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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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NASA NTRS1980

Photocell heat engine solar power systems

A combined photocell heat engine concept is proposed for high efficiency solar energy conversion in space. In this concept the short wavelength portion of the solar spectrum is split by a dichroic filter and sent to a bank of photocells. The long wave-length remainder of the spectrum is used by the heat engine. This technique allows the photocells to operate with the minimum amount of waste heat, increasing their efficiency and reducing the amount of cooling required. The heat engine operates by direct absorption in a working fluid containing broadband absorber molecules or particulates. A window in the heat engine admits the long wave-lengths from the solar spectrum. The window may also reflect a portion of the internal gaseous reradiation spectrum (e.g., a heat mirror) to help reduce radiation losses. Flow-induced thermal gradients may also reduce reradiation losses in the case of optically thick working fluids. The efficiencies computed for the photocell heat engine solar energy converter can be as high as 42 percent.

Taussig, R. T.↗
NASA NTRS2018

Constraining the Models' Response of Tropical Clouds to SST Forcings Using CALIPSO Observations

Here we present preliminary results from the analysis of the low cloud cover (LCC) and cloud radiative effect (CRE) interannual changes in response to sea surface temperature (SST) forcings in two GISS climate models, and 12 other climate models. We further classify them as a function of their ability to reproduce the vertical structure of the cloud response to SST change against 10 years of CALIPSO observations: “the constrained models, which match the observation constraint, and the unconstrained models”. The constrained models replicate the observed interannual LCC change particularly well (ΔLCC(sub con)=-3.49 ±1.01 %/K vs. ΔLCC(sub obs)=-3.59 ±0.28 %/K) as opposed to the unconstrained models, which largely underestimate it (ΔLCC(sub unc) = -1.32 ± 1.28 %/K). As a result, the amount of short-wave warming simulated by the constrained models (ΔCRE(sub con)=2.60 ±1.13 W/m2/K) is in better agreement with the observations (ΔCRE(sub obs)=3.05 ±0.28 W/m2/K) than the unconstrained models (ΔCRE(sub con)=0.87 ±2.63 W/m2/K). Depending on the type of low cloud, the observed relationship between cloud/radiation and surface temperature varies. Over the stratocumulus regions, increasing SSTs generate higher cloud top height along with a large decrease of the cloud fraction below as opposed to a slight decrease of the cloud fraction at each level over the trade cumulus regions. Our results suggest that the models must generate sustainable stratocumulus decks and moist processes in the planetary boundary layer to reproduce these observed features. Future work will focus on defining a method to objectively discriminate these cloud types that can be applied consistently in both the observations and the models.

Cesana, Gregory↗
NASA NTRS1988

SUMER: Solar Ultraviolet Measurements of Emitted Radiation

The SUMER (solar ultraviolet measurements of emitted radiation) experiment is described. It will study flows, turbulent motions, waves, temperatures and densities of the plasma in the upper atmosphere of the Sun. Structures and events associated with solar magnetic activity will be observed on various spatial and temporal scales. This will contribute to the understanding of coronal heating processes and the solar wind expansion. The instrument will take images of the Sun in EUV (extreme ultra violet) light with high resolution in space, wavelength and time. The spatial resolution and spectral resolving power of the instrument are described. Spectral shifts can be determined with subpixel accuracy. The wavelength range extends from 500 to 1600 angstroms. The integration time can be as short as one second. Line profiles, shifts and broadenings are studied. Ratios of temperature and density sensitive EUV emission lines are established.

Wilhelm, K.↗
NASA NTRS2010

NASA's Advancements in Space-Based Spectrometry Lead to Improvements in Weather Prediction and Understanding of Climate Processes

