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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 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Uranium Mill Tailings Radiation Control Act Title II DOE Due Diligence and Lessons Learned from a Previous Site Transfer - 20352

Title II of the Uranium Mill Tailings Radiation Control Act (UMTRCA) established that a government agency will provide perpetual care for closed uranium and thorium ore-processing sites that were operating under an NRC source material license in 1978 or were licensed thereafter. Commercial owners (licensees) operating under an NRC or agreement state specific license when UMTRCA was passed are responsible for conducting reclamation of any byproduct material remaining from uranium-ore processing operations in accordance with an NRC or agreement state approved reclamation plan. Reclamation includes both surface and groundwater remedies. Upon completion of reclamation and approval by NRC, the site is required to be transferred to either the host state or the DOE for long-term surveillance and maintenance. Since UMTRCA's enactment, six Title II sites have been transferred to DOE; an additional 24 Title II sites are anticipated to be transferred before 2050. DoE's role mandated under UMTRCA Title II as the long-term care custodian is to perform 'monitoring, maintenance, and emergency measures necessary to protect the public health and safety.' UMTRCA requires that the licensee pay a long-term surveillance charge 'sufficient to cover the annual costs of site surveillance.' However, at some sites such as the Bluewater, New Mexico, Disposal Site, this mandate has required additional effort and expense by DOE, beyond the originally anticipated and intended scope within UMTRCA, but within the authority of DOE under UMTRCA. In 1997, the Bluewater site became the second UMTRCA Title II site to be transferred to DOE. The site was the location of a uranium mill operated from 1953 until 1982. The specific licensee began site reclamation in 1991, and by 1995 all tailings and contaminated materials were encapsulated in two tailings disposal cells and other disposal areas. In addition to surface contamination, milling activities impacted groundwater in the two upper aquifers. In 1989, the specific licensee attempted active groundwater remediation; however, no significant reduction in contaminant concentrations was observed. As a result, the specific licensee applied to NRC for alternate concentration limits (ACLs) in 1990, which were approved in 1996 as being protective, after additional corrective actions were performed. Since transfer of the Bluewater site to DOE, unforeseen challenges have occurred, requiring additional actions. The first challenge is the occurrence of surface depressions located on the northern section of the main tailings disposal cell. The depressions were first observed during DoE's initial inspection in 1998; however, evidence of these can be observed on satellite images taken prior to transfer. Since being first observed, the depressions have continued to grow both in depth and areal extent. Due to the design of the main tailings disposal cell, the depressions impede storm water from being effectively shed off the 101- hectare (250-acre) top slope of the main tailings disposal cell. Instead, storm water accumulates in the depressions, forming a large ephemeral pond that has stored up to 16.3 x 10{sup 6} liters (4.3 million gallons) of stormwater. The ponding poses a potential risk to the integrity of the main tailings disposal cell in the case of a large storm event, with the potential to cause the pond to overtop and erode the cover material and underlying waste. DOE has taken a number of short-term actions to monitor, measure, and reduce the ponding and is currently working with the US Army Corps of Engineers to design and construct a repair. Additional challenges are associated with groundwater at the Bluewater site. Nine wells were present on the 1335-hectare (3300-acre) site upon transfer. Groundwater compliance was called into question after the State of New Mexico reduced its uranium groundwater standard from 5.0 to 0.03 milligrams per liter in 2004, and when an ACL for uranium was exceeded in a site monitoring well in 2010. Acquiring historical groundwater data and subsequent evaluations as well as additional DOE groundwater monitoring led to installing 10 new monitoring wells and performing additional site hydrogeology recharacterization. DOE continues to evaluate groundwater conditions at the site and works with the NRC to determine regulatory requirements and a path forward. As a result of lessons learned at the Bluewater site and other Title II sites, improved processes have been implemented at a programmatic level to increase due diligence before site transfer and prevent similar issues from occurring at other UMTRCA Title II sites under long-term management. DoE's due diligence process is documented in the Process for Transition of UMTRCA Title II Disposal Sites to DOE for Long-Term Surveillance and Maintenance and is designed to ensure that DOE has no technical or compliance concerns with regulatory decisions that might compromise protectiveness following site transfer to DOE. Implementation of the due diligence process has increased DoE's role prior to site transfer and has been effective in identifying potential issues. Actions by NRC and specific licensees, in response to enhanced due diligence efforts by DOE, are expected to minimize, if not totally prevent, the need for unanticipated actions by DOE pertaining to the surface and groundwater remedies after site transfer. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Review of Pantex Radiation Safety Department 2020 Backup Dosimetry Processing Methodology

