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DOE OSTI2021

Pressure Effects on the Relaxation of an Excited Ethane Molecule in High-Pressure Bath Gases

Here, we use molecular dynamics to calculate the rotational and vibrational energy relaxation of C 2 H 6 in Ar, Kr, and Xe bath gases over a pressure range of 10 to 400 atm and at temperatures of 300 K and 800 K. The C 2 H 6 is instantaneously excited by 80 kcal/mol randomly distributed into both vibrational and rotational modes. The computed relaxation rates show little sensitivity to the identity of the noble gas in the bath. Vibrational relaxation rates show a non-linear pressure dependence at 300 K. At 800 K the reduced range of bath gas densities covered by the range of pressures do not yet show any non-linearity in the pressure dependence. Rotational relaxation is characterized with two relaxation rates. The slower rate is comparable to the vibrational relaxation rate. The faster rate has a linear pressure dependence at 300 K but an irregular, nonlinear pressure dependence at 800 K. To understand this, a model was developed based on approximating the periodic box used in the molecular dynamics simulations by an equal-volume collection of cubes where each cube is sized to allow only single occupancy by the noble gas or the molecule. Combinatorial statistics then leads to a pressure and temperature dependent analytic distribution of the bath gas species the molecule encounters in a collision. This distribution, the dissociation energy of molecule/bath gas complexes and bath gas clusters, and the computed energy release per collision combine to show that only at 300 K is the energy release sufficient to dissociate likely complexes and clusters. This suggests that persistent and pressure-dependent clusters and complexes at 800 K may be responsible for the non-linear pressure dependence of rotational relaxation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Physically-based strength model of tantalum incorporating effects of temperature, strain rate and pressure

In this work, we develop a tantalum strength model that incorporates e ects of temperature, strain rate and pressure. Dislocation kink-pair theory is used to incorporate temperature and strain rate e ects while the pressure dependent yield is obtained through the pressure dependent shear modulus. Material constants used in the model are parameterized from tantalum single crystal tests and polycrystalline ramp compression experiments. It is shown that the proposed strength model agrees well with the temperature and strain rate dependent yield obtained from polycrystalline tantalum experiments. Furthermore, the model accurately reproduces the pressure dependent yield stresses up to 250 GPa. The proposed strength model is then used to conduct simulations of a Taylor cylinder impact test and validated with experiments. This approach provides a physically-based multi-scale strength model that is able to predict the plastic deformation of polycrystalline tantalum through a wide range of temperature, strain and pressure regimes.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Evidence for a defect level above the conduction band edge of InAs/InAsSb type-II superlattices for applications in efficient infrared photodetectors

We report pressure-dependent photoluminescence (PL) experiments under hydrostatic pressures up to 2.16 GPa on a mid-wave infrared InAs/InAs{sub 0.86}Sb{sub 0.14} type-II superlattice (T2SL) structure at different pump laser excitation powers and sample temperatures. The pressure coefficient of the T2SL transition was found to be 93 ± 2 meV·GPa{sup −1}. The integrated PL intensity increases with pressure up to 1.9 GPa then quenches rapidly indicating a pressure induced level crossing with the conduction band states at ∼2 GPa. Analysis of the PL intensity as a function of excitation power at 0, 0.42, 1.87, and 2.16 GPa shows a clear change in the dominant photo-generated carrier recombination mechanism from radiative to defect related. From these data, evidence for a defect level situated at 0.18 ± 0.01 eV above the conduction band edge of InAs at ambient pressure is presented. This assumes a pressure-dependent energy shift of −11 meV·GPa{sup −1} for the valence band edge and that the defect level is insensitive to pressure, both of which are supported by an Arrhenius activation energy analysis.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2007

Calculational and Experimental Investigations of the Pressure Effects on Radical - Radical Cross Combinations Reactions: C2H5 + C2H3

