cell. By controlling the ratio of the 1,4-butanediol diacrylate (BDDA) monomer to ethylene carbonate, monolithic microporous membranes are readily prepared with 25 μm thickness and pore sizes and porosities ranging from 6.8 to 22 nm and 15.4% to 38.5%, respectively. With 38.5% apparent porosity and an average pore size of 22 nm, the poly(1,4-butanediol diacrylate) (pBDDA) separator takes up 127% liquid electrolyte, resulting in an ionic conductivity of 1.98 mS cm –1 , which is greater than in conventional Celgard 2500. Lithium ion battery half cells consisting of LiNi 0.5 Mn 0.3 Co 0.2 O 2 cathodes and pBDDA separators were shown to undergo reversible charge/discharge cycling with an average discharge capacity of 142 mA h g –1 and a capacity retention of 98.4% over 100 cycles – comparable to cells using state-of-the-art separators. Moreover, similar discharge capacities were achieved in rate performance tests due to the high ionic conductivity and electrolyte uptake of the film. Finally, the pBDDA separators were shown to be thermally stable to 374 °C, lack low temperature thermal transitions that can compromise cell safety, and exhibit no thermal shrinkage up to 150 °C.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

From lattice QCD to in-medium heavy-quark interactions via deep learning

Bottomonium states are key probes for experimental studies of the quark-gluon plasma (QGP) created in high-energy nuclear collisions. Theoretical models of bottomonium productions in high-energy nuclear collisions rely on the in-medium interactions between the bottom and antibottom quarks, which can be characterized by real (V R (T, r)) and imaginary (V I (T, r)) potentials, as functions of temperature and spatial separation. Recently, the masses and thermal widths of up to 3S and 2P bottomonium states in QGP were calculated using lattice quantum chromodynamics (LQCD). Starting from these LQCD results and through a novel application of deep neural network (DNN), here, we obtain model-independent results for V R (T, r) and V I (T, r). The temperature dependence of V R (T, r) was found to be very mild between T ≈ 0 - 330 MeV. Meanwhile, VI(T, r) shows rapid increase with T and r, which is much larger than the perturbation theory based expectations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