In the first quarter (Q1) of Calendar Year 2020, the Pantex Radiation Safety Department (Pantex) experienced various issues and failures with their dosimeter processing equipment. Efforts to repair the equipment resulted in limited functionality without the ability to process dosimeters assigned to personnel for monitoring dose. As a result of the impairments to the dosimeter processing equipment, Pantex called upon Nevada National Security Site (NNSS) for support, as their designated backup processor. In January of 2021, LLNL Subject Matter Experts in External Dosimetry started an NNSA-requested review of Pantex’s personnel doses in Q1 2020. Its focus was the technical validity of the means and methods used by Pantex and its conclusions and provide a level of confidence to National Nuclear Security Administration (NNSA) that the resulting personnel doses were reasonable, conservative, and defensible.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2024

Micropinch formation dynamics in X pinches

High temporal resolution x-ray streak camera studies of micropinch formation in Cu hybrid x pinches reveal key plasma conditions. Analysis of Ne-like Cu lines indicate an average electron temperature of about 200 eV and 4.5×10 28 m -3 electron density. Here, the spectra suggest that the electron temperature jumps to about 1 keV, inferred from the continuum and the postcontinuum line emission that includes Li-like Cu lines. There is no sign of a rapid temperature change or a substantial surge in radiation emission during the 200 ps precontinuum x-ray burst, suggesting that the radiative collapse process does not play a major role in micropinch formation. Two-dimensional extended Magnetohydrodynamic (MHD) simulations, coupled to a collisional-radiative spectral analysis code, suggest the significance of the rapid radial implosion of high-temperature, low-density plasma, the axial outflow, and the dynamic plasma pressure in micropinch formation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2001

Mid- and far-infrared spectroscopic studies of the influence of temperature, ultraviolet photolysis and ion irradiation on cosmic-type ices

Infrared (IR) studies of laboratory ices can provide information on the evolution of cosmic-type ices as a function of different simulated space environments involving thermal, ultraviolet (UV), or ion processing. Laboratory radiation experiments can lead to the formation of complex organic molecules. However, because of our lack of knowledge about UV photon and ion fluxes, and exposure lifetimes, it is not certain how well our simulations represent space conditions. Appropriate laboratory experiments are also limited by the absence of knowledge about the composition, density, and temperature of ices in different regions of space. Our current understanding of expected doses due to UV photons and cosmic rays is summarized here, along with an inventory of condensed-phase molecules identified on outer solar system surfaces, comets and interstellar grains. Far-IR spectra of thermally cycled H2O are discussed since these results reflect the dramatic difference between the amorphous and crystalline phases of H2O ice, the most dominant condensed-phase molecule in cosmic ices. A comparison of mid-IR spectra of products in proton-irradiated and UV-photolyzed ices shows that few differences are observed for these two forms of processing for the simple binary mixtures studied to date. IR identification of radiation products and experiments to determine production rates of new molecules in ices during processing are discussed. A new technique for measuring intrinsic IR band strengths of several unstable molecules is presented. An example of our laboratory results applied to Europa observations is included.

