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Rocket-Plume Spectroscopy Simulation for Hydrocarbon-Fueled Rocket Engines

The UV-Vis spectroscopic system for plume diagnostics monitors rocket engine health by using several analytical tools developed at Stennis Space Center (SSC), including the rocket plume spectroscopy simulation code (RPSSC), to identify and quantify the alloys from the metallic elements observed in engine plumes. Because the hydrocarbon-fueled rocket engine is likely to contain C2, CO, CH, CN, and NO in addition to OH and H2O, the relevant electronic bands of these molecules in the spectral range of 300 to 850 nm in the RPSSC have been included. SSC incorporated several enhancements and modifications to the original line-by-line spectral simulation computer program implemented for plume spectral data analysis and quantification in 1994. These changes made the program applicable to the Space Shuttle Main Engine (SSME) and the Diagnostic Testbed Facility Thruster (DTFT) exhaust plume spectral data. Modifications included updating the molecular and spectral parameters for OH, adding spectral parameter input files optimized for the 10 elements of interest in the spectral range from 320 to 430 nm and linking the output to graphing and analysis packages. Additionally, the ability to handle the non-uniform wavelength interval at which the spectral computations are made was added. This allowed a precise superposition of wavelengths at which the spectral measurements have been made with the wavelengths at which the spectral computations are done by using the line-by-line (LBL) code. To account for hydrocarbon combustion products in the plume, which might interfere with detection and quantification of metallic elements in the spectral region of 300 to 850 nm, the spectroscopic code has been enhanced to include the carbon-based combustion species of C2, CO, and CH. In addition, CN and NO have spectral bands in 300 to 850 nm and, while these molecules are not direct products of hydrocarbon-oxygen combustion systems, they can show up if nitrogen or a nitrogen compound is present as an impurity in the propellants and/or these can form in the boundary layer as a result of interaction of the hot plume with the atmosphere during the ground testing of engines. Ten additional electronic band systems of these five molecules have been included into the code. A comprehensive literature search was conducted to obtain the most accurate values for the molecular and the spectral parameters, including Franck-Cordon factors and electronic transition moments for all ten band systems. For each elemental transition in the RPSSC, six spectral parameters - Doppler broadened line width at half-height, pressure-broadened line width at half-height, electronic multiplicity of the upper state, electronic term energy of the upper state, Einstein transition probability coefficient, and the atomic line center - are required. Input files have been created for ten elements of Ni, Fe, Cr, Co, Cu, Ca, Mn, Al, Ag, and Pd, which retain only relatively moderate to strong transitions in 300 to 430 nm spectral range for each element. The number of transitions in the input files is 68 for Ni; 148 for Fe; 6 for Cr; 87 for Co; 1 for Ca; 3 for Mn; 2 each for Cu, Al, and Ag; and 11 for Pd.

Tejwani, Gopal D.↗

Modeling Global Indices for Estimating Non-Photosynthetic Vegetation Cover

Non-photosynthetic vegetation (NPV) includes plant litter, senesced leaves, and crop residues. NPV plays an essential role in terrestrial ecosystem processes, and is an important indicator of drought severity, ecosystem disturbance, agricultural resilience, and wildfire danger. Current moderate spatial resolution multispectral satellite systems (e.g., Landsat and Sentinel-2) have only a single band in the 2000–2500 nm shortwave infrared “SWIR2” range where non-pigment biochemical constituents of NPV, including cellulose and lignin, have important spectral absorption features. Thus, these current systems have suboptimal capabilities for characterizing NPV cover. This research used simulated spectral mixtures accounting for variability among NPV and soils to evaluate globally-appropriate hyperspectral and multispectral indices for estimation of fractional NPV cover. The Continuum Interpolated NPV Depth Index (CINDI), a weighted ratio index measuring lignocellulose absorption near 2100 nm, was found to produce the lowest error in estimating NPV cover. CINDI was less sensitive to variability in soil spectra and green vegetation cover than competing indices. While CINDI was sensitive to the relative water content of soil and NPV, this sensitivity allowed for correcting error in estimated NPV cover as water content increased. CINDI bands were less capable than Dual Absorption NPV Index (DANI) bands for maintaining continuity with the heritage Landsat SWIR2 band, but combining multiple CINDI bands demonstrated adequate continuity. Three SWIR2 bands with band centers at 2038, 2108, and 2211 nm can provide superior capabilities for future moderate resolution multispectral/superspectral systems targeting NPV monitoring, including the next generation Landsat mission (Landsat Next). These bands and the associated CINDI index provide potential for global NPV monitoring using a constellation of future superspectral sensors and imaging spectrometers, with applications including improving soil management, preventing land degradation, evaluating impacts of drought, mapping ecosystem disturbance, and assessing wildfire danger.