AIRS (Atmospheric Infra-Red Sounder), was launched, in conjunction with AMSU-A (Advanced Microwave Sounding Unit-A) on the NASA polar orbiting research satellite EOS (Earth Observing System) Aqua satellite in May 2002 as a next generation atmospheric sounding system. Atmospheric sounders provide information primarily about the vertical distribution of atmospheric temperature and water vapor distribution. This is achieved by measuring outgoing radiation in discrete channels (spectral intervals) which are sensitive primarily to variations of these geophysical parameters. The primary objectives of AIRS/AMSU were to utilize such information in order to improve the skill of numerical weather prediction as well as to measure climate variability and trends. AIRS is a multi-detector array grating spectrometer with 2378 channels covering the spectral range 650/cm (15 microns) to 2660/cm (3.6 microns) with a resolving power (i/a i) of roughly 1200 where a i is the spectral channel bandpass. Atmospheric temperature profile can be determined from channel observations taken within the 15 micron (the long-wave CO2 absorption band) and within the 4.2 micron (the short-wave CO2 absorption band). Radiances in these (and all other) spectral intervals in the infrared are also sensitive to the presence of clouds in the instrument?s field of view (FOV), which are present about 95% of the time. AIRS was designed so as to allow for the ability to produce accurate Quality Controlled atmospheric soundings under most cloud conditions. This was achieved by having 1) extremely low channel noise values in the shortwave portion of the spectrum and 2) a very flat spatial response function within a channel?s FOV. IASI, the high spectral resolution IR interferometer flying on the European METOP satellite, does not contain either of these important characteristics. The AIRS instrument was also designed to be extremely stabile with regard to its spectral radiometric characteristics, which is critical with regard to the ability to measure accurate long term trends.

Susskind, Joel↗
NASA NTRS2018

Explicit Cloud Representation in the Atmos 1D Climate Model for Earth and Rocky Planet Applications

1D climate models are less sophisticated than 3D global circulation models (GCMs), however their computational time is much less expensive, allowing a large number of runs in a short period of time to explore a wide parameter space. Exploring parameter space is particularly important for predicting the observable properties of exoplanets, for which few parameters are known with certainty. Therefore, 1D climate models are still very useful tools for planetary studies. In most of these 1D models, clouds are not physically represented in the atmosphere, despite having a well-known, significant impact on a planetary radiative budget. This impact is simulated by artificially raising surface albedo, in order to reproduce the observed-averaged surface temperature (i.e. 288 K for modern Earth) and a radiative balance at the top of the atmosphere. This non-physical representation of clouds, causes atmospheric long wave and shortwaves fluxes to not match observational data. Additionally, this technique represents a parameter that is highly-tuned to modern Earth’s climate, and may not be appropriate for planets that deviate from modern Earth’s climate conditions. In this paper, we present an update to the climate model within the Atmos 1­D atmospheric modeling package with a physical representation of clouds. We show that this physical representation of clouds in the atmosphere allows both long wave and shortwave fluxes to match observational data. This improvement will allow us to study the energy fluxes for a variety of cloudy rocky planets, and increase our confidence in future simulations of temperature profile and net energy balance.

Thomas Fauchez↗
DOE OSTI2021

The large scale polarization explorer (LSPE) for CMB measurements: performance forecast

The measurement of the polarization of the Cosmic Microwave Background (CMB) radiation is one of the current frontiers in cosmology. In particular, the detection of the divergence-free component of the polarization field, the B-mode component, reveals the presence of gravitational waves in the early Universe. The detection of such component is at the moment the most promising technique to probe the inflationary theory describing the very early evolution of the Universe. The measurement of the polarization of the Cosmic Microwave Background (CMB) radiation is one of the current frontiers in cosmology. In particular, the detection of the primordial divergence-free component of the polarization field, the B-mode, could reveal the presence of gravitational waves in the early Universe. The detection of such a component is at the moment the most promising technique to probe the inflationary theory describing the very early evolution of the Universe. We present the updated performance forecast of the Large Scale Polarization Explorer (LSPE), a program dedicated to the measurement of the CMB polarization. LSPE is composed of two instruments: LSPE-Strip, a radiometer-based telescope on the ground in Tenerife-Teide observatory, and LSPE-SWIPE (Short-Wavelength Instrument for the Polarization Explorer) a bolometer-based instrument designed to fly on a winter arctic stratospheric long-duration balloon. The program is among the few dedicated to observation of the Northern Hemisphere, while most of the international effort is focused into ground-based observation in the Southern Hemisphere. Measurements are currently scheduled in Winter 2022/23 for LSPE-SWIPE, with a flight duration up to 15 days, and in Summer 2022 with two years observations for LSPE-Strip. In this work, we describe the main features of the two instruments, identifying the most critical aspects of the design, in terms of impact on the performance forecast. We estimate the expected sensitivity of each instrument and propagate their combined observing power to the sensitivity to cosmological parameters, including the effect of scanning strategy, component separation, residual foregrounds and partial sky coverage. We also set requirements on the control of the most critical systematic effects and describe techniques to mitigate their impact. LSPE will reach a sensitivity in tensor-to-scalar ratio of σr < 0.01, set an upper limit r < 0.015 at 95% confidence level, and improve constraints on other cosmological parameters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Energy density and spectrum of single-cycle and sub-cycle electromagnetic pulses