Spectrophotometry, Infrared/methods↗
NASA NTRS2024

Space Weather 101

Earth has an intrinsic magnetic field. Most people know this, because they use the magnetized needle of a compass to locate the cardinal directions north, east, south, and west. Most people don’t realize however, that Earth’s magnetic field extends well out into space where it meets, combines, and interacts with the Sun’s much stronger magnetic field. The interactions happen because the Sun sends out a steady stream of mostly protons and electrons in all directions along its magnetic field -- the solar wind. The Sun also produces continuous light emissions in infrared to ultraviolet to X-ray, in addition to eruptive emissions of X-rays and bulk ionized gas, called flares and coronal mass ejections. The ionizing radiation from the Sun striking our upper atmosphere creates a layer of ionized gas that leads to our own outflowing ionized gas, called plasma, along Earth’s magnetic field lines. The Sun’s outflowing solar wind and coronal mass ejections, together with its large magnetic field, drive strong responses inside Earth’s magnetic and plasma system. Together with cosmic radiation, these processes in the space environment are called Space Weather. That term includes the responses Earth’s magnetized plasma system has to these external drivers, which cause dangerous conditions for astronauts and satellites in space, as well as to us and our systems in the atmosphere and on the ground. This lecture is intended to make you aware of the risks and lead you to a basic awareness of the processes going on in our near-Earth space environment.

Space Weather↗
DOE OSTI2022

Transient Radiation-Induced Berkelium(III) and Californium(III) Redox Chemistry in Aqueous Solution

Despite the significant impact of radiation-induced redox reactions on the accessibility and lifetimes of actinide oxidation states, fundamental knowledge of aqueous actinide metal ion radiation chemistry is limited, especially for the late actinides. A quantitative understanding of these intrinsic radiation-induced processes is essential for investigating the fundamental properties of these actinides. We present here a picosecond electron pulse reaction kinetics study into the radiation-induced redox chemistry of trivalent berkelium (Bk(III)) and californium (Cf(III)) ions in acidic aqueous solutions at ambient temperature. New, and first of a kind, second-order rate coefficients are reported for the transient radical-induced reduction of Bk(III) and Cf(III) by the hydrated electron (eaq−) and hydrogen atom (H•), demonstrating significant reactivity (up to 1011M-1s-1) indicative of a preference of these metals to adopt divalent states. Additionally, we reportthe first-ever second-order rate coefficients for the transient radical-induced oxidation of these elements by reaction with hydroxyl (•OH) and nitrate (NO3•) radicals, which also exhibited fast reactivity (ca. 108 M-1s-1). Transient Cf(II), Cf(IV), and Bk(IV) absorption spectra are also reported. Overall, the presented data highlight the existence of rich, complex, intrinsic late actinide radiation-induced redox chemistry that has the potential to influence the findings of other areas of actinide science.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2013

3D Radiative Transfer Effects in Multi-Angle/Multi-Spectral Radio-Polarimetric Signals from a Mixture of Clouds and Aerosols Viewed by a Non-Imaging Sensor

When observing a spatially complex mix of aerosols and clouds in a single relatively large field-of-view, nature entangles their signals non-linearly through polarized radiation transport processes that unfold in the 3D position and direction spaces. In contrast, any practical forward model in a retrieval algorithm will use only 1D vector radiative transfer (vRT) in a linear mixing technique. We assess the difference between the observed and predicted signals using synthetic data from a high-fidelity 3D vRT model with clouds generated using a Large Eddy Simulation model and an aerosol climatology. We find that this difference is signal--not noise--for the Aerosol Polarimetry Sensor (APS), an instrument developed by NASA. Moreover, the worst case scenario is also the most interesting case, namely, when the aerosol burden is large, hence hase the most impact on the cloud microphysics and dynamics. Based on our findings, we formulate a mitigation strategy for these unresolved cloud adjacency effects assuming that some spatial information is available about the structure of the clouds at higher resolution from "context" cameras, as was planned for NASA's ill-fated Glory mission that was to carry the APS but failed to reach orbit. Application to POLDER (POLarization and Directionality of Earth Reflectances) data from the period when PARASOL (Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar) was in the A-train is briefly discussed.

