This article reports new measurements of laser-induced plasma hypersonic expansion measurements of diatomic molecular cyanide (CN). Focused, high-peak power 1064-nm Q-switched radiation of the order of 1 TW/cm² generates optical breakdown plasma in a cell containing a 1:1 molar gas mixture of N₂ and CO₂ at a fixed pressure of 1.1 × 10⁵ Pascal and in a 100 ml/min flow of the mixture. Line-of-sight (LOS) analysis of recorded molecular spectra indicate the outgoing shockwave at expansion speeds well in excess of Mach number 5. Spectra of atomic carbon confirm an increased electron density near the shock wave, and equally, molecular CN spectra reveal higher excitation temperature near the shockwave. The results are consistent with corresponding high-speed shadow graphs obtained by visualization with an effective shutter speed of five n anosecond. In addition, LOS analysis and application of integral inversion techniques allow inferences about the spatio-temporal distribution of the plasma.

In this paper, we consider the temporal development of the optical density of the H$_\alpha$ spectral line in a hydrogen laser induced plasma. This is achieved by using the so-called duplication method in which the spectral line is re-imaged onto itself and the ratio of the spectral line with it duplication is taken to its measurement without the duplication. We asses the temporal development of the self-absorption of the H$_\alpha$ line by tracking the decay of duplication ratio from its ideal value of 2. We show that when 20% loss is considered along the duplication optical path length, the ratio is 1.8 and decays to a value of 1.25 indicating an optically thin plasma grows in optical density to an optical depth of 1.16 by 400 ns in the plasma decay for plasma initiation conditions using Nd:YAG laser radiation at 120 mJ per pulse in a 1.11$\times10^{5}$ Pa hydrogen/nitrogen gas mixture environment. We also go on to correct the H$_\alpha$ line profiles for the self-absorption impact using two methods. We show that a method in which the optical depth is directly calculated from the duplication ratio is equivalent to standard methods of self-absorption correction when only relative corrections to spectral emissions are needed.

Fundamental principles of classical (Newtonian) physics are employed to probe the cosmological lambda Λ; it yields the values ρ_vac = 2.61 x 10^-39 g cm^-3 and Λ = 4.87 x 10^-66 cm^-2. It is revealed that Λ is a fundamental physical constant defined by vacuum density-light speed ρ_vacc² correlation. However, the constant accelerates along the groups and periods of a universal spatial periodicity equivalent to the chemical periodicity. Previous results are cited to show that chemical elements are quantum harmonic (periodic) oscillators QHOs and their waveform oscillations exclusively define the vacuum field. The cosmological periodic unit CPU is introduced, it relies on the cosmological principle to argue that a relative physical quantity evaluated for the QHO applies to constituents of corresponding cosmological spatial quanta. Compelling evidences, backed with relevant data and quantitative expressions, are then presented to argue that: there was never a big bang, it is a Linde-universe sans “chaotic”; nature posts no singularity; mass does not curve spacetime, neither does metric space curvature trace directly to gravitation nor particle creation, gravity is classical, not quantum; reality is quadri-phasic not mono-phasic with a clear distinction between the atomic waveform defined with absolute atomic mass and condensed matter defined with relative atomic mass; every chemical element exists in three particle-generations thus, dark matter is invisible form (conjugate) of the visible element, its waveform manifests dark energy, it is not implicated in metric space expansion; Planck scale does not exist, radioactivity constrains fundamental length to atomic radius of the heaviest element.

In a previous paper\cite{simplified}, a variation of the Collision-time Statistics method was applied to identify the relevant perturbers for line broadening under the action of a constant magnetic field. As discussed, that version was simplified and inadequate for low magnetic field and/or large perturber mass (ions). The purpose of the present work is to augment the previous work, so that such cases, corresponding to the Larmor radius exceeding the maximum impact parameter, can be handed efficiently. The results may also be used to construct analytic, i.e. impact/unified models under the usual assumptions in these models.