Based on the exact solution of the Maxwell equations in the form of a collapsing spherical vector wave specified by an arbitrary function of time, we have calculated the maximum energy density that can be achieved when focusing extremely short pulses of various shapes. It is shown that our earlier formula expressing the maximum energy density in terms of the spectrum parameters for Gaussian quasi-monochromatic pulses is approximately (with an accuracy of ±40 %) valid for the main types of extremely short pulses. (extremely short laser pulses)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2021

All-Sky Search for Short Gravitational-Wave Bursts in the Third Advanced LIGO and Advanced Virgo Run

This paper presents the results of a search for generic short-duration gravitational-wave transients in datafrom the third observing run of Advanced LIGO and Advanced Virgo. Transients with durations ofmilliseconds to a few seconds in the 24–4096 Hz frequency band are targeted by the search, with noassumptions made regarding the incoming signal direction, polarization, or morphology. Gravitationalwaves from compact binary coalescences that have been identified by other targeted analyses are detected,but no statistically significant evidence for other gravitational wave bursts is found. Sensitivities to a varietyof signals are presented. These include updated upper limits on the source rate density as a function of thecharacteristic frequency of the signal, which are roughly an order of magnitude better than previous upperlimits. This search is sensitive to sources radiating as little as∼10−10M⊙c2in gravitational waves at∼70Hz from a distance of 10 kpc, with 50% detection efficiency at a false alarm rate of one per century.The sensitivity of this search to two plausible astrophysical sources is estimated: neutron starfmodes,which may be excited by pulsar glitches, as well as selected core-collapse supernova models.

R Abbott↗
DOE OSTI2023

Inner Belt Electron Decay Timescales: A Comparison of Van Allen Probes and DREAM3D Losses Following the June 2015 Storm

Abstract NASA's Van Allen Probes observed significant, long‐lived fluxes of inner belt electrons up to ∼1 MeV after geomagnetic storms in March and June 2015. Reanalysis of Magnetic Electron Ion Spectrometer (MagEIS) data with improved background correction showed a clearer picture of the relativistic electron population that persisted through 2016 and into 2017 above the Fennell et al. (2015, https://doi.org/10.1002/2014gl062874 ) limit. The intensity and duration of these enhancements allow estimation of decay timescales for comparison with simulated decay rates and theoretical lifetimes. We compare decay timescales from these data and DREAM3D simulations based on them using geomagnetic activity‐dependent pitch angle diffusion coefficients derived from plasmapause‐indexed wave data (Malaspina et al., 2016, https://doi.org/10.1002/2016gl069982 , 2018, https://doi.org/10.1029/2018gl078564 ) and phase space densities derived from MagEIS observations. Simulated decay rates match observed decay rates more closely than the theoretical lifetime due to significantly nonequilibrium pitch angle distributions in simulation and data. We conclude that nonequilibrium effects, rather than a missing diffusion or loss process, account for observed short decay rates.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2016