Index optimization↗

Comparison between Hayabusa 2 Spectral Measurements and Simulations

This paper compares recent Hayabusa 2 spectral measurements with state-of-the-art shock-layer radiation simulations resulting from the LAURA/HARA code suite. These simulations include coupled ablation, which accounts for the injection of ablation products into the flowfield, and coupled radiation, which accounts for radiative energy loss in the flowfield. To enable the coupled ablation simulations, a best-estimate model is developed for Hayabusa’s carbon-phenolic ablator, based on the limited available published information. The comparison between the simulations and measurements focuses on two atomic nitrogen lines and two atomic oxygen lines, as well as the CN Violet band system. For the atomic lines, the measurements and simulations agree within 25% over most of the trajectory. This excellent agreement is unprecedented for observed radiation measurements of atomic lines, where previous Stardust and Hayabusa 1 comparisons were significantly worse. The improved agreement for these Hayabusa 2 comparisons is both the result of improved measurement quality and enhanced flowfield/radiation modeling. To provide a link between these observed radiation measurements and the radiative heating to a vehicle surface, the recently developed flowfield property binning approach is used to identify flowfield properties that provide the dominant emission contribution to the measured spectrum. These identified flowfield properties are then shown to match those for the surface radiative heating to the currently developed Mars Sample Return (MSR) Earth Entry System (EES) at a specific trajectory point and surface location. This matching of flowfield properties indicates that this EES radiative heating and Hayabusa 2 observed radiation simulations are equivalent radiation problems. Therefore, the excellent agreement between Hayabusa 2 measurements and simulations may be leveraged to inform the radiation heating margin for the MSR EES.

Christopher O Johnston↗

Calibrating Laser Gas Measurements by Use of Natural CO2

An improved method of calibration has been devised for instruments that utilize tunable lasers to measure the absorption spectra of atmospheric gases in order to determine the relative abundances of the gases. In this method, CO2 in the atmosphere is used as a natural calibration standard. Unlike in one prior calibration method, it is not necessary to perform calibration measurements in advance of use of the instrument and to risk deterioration of accuracy with time during use. Unlike in another prior calibration method, it is not necessary to include a calibration gas standard (and the attendant additional hardware) in the instrument and to interrupt the acquisition of atmospheric data to perform calibration measurements. In the operation of an instrument of this type, the beam from a tunable diode laser or a tunable quantum-cascade laser is directed along a path through the atmosphere, the laser is made to scan in wavelength over an infrared spectral region that contains one or two absorption spectral lines of a gas of interest, and the transmission (and, thereby, the absorption) of the beam is measured. The concentration of the gas of interest can then be calculated from the observed depth of the absorption line(s), given the temperature, pressure, and path length. CO2 is nearly ideal as a natural calibration gas for the following reasons: CO2 has numerous rotation/vibration infrared spectral lines, many of which are near absorption lines of other gases. The concentration of CO2 relative to the concentrations of the major constituents of the atmosphere is well known and varies slowly and by a small enough amount to be considered constant for calibration in the present context. Hence, absorption-spectral measurements of the concentrations of gases of interest can be normalized to the concentrations of CO2. Because at least one CO2 calibration line is present in every spectral scan of the laser during absorption measurements, the atmospheric CO2 serves continuously as a calibration standard for every measurement point. Figure 1 depicts simulated spectral transmission measurements in a wavenumber range that contains two absorption lines of N2O and one of CO2. The simulations were performed for two different upper-atmospheric pressures for an airborne instrument that has a path length of 80 m. The relative abundance of CO2 in air was assumed to be 360 parts per million by volume (approximately its natural level in terrestrial air). In applying the present method to measurements like these, one could average the signals from the two N2O absorption lines and normalize their magnitudes to that of the CO2 absorption line. Other gases with which this calibration method can be used include H2O, CH4, CO, NO, NO2, HOCl, C2H2, NH3, O3, and HCN. One can also take advantage of this method to eliminate an atmospheric-pressure gauge and thereby reduce the mass of the instrument: The atmospheric pressure can be calculated from the temperature, the known relative abundance of CO2, and the concentration of CO2 as measured by spectral absorption. Natural CO2 levels on Mars provide an ideal calibration standard. Figure 2 shows a second example of the application of this method to Mars atmospheric gas measurements. For sticky gases like H2O, the method is particularly powerful, since water is notoriously difficult to handle at low concentrations in pre-flight calibration procedures.