APS↗
NASA NTRS1998

Airborne lidar observations of smoke haze during SCAR-B 1995

The Smoke, Clouds, Aerosol, and Radiation Brazil(SCAR-B) field campaign was conducted to study the effects that widespread and persistent biomass burning have upon radiative and chemical processes in the atmosphere. The radiative transfer characteristics of the atmosphere are altered by the introduction of particulate and gaseous materials which are the products of the combustion of vegetative material at ground level. These substances are transported and distributed horizontally and vertically by atmospheric dynamical processes which may be perturbed by the heat energy from the fires. As the pollutants disperse, their physical and chemical properties change substantially. A complete description of the effects of smoke requires that the evolution back to the natural situation be fully examined. A most important component of smoke haze investigation is finding its vertical and horizontal distribution in relation to the driving factors of dynamics and the related horizontal transport. In this presentation, we employ data from the Cloud Lidar System(CLS), carried aboard the NASA ER-2 aircraft, to provide a unique view of the particulate or aerosol loading produced by fires, especially with regard to the geometrical distribution of the aerosols in the vertical plane. The lidar has the ability to measure aerosol optical properties in a continuous fashion at quite fine vertical and horizontal resolution. The results from the lidar provide measurements that are largely independent of influences that corrupt passive instruments and thus it can serve to corroborate their results. The extended horizontal and vertical range of lidar results can also augment ground based and airborne in situ measurements which have limited horizontal and vertical scope. We present the results of our analysis of CLS observations taken during the SCAR-B field campaign. Observations of the the aerosol optical thickness from the Aerosol Robotic Network(AERONET) of solar photometers are employed in conjunction with CLS data to derive extinction to backscatter ratio values which are used to convert the lidar backscatter coefficient into extinction coefficient. The extinction coefficient is integrated vertically to find aerosol optical thickness along ER-2 flight tracks. We use images of the CLS derived extinction coefficient to depict its horizontal and vertical distribution. Multispectral photometer optical thickness is used to compute the Angstrom exponent. With these, we examine the hypothesis that the values of extinction to backscatter ratio can be related to the Anstrom coefficient since both of these would be a function of the refractive index and size distribution of the aerosols.

Hart, William D.↗
NASA NTRS1984

Extinction of premixed flames by stretch and radiative loss

The extinction of laminar premixed flames by stretch and radiative loss is studied for the model problem of counterflow opposed-jet combustion by using the matched asymptotic expansion technique for the highly temperature sensitive processes of radiative heat loss and large-activation-energy reaction kinetics. Explicit expressions for the critical Damkoehler number at extinction are derived and the influence of upstream vs downstream heat losses assessed. Results show that stretch exerts a much stronger influence than radiative loss on flame extinction.

Sohrab, S. H.↗
NASA NTRS1980

A probabilistic approach to radiative energy loss calculations for optically thick atmospheres - Hydrogen lines and continua

An approximate probabilistic radiative transfer equation and the statistical equilibrium equations are simultaneously solved for a model hydrogen atom consisting of three bound levels and ionization continuum. The transfer equation for L-alpha, L-beta, H-alpha, and the Lyman continuum is explicitly solved assuming complete redistribution. The accuracy of this approach is tested by comparing source functions and radiative loss rates to values obtained with a method that solves the exact transfer equation. Two recent model solar-flare chromospheres are used for this test. It is shown that for the test atmospheres the probabilistic method gives values of the radiative loss rate that are characteristically good to a factor of 2. The advantage of this probabilistic approach is that it retains a description of the dominant physical processes of radiative transfer in the complete redistribution case, yet it achieves a major reduction in computational requirements.

Canfield, R. C.↗
DOE OSTI2025

Effective field theory for radiative corrections to charged-current processes. II. Axial-vector coupling

Here we discuss the hadronic structure-dependent radiative corrections to the axial-vector coupling that controls single-nucleon weak charged-current processes—commonly denoted by 𝑔 𝐴 . We match the Standard Model at the GeV scale onto chiral perturbation theory at next-to-leading order in the one-nucleon sector, in the presence of electromagnetic and weak interactions. As a result, we provide a representation for the corrections to 𝑔 𝐴 in terms of infrared finite convolutions of simple kernels with the single-nucleon matrix elements of time-ordered products of two and three quark bilinears (vector, axial-vector, and pseudoscalar). We discuss strategies to determine the required nonperturbative input from data, lattice-QCD (+QED), and possibly hadronic models. This work paves the way for a precise comparison of the values of the ratio 𝑔 𝐴 ⁡/𝑔 𝑉 extracted from experiment and from lattice QCD, which constrain physics beyond the Standard Model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Power balance and divertor asymmetries in the Super-X divertors of MAST-U using SOLPS-ITER