Acne vulgaris is a chronic skin disease which occurs due to inflammation of the hair follicles and sebum-producing (sebaceous) glands of the skin called pilosebaceous unit and the anaerobic propionic acne bacterium, P.acne. Human sebum is dominantly made up of 57.5% of triglycerides and fatty acids, 26%wax esters, 12% Squalene and 4.5% Cholesterol. The increased level Androgen hormone, sebum lipid composition, P.acne overgrowth which induces monocytes and pro-inflammatory cytokines attract neutrophils, basophils, and T cells to the pilosebaceous unit and drive epithelial hyperproliferation i.e., Acne vulgaris. The actual biomolecular changes due to acne vulgaris disease are present in the blood and in the sebum and also in the noninvasive sample of human scalp hair follicles. The main objectives of the present study are to analyze human scalp hair follicles samples using FTIR-ATR spectroscopy to compare and discriminate the spectral signatures of acne vulgaris and healthy scalp hair tissue samples through acne bio-markers Protein, Amide I, Amide II and Squalene (LDL), using the method of internal ratio parameters.

Fundamental principles of classical (Newtonian) physics are employed to probe the cosmological lambda Λ; it yields the values ρvac = 2.61 x 10-39 g cm-3 and Λ = 4.78 x 10-62. The results reveal that Λ is a fundamental physical constant defined by vacuum density-light speed ρvacc2 correlation. However, the constant accelerates along the groups and periods of a universal spatial periodicity equivalent to the chemical periodicity. Previous results are cited to show that chemical elements are quantum harmonic (periodic) oscillators QHOs and their waveform oscillations exclusively define the vacuum field. A cosmological periodic unit CPU is introduced, it relies on the cosmological principle to argue that a relative physical quantity evaluated for the QHO applies to constituents of corresponding cosmological spatial quanta. Compelling evidences, backed with relevant data and quantitative expressions, are then presented to argue that: there was never a big bang, it is a Linde-universe sans “chaotic”; nature posts no singularity; mass does not curve spacetime, neither does metric space curvature trace directly to gravitation nor particle creation, gravity is classical, not quantum; reality is quadri-phasic not mono-phasic with a clear distinction between the atomic waveform defined with absolute atomic mass and condensed matter defined with relative atomic mass; every chemical element exists in three particle-generations thus, dark matter is invisible form (conjugate) of the visible element, its waveform manifests dark energy, it is not implicated in metric space expansion; Planck scale does not exist, radioactivity constrains fundamental length.

With new discoveries and insights in atomic and optical physics, the field of spectroscopy is advancing to a new level with applications ranging from material science to astronomy. We here propose a theoretical description of a potential new phenomenon resulting from the extension of Compton's experiment on the scattering of high energy photons through atomic electrons. How the proposed phenomenon can be tested experimentally is discussed in the paper as well.

A hand-held laser-induced breakdown spectroscopy device was used to acquire spectral emission data from laser-induced plasmas created on the surface of cerium-gallium alloy samples with Ga concentrations ranging from 0 to 3 weight percent. Ionic and neutral emission lines of the two constituent elements were then extracted and used to generate calibration curves relating the emission line intensity ratios to the gallium concentration of the alloy. The Ga I 287.4 nm emission line was determined to be superior for the purposes of Ga detection and concentration determination.A limit of detection below 0.25% was achieved using a multivariate regression model of the Ga I287.4 nm line ratio versus two separate Ce II emission lines. This LOD is considered a conservative estimation of technique’s capability given the type of the calibration samples available and low power( 5 mJ per 1 ns pulse) and resolving power (λ/∆λ= 4000) of this handheld device. Nonetheless, the utility of the technique is demonstrated via a detailed mapping analysis of the surface Ga distribution of a Ce-Ga sample which reveals significant heterogeneity resulting from the sample production process.

Spatially resolved, line-of-sight measurements of aluminum monoxide emission spectra in laser ablation plasma are used with Abel inversion techniques to extract radial plasma temperatures. Contour mapping of the radially deconvolved signal intensity shows a ring of AlO formation near the plasma boundary with the ambient atmosphere. Simulations of the molecular spectra were coupled with the line profile fitting routines. Temperature results are presented with simultaneous inferences from lateral, asymmetric radial, and symmetric radial AlO spectral intensity profiles. This analysis indicates that we measured shockwave phenomena in the radial profiles, including a temperature drop behind the blast wave created during plasma initiation.