Webster, Chris↗

Applications of the Lattice Boltzmann Method to Complex and Turbulent Flows

We briefly review the method of the lattice Boltzmann equation (LBE). We show the three-dimensional LBE simulation results for a non-spherical particle in Couette flow and 16 particles in sedimentation in fluid. We compare the LBE simulation of the three-dimensional homogeneous isotropic turbulence flow in a periodic cubic box of the size 1283 with the pseudo-spectral simulation, and find that the two results agree well with each other but the LBE method is more dissipative than the pseudo-spectral method in small scales, as expected.

Luo, Li-Shi↗

A line-binned treatment of opacities for the spectra and light curves from neutron star mergers

ABSTRACT The electromagnetic observations of GW170817 were able to dramatically increase our understanding of neutron star mergers beyond what we learned from gravitational waves alone. These observations provided insight on all aspects of the merger from the nature of the gamma-ray burst to the characteristics of the ejected material. The ejecta of neutron star mergers are expected to produce such electromagnetic transients, called kilonovae or macronovae. Characteristics of the ejecta include large velocity gradients, relative to supernovae, and the presence of heavy r-process elements, which pose significant challenges to the accurate calculation of radiative opacities and radiation transport. For example, these opacities include a dense forest of bound–bound features arising from near-neutral lanthanide and actinide elements. Here we investigate the use of fine-structure, line-binned opacities that preserve the integral of the opacity over frequency. Advantages of this area-preserving approach over the traditional expansion–opacity formalism include the ability to pre-calculate opacity tables that are independent of the type of hydrodynamic expansion and thus eliminate the computational expense of calculating opacities within radiation-transport simulations. Tabular opacities are generated for all 14 lanthanides as well as a representative actinide element, uranium. We demonstrate that spectral simulations produced with the line-binned opacities agree well with results produced with the more accurate continuous Monte Carlo Sobolev approach, as well as with the commonly used expansion–opacity formalism. The agreement between the line-binned and expansion–opacity results is explained as arising from the similarity in their opacities in the limit of low optical depth, where radiation transport is important in the ejecta. Additional investigations illustrate the convergence of opacity with respect to the number of included lines, and elucidate sensitivities to different atomic physics approximations, such as fully and semirelativistic approaches.