Enabling Wireless Avionics Intra-Communications

The Electromagnetics and Sensors Branch of NASA Langley Research Center (LaRC) is investigating the potential of an all-wireless aircraft as part of the ECON (Efficient Reconfigurable Cockpit Design and Fleet Operations using Software Intensive, Networked and Wireless Enabled Architecture) seedling proposal, which is funded by the Convergent Aeronautics Solutions (CAS) project, Transformative Aeronautics Concepts (TAC) program, and NASA Aeronautics Research Institute (NARI). The project consists of a brief effort carried out by a small team in the Electromagnetic Environment Effects (E3) laboratory with the intention of exposing some of the challenges faced by a wireless communication system inside the reflective cavity of an aircraft and to explore potential solutions that take advantage of that environment for constructive gain. The research effort was named EWAIC for "Enabling Wireless Aircraft Intra-communications." The E3 laboratory is a research facility that includes three electromagnetic reverberation chambers and equipment that allow testing and generation of test data for the investigation of wireless systems in reflective environments. Using these chambers, the EWAIC team developed a set of tests and setups that allow the intentional variation of intensity of a multipath field to reproduce the environment of the various bays and cabins of large transport aircraft. This setup, in essence, simulates an aircraft environment that allows the investigation and testing of wireless communication protocols that can effectively be used as a tool to mitigate some of the risks inherent to an aircraft wireless system for critical functions. In addition, the EWAIC team initiated the development of a computational modeling tool to illustrate the propagation of EM waves inside the reflective cabins and bays of aircraft and to obtain quantifiable information regarding the degradation of signals in aircraft subassemblies. The nose landing gear of a UAV CAD model was used to model the propagation of a system in a "deployed" configuration versus a "stowed" configuration. The differences in relative field strength provide valuable information about the distribution of the field that can be used to engineer RF links with optimal radiated power and antenna configuration that accomplish the intended system reliability. Such modeling will be necessary in subsequent studies for managing multipath propagation characteristics inside a main cabin and to understand more complex environments, such as the inside wings, landing gear bays, cargo bays, avionics bays, etc. The results of the short research effort are described in the present document. The team puts forth a set of recommendations with the intention of informing the project and program leadership of the future work that, in the opinion of the EWAIC team, would assist the ECON team reach the intended goal of developing an all-wireless aircraft.

Torres, Omar↗
DOE OSTI2024

Temperature effects on the nanoscale thermoelastic response of a SiO2 membrane

We crossed two femtosecond extreme ultraviolet (EUV) pulses on a 100 nm thick amorphous membrane of SiO2, generating transient gratings (TGs) of light intensity with 84 nm spatial periodicity. The EUV TG excitation gave rise to the efficient generation of Lamb waves (LWs) and of a temperature grating, whose dynamics was studied at two different initial sample temperatures, 50 and 300 K. The short penetration depth of the EUV excitation pulses turned into a strong non-uniformity in the actual temperature as a function of the depth from the sample surface. At the lowest temperature, the LW frequencies presented a sizable shift in time due to the thermal equilibration along the membrane thickness. The analysis of the EUV TG waveforms allowed us to determine the decay time of the thermal grating and the sound attenuation coefficient, both found in reasonable agreement with the literature. The results show how EUV TG can provide information of non-equilibrium thermoelastic dynamics in thin membranes transparent to optical radiation.

Materials Science↗
NASA NTRS2017

Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A

On 2017 August 17, the gravitational-wave event GW170817 was observed by the Advanced LIGO and Virgo detectors, and the gamma-ray burst (GRB) GRB170817A was observed independently by the Fermi Gamma-ray Burst Monitor, and the Anti-Coincidence Shield for the Spectrometer for the International Gamma-Ray Astrophysics Laboratory. The probability of the near-simultaneous temporal and spatial observation of GRB 170817A and GW170817 occurring by chance is 5.0 x 10(exp -8). We therefore confirm binary neutron star mergers as a progenitor of short GRBs. The association of GW170817 and GRB 170817A provides new insight into fundamental physics and the origin of short GRBs. We use the observed time delay of (+1.74 +/- 0.05) s between GRB170817A and GW170817 to: (i) constrain the difference between the speed of gravity and the speed of light to be between -3 x 10(exp-16) times the speed of light, (ii) place new bounds on the violation of Lorentz invariance, (iii) present a new test of the equivalence principle by constraining the Shapiro delay between gravitational and electromagnetic radiation. We also use the time delay to constrain the size and bulk Lorentz factor of the region emitting the gamma-rays. GRB170817A is the closest short GRB with a known distance, but is between 2 and 6 orders of magnitude less energetic than other bursts with measured redshift. A new generation of gamma-ray detectors, and subthreshold searches in existing detectors, will be essential to detect similar short bursts at greater distances. Finally, we predict a joint detection rate for the Fermi Gamma-ray Burst Monitor and the Advanced LIGO and Virgo detectors of 0.1 - 1.4 per year during the 2018--2019 observing run and 0.3 - 1.7 per year at design sensitivity.