Pressure-dependent product yields have been experimentally determined for the cross-radical reaction C2H5 + C2H3. These results have been extended by calculations. It is shown that the chemically activated combination adduct, 1-C4H8*, is either stabilized by bimolecular collisions or subject to a variety of unimolecular reactions including cyclizations and decompositions. Therefore the "apparent" combination/disproportionation ratio exhibits a complex pressure dependence. The experimental studies were performed at 298 K and at selected pressures between about 4 Torr (0.5 kPa) and 760 Torr (101 kPa). Ethyl and vinyl radicals were simultaneously produced by 193 nm excimer laser photolysis of C2H5COC2H3 or photolysis of C2H3Br and C2H5COC2H5. Gas chromatograph/mass spectrometry/flame ionization detection (GC/MS/FID) were used to identify and quantify the final reaction products. The major combination reactions at pressures between 500 (66.5 kPa) and 760 Torr are (1c) C2H5 + C2H3 yields 1-butene, (2c) C2H5 + C2H5 yields n-butane, and (3c) C2H3 + C2H3 yields 1,3-butadiene. The major products of the disproportionation reactions are ethane, ethylene, and acetylene. At moderate and lower pressures, secondary products, including propene, propane, isobutene, 2-butene (cis and trans), 1-pentene, 1,4-pentadiene, and 1,5-hexadiene are also observed. Two isomers of C4H6, cyclobutene and/or 1,2-butadiene, were also among the likely products. The pressure-dependent yield of the cross-combination product, 1-butene, was compared to the yield of n-butane, the combination product of reaction (2c), which was found to be independent of pressure over the range of this study. The [ 1-C4H8]/[C4H10] ratio was reduced from approx.1.2 at 760 Torr (101 kPa) to approx.0.5 at 100 Torr (13.3 kPa) and approx.0.1 at pressures lower than about 5 Torr (approx.0.7 kPa). Electronic structure and RRKM calculations were used to simulate both unimolecular and bimolecular processes. The relative importance of C-C and C-H bond ruptures, cyclization, decyclization, and complex decompositions are discussed in terms of energetics and structural properties. The pressure dependence of the product yields were computed and dominant reaction paths in this chemically activated system were determined. Both modeling and experiment suggest that the observed pressure dependence of [1-C4H8]/[C4H10] is due to decomposition of the chemically activated combination adduct 1-C4H8* in which the weaker allylic C-C bond is broken: H2C=CHCH2CH3 yields C3H5 + CH3. This reaction occurs even at moderate pressures of approx.200 Torr (26 kPa) and becomes more significant at lower pressures. The additional products detected at lower pressures are formed from secondary radical-radical reactions involving allyl, methyl, ethyl, and vinyl radicals. The modeling studies have extended the predictions of product distributions to different temperatures (200-700 K) and a wider range of pressures (10(exp -3) - 10(exp 5) Torr). These calculations indicate that the high-pressure [1-C4H8]/[C4H10] yield ratio is 1.3 +/- 0.1.

Fahr, Askar↗

DOE OSTI2017

Predicting Large-scale Effects During Cookoff of Plastic-Bonded Explosives (PBX 9501 PBX 9502 and LX-14)

In this study, we have made reasonable cookoff predictions of large-scale explosive systems by using pressure-dependent kinetics determined from small-scale experiments. Scale-up is determined by properly accounting for pressure generated from gaseous decomposition products and the volume that these reactive gases occupy, e.g. trapped within the explosive, the system, or vented. The pressure effect on the decomposition rates has been determined for different explosives by using both vented and sealed experiments at low densities. Low-density explosives are usually permeable to decomposition gases and can be used in both vented and sealed configurations to determine pressure-dependent reaction rates. In contrast, explosives that are near the theoretical maximum density (TMD) are not as permeable to decomposition gases, and pressure-dependent kinetics are difficult to determine. Ignition in explosives at high densities can be predicted by using pressure-dependent rates determined from the low-density experiments as long as gas volume changes associated with bulk thermal expansion are also considered. In the current work, cookoff of the plastic-bonded explosives PBX 9501 and PBX 9502 is reviewed and new experimental work on LX-14 is presented. Reactive gases are formed inside these heated explosives causing large internal pressures. The pressure is released differently for each of these explosives. For PBX 9501, permeability is increased and internal pressure is relieved as the nitroplasticizer melts and decomposes. Internal pressure in PBX 9502 is relieved as the material is damaged by cracks and spalling. For LX-14, internal pressure is not relieved until the explosive thermally ignites. The current paper is an extension of work presented at the 26th ICDERS symposium [1].