79 ASTRONOMY AND ASTROPHYSICS↗

Discrimination of alkalinity in granitoid Rocks: A potential TIMS application

In mineral exploration, the ability to distinguish and map petrochemical variations of magmatic rocks can be a useful reconnaissance tool. Alkalinity is one such petrochemical parameter and is used in the characterization of granitoid rocks. In quartz normative plutonic rocks, alkalinity is related to the composition and abundance of feldspars. Together with quartz abundance, knowledge of feldspar modes allows the classification of these igneous rocks according to the Streckeisen diagram. Alternative classification schemes rely on whole rock geochemistry instead of mineral identifications. The relative ease of obtaining whole rock analyses means that geochemical classifications tend to be favored in exploration geology. But the technique of thermal infrared spectroscopy of rocks yields information on mineralogy and is one that can be applied remotely. The goal of the current work then is to establish whether data from TIMS can be used to distinguish the mineralogical variations that relate to alkalinity. An ideal opportunity to test this thesis arises from the work presented in a paper by Dewitt (1989). This paper contains the results of mapping and analysis of Proterozoic plutonic rocks in north-central Arizona. The map resulting from this work delineates plutons according to alkalinity in an effort to establish a trend or polarity in the regional magmatism. Also contained within this paper are brief descriptions of the mineralogy of half of the region's plutons. This combination of mineralogical and geochemical information was the rationale behind choosing this area as a site for TIMS over flights. A portion of the region centered on the northern Bradshaw Mountains was selected because it contains plutons of all three alkalinity classifications (alkali-calcic, calc-alkalic, and calic) present on DeWitt's map within a relatively small area. The site was flown in August of 1994 and the data received a few days before the writing of this manuscript. Most of this paper is devoted to the description of laboratory based spectroscopy and spectral simulations. These are required to gain insight into the correct procedures for enhancing the relatively small differences in the low spectral resolution TIMS data.

Ruff, Steven W.↗

Multielectronic and multiatomic effects in the U O 4,5 x-ray absorption spectroscopy of uranium dioxide

In order to explain all of the spectral features observed in the U O 4,5 x-ray absorption spectrum of uranium dioxide (UO 2 ), it is necessary to include both multielectron effects and multiatomic effects. The 5d (core hole)-5f (electron) angular momentum coupling that gives rise to the giant resonance has been treated within ligand field density functional theory, and the electron scattering that generates the extended x-ray absorption fine structure has been included via the spectral simulation program FEFF: both within a UO 8 fluorite cluster picture. An atomic model is insufficient to explain all of the observed spectral features.

36 MATERIALS SCIENCE↗

Tip-Enhanced Raman Nanospectroscopy of Smooth Spherical Gold Nanoparticles

We record nanoscale-resolved chemical images of thiobenzonitrile (TBN)-functionalized smooth gold nanospheres on silicon via tip-enhanced Raman (TER) nano-spectroscopy. The recorded images trace the nascence of the familiar doughnut-shaped scattering profile of nanoparticles on silicon at its origin (the particle surface), which appears as a horseshoe-shaped scattering pattern under our experimental conditions. The local optical field maps are in agreement with their simulated finite-difference time-domain analogues. Analysis of the recorded spectra with the aid of ab initio molecular dynamics-based Raman spectral simulations further suggests that optical rectification and molecular charging take place throughout the course of atomic force microscopy-based TER nanoscale chemical imaging.

Bhattarai, Ashish↗

Spectroscopic Observation of the Stardust Re-Entry in the Near UV with SLIT: Deduction of Surface Temperatures and Plasma Radiation