We report on the design and construction of a spin-flip Zeeman slower, quadrupole magnetic trap, and Feshbach fields for a new machine for ultra-cold Li-7. The small mass of the Li-7 atom, and the tight lattice spacing, will enable us to achieve a 100-fold increase in tuneling rates over comparable Rb-87 optical lattice emulator experiments. These improvements should enable to access new regimes in quantum magnetic phase transitions and spin dynamics.

The first detection of gypsum (CaSO4.2H2O) by the Mars Science Laboratory (MSL) rover Curiosity in the Gale Crater, Mars created a profound impact on planetary science and exploration. The unique capability of plasma spectroscopy involving in situ elemental analysis in extraterrestrial environments, suggesting the presence of water in the red planet based on phase characterization and providing a clue to Martian paleoclimate. The key to gypsum as an ideal paleoclimate proxy lies in its textural variants, and in this study terrestrial gypsum samples from varied locations and textural types have been analyzed by Laser Induced Breakdown Spectroscopy (LIBS) technique. Petrographic, sub-microscopic and powder X-ray diffraction characterizations confirm the presence of gypsum (hydrated calcium sulphate; CaSO4.2H2O), bassanite (semi-hydrated calcium sulphate; CaSO4.1/2H2O) and anhydrite (anhydrous calcium sulphate; CaSO4) along with accessory phases (quartz and jarosite). The principal component analysis of LIBS spectra from texturally varied gypsums can be differentiated from one another because of the chemical variability in their elemental concentrations. The concentration of gypsum is determined from the partial least-square regressions model. Rapid characterization of gypsum samples with LIBS is expected to work well in extraterrestrial environments.

Q-switched laser radiation at wavelengths of 355 nm, 532 nm, and 1064 nm from a Nd: YAG laser was used to generate plasma in laboratory air at the target surface made of compressed nano-silver particles of size 95 ± 10 nm. The emitted resonance spectra from the neutral silver at wavelengths of 327.9 nm and 338.2 nm indicate existence of self-reversal in addition to plasma self-absorption. Both lines were identified in emission spectra at different laser irradiation wavelengths with characteristic dips at the un-shifted central wavelengths. These dips are usually associated with self-reversal. Under similar conditions, plasmas at the corresponding bulk silver target were generated. The recorded emission spectra were compared to those obtained from the nano-material target. The comparisons confirm existence of self-reversal of resonance lines that emerge from plasmas produced at nano-material targets. This work suggests a method for recovery of the spectral line shapes and discusses practical examples. In addition, subsidiary calibration efforts that utilize the Balmer series Hα-line reveal that other Ag I lines at 827.35 nm and 768.7 nm are optically thin under variety of experimental conditions and are well-suited as reference lines for measurement of the laser plasma electron density.

To determine the photon emission or absorption probability for a diatomic system in the context of the semiclassical approximation it is necessary to calculate the characteristic canonical oscillatory integral which has one or more saddle points. Integrals like that appear in a whole range of physical problems, e.g. the atom-atom and atom-surface scattering and various optical phenomena. A uniform approximation of the integral, based on the stationary phase method is proposed, where the integral with several saddle points is replaced by a sum of integrals each having only one or at most two real saddle points and is easily soluble. In this way we formally reduce the codimension in canonical integrals of "elementary catastrophes" with codimensions greater than 1. The validity of the proposed method was tested on examples of integrals with three saddle points ("cusp" catastrophe) and four saddle points ("swallow-tail" catastrophe).

In this work, a tailored extreme learning machine (ELM) algorithm to enhance the overall robustness of gas analyzer based on the tunable diode laser absorption spectroscopy (TDLAS) method is presented. The ELM model is tailored through activation function selection, input weight and bias searching, and cross validation method to address the analyzer robustness issues for industrial process analysis field application. The two particular issues are the inaccurate gas concentration measurement caused by the process gas background components variation, and the inaccurate spectra shift calculation caused by spectral interference. By using our algorithm, the concentration error is reduced by one order of magnitude over a much larger stream pressure and component range compared with that obtained by classical least square (CLS) fitting methods based on reference curves. Additionally, it is shown that with our algorithm, the wavelength shift accuracy is improved to less than 1 count over 1000 counts spectra length. In order to test the viability of our algorithm, a trace ethylene (C₂H₄) TDLAS analyzer with coexisting methane was implemented, and its experimental measurements support analyzing robustness enhancement effect.