Spherical tokamaks (STs) present unique challenges and opportunities in the area of particle and power exhaust, intensified due to their more compact sizes. Substantial efforts are underway in STs to determine the limits in dissipative operational regimes and advanced divertor solutions, including at MAST-U which provides access to the Super-X divertor configuration. Power balance, and upper/lower divertor asymmetries have been studied using SOLPS-ITER simulations of the MAST-U Super-X divertor. A set of simulations with experimentally inferred transport coefficients with E x B and diamagnetic drifts activated, consisting of density and power scans, and high field side vs low field side gas puff locations, have been used for code experimentation to uncover trends beyond the current experimental parameter space. The upper biased asymmetry (U:L > 1) of the ratio of the peaks of the plasma energy flux densities at the outer targets increases with heating power and decreases with gas puff strength, going from symmetric to up to a factor of 15. The upper target electron temperature has been found to be a good ordering quantity for the magnitude of this asymmetry for all heating powers, gas puff strength, and gas puff locations. The lower divertor biased asymmetry (U:L < 1) of the radiation patterns processed through SOLPS-based bolometry synthetic diagnostics is in qualitative agreement with resistive bolometry experimental results, and it is in quantitative agreement with the trend of the total volume radiation within the divertors of SOLPS. However, radiation measurements alone are not sufficient to infer the magnitude of the asymmetry of the peaks of the power loads at the targets.

MAST-U↗
DOE OSTI2025

Direct numerical simulations for hybrid rocket boundary layers: Performance modeling and scaling

This paper presents a comprehensive performance and scaling analysis of direct numerical simulations for reacting boundary layers, focusing on slab burner configurations. Using a PETSc-based finite volume CFD framework, the study evaluates the scalability and computational cost of flow, chemistry, and radiation evaluations across 2D and 3D simulations. Polymethyl methacrylate (PMMA) is the fuel with pure O 2 as the oxidizer, modeled using a detailed chemical kinetics mechanism with 113 species and 660 reactions. A ray-tracing-based radiation solver, designed for distributed memory applications, is implemented to model radiation heat transfer. Parallel scalability is analyzed for the coupled flow, chemistry, and radiation heat transfer processes. Weak and strong scaling studies are conducted on up to 15,000 computational ranks, revealing robust performance when flow cells exceed 200 per rank. Chemistry evaluations dominate the computational cost in large 3D simulations, accounting for approximately 40% of the total runtime, while flow processes contribute around 35%, and radiation solver contributions remain below 10% due to reduced evaluation frequencies. GPU accelerated chemistry evaluation, implemented with Zero-RK, demonstrates significant promise, achieving up to a 4x speedup for workloads exceeding 30,000 cells per GPU. However, diminishing returns are observed for smaller workloads due to CPU-GPU communication overhead. This study identifies key challenges, including memory bottlenecks and the effects of domain partitioning on flow scalability, while highlighting the potential of GPU-accelerated chemistry to reduce computational costs. In conclusion, these findings provide realizable run configurations for 2D, 3D, and GPU-accelerated cases, offering insights for optimizing reactive flow solvers.

CFD Scalability↗
NASA NTRS2007

Radiation-Hardened Electronics for the Space Environment

RHESE covers a broad range of technology areas and products. - Radiation Hardened Electronics - High Performance Processing - Reconfigurable Computing - Radiation Environmental Effects Modeling - Low Temperature Radiation Hardened Electronics. RHESE has aligned with currently defined customer needs. RHESE is leveraging/advancing SOA space electronics, not duplicating. - Awareness of radiation-related activities through out government and industry allow advancement rather than duplication of capabilities.