Thermal radiation of the heat-shield and the emission of the post-shock layer around the Stardust capsule, during its re-entry, were detected by a NASA-led observation campaign aboard NASA's DC-8 airborne observatory involving teams from several nations. The German SLIT experiment used a conventional spectrometer, in a Czerny-Turner configuration (300 mm focal length and a 600 lines/mm grating), fed by fiber optics, to cover a wavelength range from 324 nm to 456 nm with a pixel resolution of 0.08 nm. The reentering spacecraft was tracked m uansuinaglly a camera with a view angle of 20 degrees, and light from the capsule was collected using a small mirror telescope with a view angle of only 0.45 degrees. Data were gathered with a measurement frequency of 5 Hz in a 30-second time interval around the point of maximum heating until the capsule left the field of view. The emission of CN (as a major ablation product), N2(+) and different atoms were monitored successfully during that time. Due to the nature of the experimental set up, spatial resolution of the radiation field was not possible. Therefore, all measured values represent an integration of radiation from the visible part of the glowing heat shield, and from the plasma in the post-shock region. Further, due to challenges in tracking not every spectrum gathered contained data. The measured spectra can be split up into two parts: (i) continuum spectra which represent a superposition of the heat shield radiation and the continuum radiation of potential dust particles in the plasma, and (ii) line spectra from the plasma in the shock layer. Planck temperatures (interpreted as the surface temperatures of the Stardust heat shield) were determined assuming either a constant surface temperature, or a temperature distribution deduced from numerical simulation. The constant surface temperatures are in good agreement with numerical simulations, but the peak values at the stagnation point are significantly lower than those in the numerical simulation if a temperature distribution over the surface is assumed. Emission bands of CN and N2(+) were tracked along the visible trajectory and compared to a spectral simulation with satisfying agreement. Values for the integrated radiation of the transitions of interest for these species were extracted from this comparison.

Winter, Michael W.↗

Parametric description of intermittent probability distribution functions in solar wind and magnetohydrodynamic turbulence

ABSTRACT In this work, we find empirical evidence that the scale-dependent statistical properties of solar wind and magnetohydrodynamic (MHD) turbulence can be described in terms of a family of parametric probability distribution functions (PDFs) known as Normal Inverse Gaussian (NIG). Understanding these PDFs is one of the most important goals in turbulence theory, as they are inherently connected to the intermittent properties of solar wind turbulence. We investigate the properties of PDFs of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics on a 23-yr-long sample of WIND data near 1 au and high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a $2048^3$ mesh are used to construct scale-dependent PDFs. The empirical PDFs are fitted to NIG distributions, which depend on four free parameters. Our analysis shows that NIG distributions accurately capture the evolution of the PDFs, with scale-dependent parameters, from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. We also show that empirically-measured NIG parameters exhibit well-defined scaling properties that are similar across the three empirical data sets, which may be indicative of universal behaviour.

Astronomy & Astrophysics↗

Spectral Method For Simulation Of Vortex Rings

Method of computation relying on spectral basis functions developed especially for simulation of axisymmetric vortex rings in incompressible, viscous fluid with quiescent far field. Contributes to understanding of flows in and around vortex rings during long propagation times, including such theoretically and practically important phenomena as drift and expansion of ring, "leapfrogging" and coalescence of two rings, and shedding of vorticity into wake of propagating ring.

Stanaway, S. K.↗

An Updated Model for the Effect of Atmospheric Absorption on Sounding Rockets

A very high-resolution R > 20,000 Far Ultraviolet full-disk, solar spectrograph will be launched in the Spring of 2023. This paper describes the in-flight wavelength calibration techniques and the fortuitous retrieval of Earth’s thermospheric information during the flight. Building and calibration of the Full-sun Ultraviolet Rocket Spectrograph (FURST) is currently underway. The purpose of this instrument is to obtain the highest resolution and most complete Far Ultra-Violet (FUV) spectra of the full disk Sun. This so-called "Sun-as-a-star" spectra will allow direct comparisons between our Sun and other stars measured by the Hubble Space Telescope(HST) and the upcoming James Webb Space Telescope (JWST). The Solar Physics groups at NASA Marshall Space Flight Center (MSFC) and Montana State University (MSU) have been developing the tools and procedures necessary to achieve the high spectral resolution goal. These include, among other things, improved tracking of error propagation, in-situ monitoring of the camera gain with a radioactive Fe-55 source, and the development of a simulated spectral calibration map under a noisy diagnostic-lamp signal. This mapping introduces a clocked CCD in order to obtain sub-pixel spectral resolution and overcome the Nyquist limit by about a factor of 2. Aside from the main purpose of FURST, we have been investigating the effect of absorption in the upper atmosphere at sounding-rocket altitudes (about 100-300 km). We present here an improved model of the optical depth caused by the thermospheric Oxygen cross-section and H and O self-absorption. This data-based model uses concentric spherical shells to account for the curvature of the Earth’s atmosphere and refraction. Using these calculations, we present the anticipated effect on the signal received by FURST, how that signal changes over the course of the flight-path These absorption peaks would provide wavelength fiducials at line-center that might add to in-flight calibration of the instrument. Many studies have found ways to correct for these so-called "Telluric" lines. However, it may be that these lines can in fact be a useful tool to further improve our calibration, rather than simply a nuisance to be corrected for! Finally, we discuss the inversion problem: how we could take actual flight data and back-out the atmospheric data (such as density and temperature) from any such sounding rocket flight that shows evidence of atmospheric absorption.