Gravitational wave↗
DOE OSTI2024

A new-old approach to composite scalars with chiral fermion constituents

We develop a dynamical, Lorentz invariant theory of composite scalars in configuration space consisting of chiral fermions, interacting by the perturbative exchange of a massive “gluon” of coupling g 0 and mass M 0 2 (the coloron model). The formalism is inspired by, but goes beyond, old ideas of Yukawa and the Nambu-Jona-Lasinio (NJL) model. It yields a non-pointlike internal wave-function of the bound state, ϕ ( r ) , which satisfies a Schrödinger-Klein-Gordon (SKG) equation with eigenvalue μ 2 . For super-critical coupling, g 0 2 > g 0 c 2 , we have μ 2 < 0 leading to spontaneous symmetry breaking. The binding of chiral fermions is semiclassical, not loop-level as in NJL. The mass scale is determined by the interaction as in NJL. We mainly focus on the short-distance, large M 0 2 limit, yielding an NJL pointlike interaction, but the bound state internal wave-function, ϕ ( r → ) , remains spatially extended and dilutes ϕ ( 0 ) . This leads to power-law suppression of the induced Yukawa and quartic couplings and requires radically less fine-tuning of a hierarchy than does the NJL model. We include a discussion of loop corrections of the theory. A realistic top condensation model appears possible.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1994

Study of atmospheric parameters measurements using MM-wave radar in synergy with LITE-2

The Lidar In-Space Technology Experiment, (LITE), has been developed, designed, and built by NASA Langley Research Center, to be flown on the space shuttle 'Discovery' on September 9, 1994. Lidar, which stands for light detecting and ranging, is a radar system that uses short pulses of laser light instead of radio waves in the case of the common radar. This space-based lidar offers atmospheric measurements of stratospheric and tropospheric aerosols, the planetary boundary layer, cloud top heights, and atmospheric temperature and density in the 10-40 km altitude range. A study is being done on the use, advantages, and limitations of a millimeterwave radar to be utilized in synergy with the Lidar system, for the LITE-2 experiment to be flown on a future space shuttle mission. The lower atmospheric attenuation, compared to infrared and optical frequencies, permits the millimeter-wave signals to penetrate through the clouds and measure multi-layered clouds, cloud thickness, and cloud-base height. These measurements would provide a useful input to radiation computations used in the operational numerical weather prediction models, and for forecasting. High power levels, optimum modulation, data processing, and high antenna gain are used to increase the operating range, while space environment, radar tradeoffs, and power availability are considered. Preliminary, numerical calculations are made, using the specifications of an experimental system constructed at Georgia Tech. The noncoherent 94 GHz millimeter-wave radar system has a pulsed output with peak value of 1 kW. The backscatter cross section of the particles to be measured, that are present in the volume covered by the beam footprint, is also studied.

Andrawis, Madeleine Y.↗
NASA NTRS2014

Transition-Edge Hot-Electron Microbolometers for Millimeter and Submillimeter Astrophysics