42 ENGINEERING↗

DOE OSTI2021

Cookoff of Black Powder and Smokeless Powder

We have completed a series of both vented and sealed cookoff experiments of black powder and smokeless powder in our Sandia Instrumented Thermal Ignition (SITI) apparatus at bulk densities of 1078 and 729 kg/m 3 , respectively. The confining aluminum cylinder was ramped from room temperature to a set point temperature and then held at the setpoint temperature until ignition. The setpoint temperatures varied between 495 to 523 K for the black powder and 401 to 412 K for the more sensitive smokeless powder. The vented experiments show a significant delay in thermal ignition, indicating that the ignition is dependent on pressure. Post experimental debris shows greater violence for our smokeless powder experiments than our black powder experiments. A simplified universal cookoff model (UCM) was calibrated using the black powder and smokeless powder SITI data and used to predict pressurization and thermal ignition. The current work presents the first calibration of the UCM with a double base propellant. Finally, this work also presents the first pressure-dependent cookoff model for black powder and smokeless powder.

42 ENGINEERING↗

NASA NTRS1992

Constraints on the thermal evolution of Venus inferred from Magellan data

The impact craters with diameters from 1.5 to 280 km compiled from Magellan observations indicate that the crater population on Venus has a completely spatially random distribution and the size/density distribution of craters with diameters greater than or equal to 35 km is consistent with a 'production' population with an age of 500 plus or minus 250 m.y. The similarity in size distribution from area to area indicates that the crater distribution is independent of crater size. Also, the forms of the modified craters are virtually identical to those of the pristine craters. These observations imply that Venus reset its cratering record by global resurfacing 500 m.y. ago, and resurfacing declined relatively fast. The fact that less than 40 percent of all craters have been modified and that the few volcanically embayed craters are located on localized tectonic regions indicate that only minor and localized volcanism and tectonism have occurred since the latest vigorous resurfacing event approximately 500 m.y. ago and the interior of Venus has been solid and possibly colder than Earth's. This is because the high-temperature lithosphere of Venus would facilitate upward ascending of mantle plumes and result in extensive volcanism if the venusian upper mantle were as hot as or hotter than Earth's. Therefore, the present surface morphology of Venus may provide useful constraints on the pattern of that vigorous convection, and possibly on the thermal state of the venusian mantle. We examine this possibility through numerical calculations of three-dimensional thermal convection models in a spherical shell with temperature- and pressure-dependent Newtonian viscosity, temperature-dependent thermal diffusivity, pressure-dependent thermal expansion coefficient, and time-dependent internal heat production rate solar magnitude.

Arkani-Hamed, Jafar↗

DOE OSTI2020

Sensitivity of pore collapse heating to the melting temperature and shear viscosity of HMX

A multiscale modeling strategy is used to quantify factors governing the temperature rise in hot spots formed by pore collapse from supported and unsupported shock waves in the high explosive HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine). Two physical aspects are examined in detail, namely the melting temperature and liquid shear viscosity. All-atom molecular dynamics simulations of phase coexistence are used to predict the pressure-dependent melting temperature up to 5 GPa. Equilibrium simulations and the Green–Kubo formalism are used to obtain the temperature- and pressure-dependent liquid shear viscosity. Starting from a simplified continuum-based grain-scale model of HMX, in this study we systematically increase the complexity of treatments for the solid–liquid phase transition and liquid shear viscosity in simulations of pore collapse. Using a realistic pressure-dependent melting temperature completely suppresses melting for supported shocks, which is otherwise predicted when treating it as a constant determined at atmospheric pressure. Alternatively, melt pools form around collapsed pores when the pressure (and melting temperature) are reduced during the release stage of unsupported shocks. Capturing the pressure dependence of the shear viscosity increases the peak temperature of melt pools by hundreds of Kelvin through viscous work. The complicated interplay of the solid-phase plastic work, solid–liquid phase transition, and liquid-phase viscous work identified here motivate taking a systematic approach to building increasingly complex grain-scale models.