Modern development of high-intensity and high-resolution X-ray technology allows detailed studies of the multiphoton absorption and scattering of X-ray photons by deep and subvalent shells of molecular systems on a wide energy range. The interpretation of experimental data requires the improvement of computational methods for obtaining excited and ionized electron states of molecular systems with one or several vacancies. The specificity of solving these problems requires the use of molecular orbitals obtained in one-center representation. Slow convergence of one-center expansions is a significant disadvantage of this approach; it affects the accuracy of the calculation of spectroscopic quantities. We offer a method of including higher harmonics in one-center expansion of a molecular orbital with the use of wave functions of electrons of deep shells of a ligand (off-center atom of a molecule). The method allows one to take into account correctly electron density of a linear molecule near the ligand when describing vacancies created in a molecular core leading to radial relaxation of electron density. The analysis of the parameters of one-center expansion of the ligand functions depending on ligand’s charge is performed. The criteria for the inclusion of higher harmonics of one-center decomposition of the ligand functions in the molecular orbital are determined. The efficiency of the method is demonstrated by the example of diatomic molecules HF, LiF, and BF by estimating energy characteristics of their ground and ionized states.

In this article various heuristic approaches are discussed to solve the dark matter phenomenon by the concept of vacuum polarization. They are compared with a more fundamental approach, based upon an entropy model of the visible universe. They all make use of some kind of gravitational dipole. These dipoles seem to violate Einstein’s equivalence principle between inertial mass and gravitational mass. It is shown how the paradox can be solved by a quantum mechanical principle.

Vibrational overtones in deeply bound molecules are sensitive probes for variation of the proton-to-electron mass ratio μ. In nonpolar molecules, these overtones may be driven as two-photon transitions. Here, we present procedures for experiments with O₂⁺, including state-preparation through photoionization, a two-photon probe, and detection. We calculate transition dipole moments between all X²П_g vibrational levels and those of the A²П_u excited electronic state. Using these dipole moments, we calculate two-photon transition rates and AC-Stark-shift systematics for the overtones. We estimate other systematic effects and statistical precision. Two-photon vibrational transitions in O₂⁺ provide multiple routes to improved searches for μ variation.

The use of mixed-state ionic beams in collision dynamics investigations is examined. Using high resolution Auger projectile spectroscopy involving He-like ($1s^2\thinspace^1\!S, 1s2s\thinspace^{3,1}\!S$) mixed-state beams, the spectrum contributions of the $1s2s\thinspace^3\!S$ metastable beam component is effectively separated and clearly identified. This is performed with a technique that exploits two independent spectrum measurements under the same collision conditions, but with ions having quite different metastable fractions, judiciously selected by varying the ion beam charge-stripping conditions. Details of the technique are presented together with characteristic examples. In collisions of 4 MeV B$^{3+}$ with H$_2$ targets, the Auger electron spectrum of the separated $1s2s\thinspace^{3}S$ boron beam component allows for a detailed analysis of the formation of the $1s2s(^3\!S)nl \thinspace^2\!L$ states by direct $nl$ transfer. In addition, the production of hollow $2s2p\thinspace^{1,3}\!P$ doubly- and $2s2p^2\thinspace^2\!D$ triply-excited states, by direct excitation and transfer-excitation processes, respectively, can also be independently studied. In similar mixed-state beam collisions of 15 MeV C$^{4+}$ with H$_2$, He, Ne and Ar targets, the contributions of the $1s^2$, $1s2s\thinspace^{3,1}S$ beam components to the formation of the $2s2p\thinspace^{3,1}\!P$ states by double-excitation, $1s\rightarrow2p$ excitation and transfer-loss processes can be clearly identified, facilitating comparisons with theoretical calculations.

In this work, the parameters of plasma (electron temperature (T_e), electron density n_e, plasma frequency (f_p) , Debye length (λ_D) and Debye number (N_D)) have been studied by using the spectrometer that collect the spectrum of Laser produce Cadmium telluride plasma at different energies. The results of electron temperature for CdTe range 0.93-1.18 eV also the electron density 5 × 10¹⁰ – 3.8 × 10¹¹ cm^-3   have been measured under vacuum reaching 2.5 × 10^-2 mbar .Optical properties of CdTe were determined through the optical transmission method using ultraviolet visible spectrophotometer within the range 190 – 1100 nm.