Nicolas Donders↗

A CLOUDY/XSPEC Interface

We discuss new functionality of the spectral simulation code CLOUDY which allows the user to calculate grids with one or more initial parameters varied and formats the predicted spectra in the standard FITS format. These files can then be imported into the x-ray spectral analysis software XSPEC and used as theoretical models for observations. We present and verify a test case. Finally, we consider a few observations and discuss our results.

Porter, R. L.↗

Investigation of computational and spectral analysis methods for aeroacoustic wave propagation

Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the capabilities of two traditional methods for spectral analysis, namely, the Blackman-Tukey method and periodogram method, are compared in estimating the spectra of a simple-periodic process. The periodogram is then applied to analyze transitory-deterministic processes. Finally, these two methods are compared with a more recent method, referred as the Weighted-Overlapped-Segment-Averaging (WOSA) method, in estimating the spectra of a chaotic (random-like) process. From the demonstrative case for the spectral analyses of data generated by simple-periodic process, the periodogram method is found to give a better estimate of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window is found to perform better with the periodogram method than with the Blackman-Tukey method. Finally, for the spectral analysis of data generated by the chaotic process, the periodogram method does not perform well, whereas, the WOSA and Blackman-Tukey methods give equivalently good results.

Vanel, Florence O.↗

Improved Simulations of Astrophysical Plasmas: Computation of New Atomic Data

Our research program is designed to carry out state-of-the-art atomic physics calculations crucial to advancing our understanding of fundamental astrophysical problems. We redress the present inadequacies in the atomic data base along two important areas: dielectronic recombination and inner-shell photoionization and multiple electron ejection/Auger fluorescence therefrom. All of these data are disseminated to the astrophysical community in the proper format for implementation in spectral simulation code.

Gorczyca, Thomas W.↗

A simple bidirectional-reflectance model applied to a tallgrass canopy

The present bidirectional reflectance model is used to simulate spectral reflectance direction-changes in a tallgrass canopy; comparisons with field measurements show generally good agreement. An examination of the effects of 'hot spot' and soil-reflection inhomogeneous canopy characteristics indicates that both modeled and observed reflectances are strongly backscattered in the red band, but there is a more symmetric back/forward-scattering distribution in the near-IR. Modeled simulations for three leaf-angle distributions show that hemispherical reflectance errors could be reduced at an optimal solar zenith angle having the same magnitude for the three leaf-angle distributions, but decreasing with increasing canopy leaf-area index.

Gao, W.↗

Rovibronic molecular line list for the $N_2(C^3Π_u–B^3Π_g)$ second positive system

Here, a line list for the N second positive system, $B^3Π_g—C^3Π_u$, has been compiled using the PGOPHER spectral simulation software. The line list extends the number of vibrational states of the $B^3Π_g$ up to v=29 and a maximum rotational state of J=150 for simulation temperatures up to 7000 K. New electronic–vibrational transition moments were calculated using refined potential energy curves and a transition dipole moment with the DUO software. Comparisons to experimental data and the SPECAIR software have been used to validate the new line list. The results are available in ASCII ExoMol .state and .trans files and as a PGOPHER input file for use in spectral analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