36 MATERIALS SCIENCE↗

NASA NTRS2000

Vapor Transport Within the Thermal Diffusion Cloud Chamber

A review of the equations used to determine the 1-D vapor transport in the thermal diffusion cloud chamber (TDCC) is presented. These equations closely follow those of the classical Stefan tube problem in which there is transport of a volatile species through a noncondensible, carrier gas. In both cases, the very plausible assumption is made that the background gas is stagnant. Unfortunately, this assumption results in a convective flux which is inconsistent with the momentum and continuity equations for both systems. The approximation permits derivation of an analytical solution for the concentration profile in the Stefan tube, but there is no computational advantage in the case of the TDCC. Furthermore, the degree of supersaturation is a sensitive function of the concentration profile in the TD CC and the stagnant background gas approximation can make a dramatic difference in the calculated supersaturation. In this work, the equations typically used with a TDCC are compared with very general transport equations describing the 1-D diffusion of the volatile species. Whereas no pressure dependence is predicted with the typical equations, a strong pressure dependence is present with the more general equations given in this work. The predicted behavior is consistent with observations in diffusion cloud experiments. It appears that the new equations may account for much of the pressure dependence noted in TDCC experiments, but a comparison between the new equations and previously obtained experimental data are needed for verification.

Ferguson, Frank T.↗

DOE OSTI2025

Low fractional volume superconductivity in single crystals of Pr{sub 4}Ni{sub 3}O{sub 10} under pressure

Magnetotransport measurements of P⁢r4⁢N⁢i3⁢O10 single crystals performed under externally applied pressures up to 73 GPa in diamond anvil cells with either KBr or Nujol oil as pressure media yield signatures of superconductivity with a maximum onset temperature of approximately 31 K. True zero resistance was not observed, consistent with a nonpercolating superconducting volume fraction. Magnetization measurements provided corroborating evidence of superconductivity, with a pressure-dependent diamagnetic signal occurring below the onset temperature, and an estimate from the absolute value of the susceptibility suggests a superconducting volume fraction on the order of 10%. We observe sample to sample variations in the magnitude and pressure dependence of 𝑇𝑐 as well as a dependence on the configuration of electrical contacts on a given sample. Possible causes of this behavior may be significant inhomogeneities in the pressure and/or damage to the samples induced by the pressure media as well as inhomogeneities in the crystals themselves. The results imply that our as-grown P⁢r4⁢N⁢i3⁢O10 single crystals are not bulk superconductors but that there is a minority structure present within the crystals that is indeed superconductin

Chen, Xinglong↗

DOE OSTI2014

High tunability of the work function of (001) surface of ReO{sub 3} with O-vacancies: First principles analysis

Physical and chemical properties of transition metal oxides are central to the emerging field of oxide electronics. However, they are greatly influenced by defects, particularly, oxygen vacancies, which are always present in oxides. Here, we show how the control of oxygen vacancies at (001) surface of ReO{sub 3} can be used to tune its work function from 7 to 3 eV, based on first-principles density functional theoretical calculations of its structure, electronic and magnetic properties. The work function is shown to correlate directly with the stability of surface and exhibit a linear dependence on surface energy. We further assess the stability of ReO{sub 3} surface by determining its phonon dispersion, and explain how the surface stresses effectively strengthen structural instability leading to size dependence of its pressure dependent structural phase transitions observed experimentally. Our results highlight how significantly oxygen vacancies alter the work function of a metallic oxide and has important consequences to development of electronic devices and catalysts based on oxide heterostructures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2013