We explore the use of inverse multiquadratic (IMQ) functions as basis functions when solving the vibrational Schrödinger equation with the rectangular collocation method. The quality of the vibrational spectrum of formaldehyde (in six dimensions) is compared to that obtained using Gaussian basis functions when using different numbers of width-optimized IMQ functions. The effects of the ratio of the number of collocation points to the number of basis functions and of the choice of the IMQ exponent are studied. We show that the IMQ basis can be used with parameters where the IMQ function is not integrable. We find that the quality of the spectrum with IMQ basis functions is somewhat lower that that with a Gaussian basis when the basis size is large and for a range of IMQ exponents. The IMQ functions are, however, advantageous when a small number of functions is used or with a small number of collocation points e.g. when using square collocation.

Photoacoustic spectroscopy allows the identification of specific molecules in gases. We evaluate the spectral resolution and detection limits for a PAS system in the broadband infrared wavelength region 3270 nm ≲ λ ≲ 3530 nm driven by a continuous wave optical parametric oscillator with P ≈ 1.26 W by measuring the absorption of diluted propane, ethane and methane test gases at low concentrations c ~ 100 ppm for ~1350 discrete wavelengths λ_i. The resulting spectra I_PAS(λ_i) were compared to the high resolution cross section data σ_FTIR obtained by Fourier Transform Infrared Spectroscopy from the HITRAN database. Deviations as little as 7.1(6)% for propane, 8.7(11)% for ethane and 15.0(14)% for methane with regard to the average uncertainty between I_PAS(λ_i) and the expected reference values based on σ_FTIR were recorded. The wavelengths λ_res of the characteristic absorption lines can be pinpointed with a high relative accuracy <5 × 10⁻⁵ corresponding to a resolution of λ_res ~ 0.16 nm. Detection limits range between 7.1 ppb (ethane) to 13.6 ppb (methane) coinciding with high experimental signal-to-noise ratios. Moreover, using EUREQA, an artificial intelligence program, simulated mixed gas samples at low limits of detection could be deconvoluted. These results justify a further development of PAS technology to support, e.g., biomedical research.

This work communicates results from optical emission spectroscopy following laser-induced optical breakdown at or near nanomaterial. Selected atomic lines of silver are evaluated for consistent determination of electron density. Comparisons are presented with Balmer series hydrogen results. Of particular interest are measurements free of self-absorption effects. For several silver lines, asymmetries are observed in the recorded line profiles. Electron densities of interest range from 0.5 to 3 × 10¹⁷ cm^-3, for 5 nanosecond Q-switched Nd:YAG radiation at wavelengths of 1064, 532, and 355 nm, and for selected silver emission lines including 328.0, 338.2, 768.7, and 827.3 nm, and the hydrogen alpha Balmer series line at 656.3 nm. Line asymmetries are presented for the 328.0 nm Ag I line that is measured following generation of the plasma due to multiple photon absorption. This work explores electron density variations for different irradiance levels, and reports spectral line asymmetry of resonance lines for different laser fluence levels.

This brief review highlights some current issues in Galactic stellar nucleosynthesis, and some recent laboratory studies by the Wisconsin atomic physics group that have direct application to stellar spectroscopy, in order to advance our understanding of the chemical evolution of our Galaxy. The relevant publication history of the lab studies are summarized, and investigations into the abundances of neutron-capture and iron-peak elements in low metallicity stars are described. Finally, new initatives in near-infrared spectroscopy are briefly explored.

The resonance spectra of neutral silver indicate self-absorption for the studied Ag I lines at the wavelengths of 327.9 nm and 338.2 nm. The center dip is associated with self-reversal due to self-absorption in the plasma. The Q-switched radiation of 355 nm, 532 nm, or 1064 nm from a Nd:YAG laser device generates the plasma at the surface of silver nano-material targets, with experiments conducted in standard ambient temperature and pressure laboratory air. Procedures for recovery of the spectral line shapes confirm that over and above the effects of self-reversal, line shape distortion are important in the analysis. The work discusses parameters describing self-absorption when using fluence levels of 2 to 33 J/cm² to generate the plasma. Furthermore, subsidiary calibration efforts that utilize the hydrogen alpha line of the Balmer series show that the Ag I lines at 827.35 nm and 768.7 nm are optically thin.