The millimeter and the submillimeter wavelengths of the electromagnetic spectrum hold a wealth of information about the evolution of the universe. In particular, cosmic microwave background (CMB) radiation and its polarization carry the oldest information in the universe, and provide the best test of the inflationary paradigm available to astronomy today. Detecting gravity waves through their imprint on the CMB polarization would have extraordinary repercussions for cosmology and physics. A transition-edge hot-electron micro - bolometer (THM) consists of a superconducting bilayer transition-edge sensor (TES) with a thin-film absorber. Unlike traditional monolithic bolometers that make use of micromachined structures, the THM em ploys the decoupling between electrons and phonons at millikelvin temperatures to provide thermal isolation. The devices are fabricated photolithographically and are easily integrated with antennas via microstrip transmission lines, and with SQUID (superconducting quantum interference device) readouts. The small volume of the absorber and TES produces a short thermal time constant that facilitates rapid sky scanning. The THM consists of a thin-film metal absorber overlapping a superconducting TES. The absorber forms the termination of a superconducting microstripline that carries RF power from an antenna. The purpose of forming a separate absorber and TES is to allow flexibility in the optimization of the two components. In particular, the absorbing film's impedance can be chosen to match the antenna, while the TES impedance can be chosen to match to the readout SQUID amplifier. This scheme combines the advantages of the TES with the advantages of planar millimeter-wave transmission line circuits. Antenna-coupling to the detectors via planar transmission lines allows the detector dimensions to be much smaller than a wavelength, so the technique can be extended across the entire microwave, millimeter, and submillimeter wavelength ranges. The circuits are fabricated using standard microlithographic techniques and are compatible with uniform, large array formats. Unlike traditional monolithic bolometers that make use of micromachined structures, the THM employs the decoupling between electrons and phonons at millikelvin temperatures to provide thermal isolation. There is no fragile membrane in the structure for thermal isolation, which improves the fabrication yield.

Hsieh, Wen-Ting↗
DOE OSTI2024

Scattering phase shifts from a quantum computer

We calculate two-body scattering phase shifts on a quantum computer using a leading order short-range effective field theory Hamiltonian. The algorithm combines the variational quantum eigensolver and the quantum subspace expansion. As an example, we consider scattering in the deuteron 3S1 partial wave. We calculate scattering phase shifts with a quantum simulator and on real hardware. Here, we also study how noise impacts these calculations and discuss noise mitigation required to extend our work to larger quantum processing units. With current hardware, up to five superconducting qubits can produce acceptable results, and larger calculations will require a significant noise reduction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1989

Radiative transfer theory for inhomogeneous media with random extinction and scattering coefficients

The small-angle scattering approximation of the scalar radiative transfer equation (RTE) is examined for the case where the extinction and scattering coefficients have a component that is a deterministic function of position along the propagation path and a component that is a random function of position transverse to the propagation direction. It is found that the resulting stochastic RTE can be reduced to a system of two stochastic integrodifferential equations for the average and fluctuating components of the radiant intensity. Two transfer equations are obtained describing the average radiant intensity and the spatial correlation function of the intensity fluctuations. The average intensity equation is then solved and applied to a simple propagation scenario. An approximate solution is also derived for the equation giving the correlation function. The developed equations can be applied to problems involving short wavelength electromagnetic wave propagation through media possessing the variable characteristics of turbulence and turbidity, such as plasmas, the atmosphere, and the ocean.

Manning, Robert M.↗
DOE OSTI2023

Measures of complexity and entanglement in many-fermion systems

There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in the case of CI calculations reaches about 20 billion terms [Johnson, arXiv:1809.07869]. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. Further, the canonical wave functions and/or natural orbitals [Löwdin, Adv. Phys. 5, 1 (1956); Löwdin and Shull, Phys. Rev. 101, 1730 (1956); Bardeen et al., Phys. Rev. 108, 1175 (1957); N. N. Bogoljubov, Il Nuovo Cimento 7, 794 (1958); Valatin, Il Nuovo Cimento 7, 843 (1958); de Gennes, Superconductivity of Metals and Alloys (CRC Press, Boca Raton, FL, 1999); Ring and Schuck, The Nuclear Many-Body Problem, 1st ed. (Springer-Verlag, Berlin, 2004)] and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex nonequilibrium time-dependent process, induced nuclear fission described within a real-time density functional theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short-range correlations between fermions. The orbital entanglement entropy of the fissioning nucleus illustrates the localization mechanism of the many-body wave function in Fock and/or Hilbert space. The (minimal) number of Slater determinants required to represent such a complex many-body wave function with a well-defined number of particles in the case presented here is about 10 500 . The realistic case of the highly nonequilibrium nuclear fission process illustrated here is equivalent to a system of 23.328×10 9 interacting quantum spin-1/2 particles, a very large system for the study of quantum entanglement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