THE HABITABLE ZONE OF EARTH-LIKE PLANETS WITH DIFFERENT LEVELS OF ATMOSPHERIC PRESSURE

As a contribution to the study of the habitability of extrasolar planets, we implemented a one-dimensional energy balance model (EBM), the simplest seasonal model of planetary climate, with new prescriptions for most physical quantities. Here we apply our EBM to investigate the surface habitability of planets with an Earth-like atmospheric composition but different levels of surface pressure. The habitability, defined as the mean fraction of the planet's surface on which liquid water could exist, is estimated from the pressure-dependent liquid water temperature range, taking into account seasonal and latitudinal variations of surface temperature. By running several thousands of EBM simulations we generated a map of the habitable zone (HZ) in the plane of the orbital semi-major axis, a, and surface pressure, p, for planets in circular orbits around a Sun-like star. As pressure increases, the HZ becomes broader, with an increase of 0.25 AU in its radial extent from p = 1/3 to 3 bar. At low pressure, the habitability is low and varies with a; at high pressure, the habitability is high and relatively constant inside the HZ. We interpret these results in terms of the pressure dependence of the greenhouse effect, the efficiency of horizontal heat transport, and the extent of the liquid water temperature range. Within the limits discussed in the paper, the results can be extended to planets in eccentric orbits around non-solar-type stars. The main characteristics of the pressure-dependent HZ are modestly affected by variations of planetary properties, particularly at high pressure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

An integrated EOS, pore‐crush, strength and damage model framework for near‐field ground‐shock

Abstract An integrated Equation of State (EOS) and strength/pore‐crush/damage model framework is provided for modeling near to source (near‐field) ground‐shock response, where large deformations and pressures necessitate coupling EOS with pressure‐dependent plastic yield and damage. Nonlinear pressure‐dependence of strength up to high‐pressures is combined with a Modified Cam‐Clay‐like cap‐plasticity model in a way to allow degradation of strength from pore‐crush damage, what we call the “Yp‐Cap” model. Nonlinear hardening under compaction allows modeling the crush‐out of pores in combination with a fully saturated EOS, that is, for modeling partially saturated ground‐shock response, where air‐filled voids crush. Attention is given to algorithmic clarity and efficiency of the provided model, and the model is employed in example numerical simulations, including finite element simulations of underground explosions to exemplify its robustness and utility.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2013

The W-W02 Oxygen Fugacity Buffer at High Pressures and Temperatures: Implications for f02 Buffering and Metal-silicate Partitioning

Oxygen fugacity (fO2) controls multivalent phase equilibria and partitioning of redox-sensitive elements, and it is important to understand this thermodynamic parameter in experimental and natural systems. The coexistence of a metal and its oxide at equilibrium constitutes an oxygen buffer which can be used to control or calculate fO2 in high pressure experiments. Application of 1-bar buffers to high pressure conditions can lead to inaccuracies in fO2 calculations because of unconstrained pressure dependencies. Extending fO2 buffers to pressures and temperatures corresponding to the Earth's deep interior requires precise determinations of the difference in volume (Delta) V) between the buffer phases. Synchrotron x-ray diffraction data were obtained using diamond anvil cells (DAC) and a multi anvil press (MAP) to measure unit cell volumes of W and WO2 at pressures and temperatures up to 70 GPa and 2300 K. These data were fitted to Birch-Murnaghan 3rd-order thermal equations of state using a thermal pressure approach; parameters for W are KT = 306 GPa, KT' = 4.06, and αKT = 0.00417 GPa K-1. Two structural phase transitions were observed for WO2 at 4 and 32 GPa with structures in P21/c, Pnma and C2/c space groups. Equations of state were fitted for these phases over their respective pressure ranges yielding the parameters KT = 190, 213, 300 GPa, KT' = 4.24, 5.17, 4 (fixed), and αKT = 0.00506, 0.00419, 0.00467 GPa K-1 for the P21/c, Pnma and C2/c phases, respectively. The W-WO2 buffer (WWO) was extended to high pressure by inverting the W and WO2 equations of state to obtain phase volumes at discrete pressures (1-bar to 100 GPa, 1 GPa increments) along isotherms (300 to 3000K, 100 K increments). The slope of the absolute fO2 of the WWO buffer is positive with increasing temperature up to approximately 70 GPa and is negative above this pressure. The slope is positive along isotherms from 1000 to 3000K with increasing pressure up to at least 100 GPa. The WWO buffer is at a higher fO2 than the IW buffer at pressures lower than 40 GPa, and the magnitude of this difference decreases at higher pressures. This qualitatively indicates an increasingly lithophile character for W at higher pressures. The WWO buffer was quantitatively applied to W metal-silicate partitioning by using the WWO-IW buffer difference in combination with literature data on W metal-silicate partitioning to model the exchange coefficient (KD) for the Fe-W exchange reaction. This approach captures the pressure dependence of W metal-silicate partitioning using the WWO-IW buffer difference and models the activities of the components in the silicate and metallic phases using an expression of the Gibbs excess energy of mixing. Calculation of KD along a peridotite liquidus predicts a decrease in W siderophility at higher pressures that supports the qualitative behavior predicted by the WWO-IW buffer difference, and agrees with findings of others. Comparing the competing effects of temperature and pressure on W metal-silicate partitioning, our results indicate that pressure exerts a greater effect.