Keys, Andrew S.↗
NASA NTRS2006

A Multi-scale Modeling System: Developments, Applications and Critical Issues

A multi-scale modeling framework (MMF), which replaces the conventional cloud parameterizations with a cloud-resolving model (CRM) in each grid column of a GCM, constitutes a new and promising approach. The MMF can provide for global coverage and two-way interactions between the CRMs and their parent GCM. The GCM allows global coverage and the CRM allows explicit simulation of cloud processes and their interactions with radiation and surface processes. A new MMF has been developed that is based the Goddard finite volume GCM (fvGCM) and the Goddard Cumulus Ensemble (GCE) model. This Goddard MMF produces many features that are similar to another MMF that was developed at Colorado State University (CSU), such as an improved .surface precipitation pattern, better cloudiness, improved diurnal variability over both oceans and continents, and a stronger, propagating Madden-Julian oscillation (MJO) compared to their parent GCMs using conventional cloud parameterizations. Both MMFs also produce a precipitation bias in the western Pacific during Northern Hemisphere summer. However, there are also notable differences between two MMFs. For example, the CSU MMF simulates less rainfall over land than its parent GCM. This is why the CSU MMF simulated less overall global rainfall than its parent GCM. The Goddard MMF overestimates global rainfall because of its oceanic component. Some critical issues associated with the Goddard MMF are presented in this paper.

Tao, Wei-Kuo↗
NASA NTRS2011

Microphysics in the Multi-Scale Modeling Systems with Unified Physics

In recent years, exponentially increasing computer power has extended Cloud Resolving Model (CRM) integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-km scales are resolved in horizontal domains as large as 10,000 km in two-dimensions, and 1,000 x 1,000 km2 in three-dimensions. Cloud resolving models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. Recently, a multi-scale modeling system with unified physics was developed at NASA Goddard. It consists of (l) a cloud-resolving model (Goddard Cumulus Ensemble model, GCE model), (2) a regional scale model (a NASA unified weather research and forecast, WRF), (3) a coupled CRM and global model (Goddard Multi-scale Modeling Framework, MMF), and (4) a land modeling system. The same microphysical processes, long and short wave radiative transfer and land processes and the explicit cloud-radiation, and cloud-surface interactive processes are applied in this multi-scale modeling system. This modeling system has been coupled with a multi-satellite simulator to use NASA high-resolution satellite data to identify the strengths and weaknesses of cloud and precipitation processes simulated by the model. In this talk, the microphysics developments of the multi-scale modeling system will be presented. In particular, the results from using multi-scale modeling system to study the heavy precipitation processes will be presented.

Tao, Wei-Kuo↗
NASA NTRS2012

The Radiation Belt Storm Probes Mission: Advancing Our Understanding of the Earth's Radiation Belts

We describe NASA's Radiation Belt Storm Probe (RBSP) mission, whose primary science objective is to understand, ideally to the point of predictability, the dynamics of relativistic electrons and penetrating ions in the Earth's radiation belts resulting from variable solar activity. The overarching scientific questions addressed include: 1. the physical processes that produce radiation belt enhancement events, 2. the dominant mechanisms for relativistic electron loss, and 3. how the ring current and other geomagnetic processes affect radiation belt behavior. The RBSP mission comprises two spacecraft which will be launched during Fall 2012 into low inclination lapping equatorial orbits. The orbit periods are about 9 hours, with perigee altitudes and apogee radial distances of 600 km and 5.8 RE respectively. During the two-year primary mission, the spacecraft orbits precess once around the Earth and lap each other twice in each local time quadrant. The spacecraft are each equipped with identical comprehensive instrumentation packages to measure, electrons, ions and wave electric and magnetic fields. We provide an overview of the RBSP mission, onboard instrumentation and science prospects and invite scientific collaboration.

Sibeck, David↗
DOE OSTI2020

Nucleus capture by macroscopic dark matter

For a class of macroscopic dark matter with a large interaction strength with Standard Model particles, a nucleus could be captured by the dense, heavy dark matter as it traverses ordinary material. The radiated photon carries most of the binding energy and is a characteristic signature for dark matter detection. We develop analytic formulas and present numerical results for this radiative capture process in the low energy, non-dipole limit. Large-volume neutrino detectors like NOνA, JUNO, DUNE and Super(Hyper)-K may detect multi-hit or single-hit radiative capture events and can search for dark matter up to one gram in mass.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