Shofner, G. A.↗

DOE OSTI2023

Response of vibrational properties and thermal conductivity of perovskites to pressure

We study the response of SrTiO 3 and KTaO 3 's vibrational properties and thermal conductivity to pressurization. Our goal is to improve the understanding of the relationship between crystal structure, vibrational dynamics, and thermal conductivity in perovskites. We measure the thermal conductivity of SrTiO 3 and KTaO 3 up to 28 GPa by time-domain thermoreflectance. We also perform Raman scattering and stimulated Brillouin scattering measurements of SrTiO 3 and KTaO 3 to characterize changes in vibrational dynamics with pressure. The thermal conductivity of SrTiO 3 increases under pressure with a slope comparable to that of other perovskites whose thermal conductivity has been measured versus pressure. Alternatively, the thermal conductivity of KTaO 3 has a stronger pressure dependence than that of other materials with similar crystal structure. We correlate pressure-induced changes in Raman and Brillouin spectra with pressure-induced changes in thermal conductivity. We show that pressure-induced changes in phonon lifetimes dominate the pressure dependence of thermal conductivity. This study provides benchmark knowledge of why depends on pressure and improves understanding of structure/thermal-property relationships.

36 MATERIALS SCIENCE↗

DOE OSTI2015

In-Reactor Oxidation of Zircaloy-4 Under Low Water Vapor Pressures

Complementary in- and ex-reactor oxidation tests have been performed to evaluate the oxidation and hydrogen absorption performance of Zircaloy-4 (Zr-4) under relatively low partial pressures (300 and 1000 Pa) of water vapor at specified test temperatures (330° and 370°C). Data from these tests will be used to support fabrication of components intended for isotope-producing targets and provide information regarding the temperature and pressure dependence of oxidation and hydrogen absorption of Zr-4 over the specified range of test conditions. Comparisons between in- and ex- reactor test results were performed to evaluate the influence of irradiation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1987

Mod II engine performance

The testing of a prototype of an automotive Stirling engine, the Mod II, is discussed. The Mod II is a one-piece cast block with a V-4 single-crankshaft configuration and an annular regenerator/cooler design. The initial testing of Mod II concentrated on the basic engine, with auxiliaries driven by power sources external to the engine. The performance of the engine was tested at 720 C set temperature and 820 C tube temperature. At 720 C, it is observed that the power deficiency is speed dependent and linear, with a weak pressure dependency, and at 820 C, the power deficiency is speed and pressure dependent. The effects of buoyancy and nozzle spray pattern on the heater temperature spread are investigated. The characterization of the oil pump and the operating cycle and temperature spread tests are proposed for further evaluation of the engine.

Richey, Albert E.↗

DOE OSTI2015

Pressure-induced structures of Si-doped HfO{sub 2}

The effect of hydrostatic pressure on the structure of Si-doped HfO{sub 2} (Si:HfO{sub 2}) was studied by using a diamond anvil cell in combination with high-energy X-ray diffraction at a synchrotron source. Diffraction data were measured in situ during compression up to pressures of 31 GPa. Si:HfO{sub 2} with 3, 5, and 9 at. % Si were found to undergo a monoclinic to orthorhombic transition at pressures between 7 and 15 GPa. Whole pattern analysis was carried out using nonpolar (Pbca) and polar (Pca2{sub 1}) crystallographic models to investigate the symmetry of the observed high-pressure orthorhombic phase. Rietveld refinement results cannot discriminate a reliable difference between the Pbca and Pca2{sub 1} structures as they nearly equally model the measured diffraction data. The pressure dependent lattice parameters, relative volume, and spontaneous strain are reported.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