Micro-plasma is generated in ultra-high-pure hydrogen gas filled inside a cell at a pressure of (1.08 ± 0.033) × 10⁵ Pa (810 ± 25 Torr) by using a Q-switched Nd:YAG laser device operated at 1064 nm wavelength and 14 ns pulse duration. Micro-plasma emission spectra of the hydrogen Balmer alpha line, H_α, are recorded with a Czerny-Turner type spectrometer and an intensified charge-coupled device. The spectra are calibrated for wavelength and corrected for detector sensitivity. During the first few tens of nanoseconds after initiating optical breakdown, significantly Stark-broadened and Stark-shifted H_α lines mark the well-above hypersonic outward expansion. The vertical diameters of the spectrally resolved plasma images are measured for time delays of 10 ns to 35 ns to determine expansion speeds of the order of 100 km/s to 10 km/s. For time delays of the order of 0.5 µs to 1 µs, the expansion decreases to the speed of sound of 1.3 km/s in the near ambient temperature and pressure hydrogen gas.

Molecular overtone transitions provide optical frequency transitions sensitive to variation in the proton-to-electron mass ratio (μ = m_p/m_e). However, robust molecular state preparation presents a challenge critical for achieving high precision. Here, we characterize infrared and optical-frequency broadband laser cooling schemes for TeH⁺, a species with multiple electronic transitions amenable to sustained laser control. Using rate equations to simulate laser cooling population dynamics, we estimate the fractional sensitivity to μ attainable using TeH⁺. We find that laser cooling of TeH⁺ can lead to significant improvements on current μ variation limits.

The rich emission and absorption line spectra of Fe I may be used to extract crucial information on astrophysical plasmas, such as stellar metallicities. There is currently a lack, in quality and quantity, of accurate level-resolved effective electron-impact collision strengths and oscillator strengths for radiative transitions. Here, we discuss the challenges in obtaining a sufficiently good structure for neutral iron and compare our theoretical fine-structure energy levels with observation for several increasingly large models. Radiative data is presented for several transitions for which the atomic data is accurately known.

Silicates are among the most abundant and important inorganic materials, not only in the Earth’s crust but also in the interstellar medium in the form of micro-/nano-particles or embedded in the matrices of comets, meteorites and other asteroidal bodies. Although the crystalline phases of silicates are indeed present in Nature, amorphous forms are also highly abundant. Here we report a theoretical investigation of the structural, dielectric and vibrational properties of the amorphous bulk for forsterite (Mg₂SiO₄) as a silicate test case by a combined approach of classical molecular dynamics (MD) simulations for structure evolution, and periodic quantum mechanical DFT calculations for electronic structure analysis. Using classical MD based on an empirical partial charge rigid ionic model within a melt-quenching scheme at different temperatures performed with the GULP 4.0 code amorphous bulk structures for Mg₂SiO₄ were generated using as initial guess the crystalline phase. This has been done for bulks with three different unit cell sizes adopting a super-cell approach; i.e., 1×1×2, 2×1×2 and 2×2×2. The radial distribution functions indicated a good degree of amorphisation of the structures. Periodic B3LYP-geometry optimizations performed with the CRYSTAL14 code on the generated amorphous systems were used to analyze their structure, to calculate their high frequency dielectric constants (ε_∞), and to simulate the IR, Raman and reflectance spectra, which were compared with the experimental and theoretical crystalline Mg₂SiO₄. The most significant changes of the physico-chemical properties of the amorphous systems compared to the crystalline ones are presented and discussed (e.g., larger deviations in the bond distances and angles, broadening of the IR bands, etc.), which are consistent with their disordered nature. It is also shown that by increasing the unit cell size the bulk structures present larger degree of amorphisation.

A method for measuring the real part of the weak value of spin for non-zero rest mass atoms is presented using a variant on the original Stern-Gerlach apparatus. The experiment utilises helium in the metastable 2³S₁ state. A full simulation for observing the real part of the weak value using the impulsive approximation has been carried out and it predicts a displacement of the beam, Δ_w, that is within the resolution of our detector. It also indicates how this shift might be increased. The full analysis also indicated that there is a limit, L, to the applicability of the weak value approximation and has been evaluated for our apparatus. This experiment has the possibility to be expanded to utilise other nobal gas species such as neon and argon in the ³P₂ metastable state, but we shall restrict this paper to metastable helium only.

A numerical application of linear-molecule symmetry properties, described by the D_∞h point group, is formulated in terms of lower-order symmetry groups D_nh with finite n. Character tables and irreducible representation transformation matrices are presented for D_nh groups with arbitrary n-values. These groups are subsequently used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules as part of the variational nuclear motion program TROVE. The TROVE symmetrisation procedure is based on a set of "reduced" vibrational eigenvalue problems with simplified Hamiltonians. The solutions of these eigenvalue problems have now been extended to include the classification of basis-set functions using ℓ, the eigenvalue (in units of ℏ) of the vibrational angular momentum operator ${\widehat{L}}_z$ . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of D_nh. ¹²C₂H₂ is used as an example of a linear molecule of D_∞h point group symmetry to illustrate the symmetrisation procedure.

Atomic structure of N-electron atoms is often determined using the Hartree-Fock method, which is an integro-differential equation. The exchange term of the Hartree-Fock equations is usually treated as an inhomogeneous term of a differential equation, or with a local density approximation. This work uses matrix methods to solve for the Hartree-Fock equations, rather than the more commonly-used shooting method to integrate an inhomogeneous differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using computer linear-algebra packages. We extend the same technique to integro-differential equations, where a discretized integral can be written as a sum in matrix form. This method is compared against experiment and standard atomic structure calculations. We also can use this method for free-electron wavefunctions. This technique is important for spectral line broadening in two ways: improving the atomic structure calculations, and improving the motion of the plasma electrons that collide with the atom.

Passive plasma spectroscopy is a well-established non-intrusive diagnostic technique. Depending on the emitter and its environment which determine the dominant interactions and effects governing emission line shapes, passive spectroscopy allows the determination of electron densities, emitter and perturber temperatures as well as other quantities like abundances. However, using spectroscopy needs appropriate line shape codes retaining all the physical effects governing the emission line profiles. This requires for line shape code developers to continuously correct or improve them to increase their accuracy when applied for diagnostics. This is exactly the aim expected from code-code and code-data comparisons. In this context, the He I 492 nm emitted in a helium corona discharge at room temperature represents an ideal case since its profile results from several broadening mechanisms: Stark, Doppler, resonance and van der Waals. The importance of each broadening mechanism depends on the plasma parameters. Here the profiles of the He I 492 nm in a helium plasma computed by various codes are compared for a selected set of plasma parameters. In addition, preliminary results related to plasma parameter determination using experimental spectra from a helium corona discharge at low pressure 1- 2 bars, are presented.

Many spectroscopic diagnostics are routinely used as a technique to infer the plasma parameters from line emission spectra but their accuracy depends on the numerical model or code used for the fitting process. However, the validation of a line shape code requires some steps : comparison of the line shape code with other similar codes for some academic (simple) cases and then more complex ones, comparison of the fitting parameters obtained from the best fit of the experimental spectra with those obtained with other diagnostic techniques and/or comparison of the fitting parameters obtained by different codes to fit the same experimental data. Here we compare the profiles of the hydrogen Balmer β line in a helium plasma computed by six codes for a selected set of plasma parameters and we report on the plasma parameters inferred by each of them from the fitting to a number of experimental spectra measured in a helium corona discharge where the pressure was in the range 1- 5 bar.

For a given set of plasma parameters, along a single series (Lyman, Balmer etc) the lines with higher principal quantum number(n) lines get progressively wider, closer to each other, and start merging for a certain critical n. In the present work four different codes(with further options) are used to calculate the entire Balmer series for moderate and high electron densities. Particular attention is paid to the relevant physics, such as the cutoff criteria, strong and penetrating electron collisions.

The emission of [O I] lines in the coma of Comet 67P/Churyumov-Gerasimenko during the Rosetta mission have been explained by electron impact dissociation of water rather than the process of photodissociation. This is the direct evidence for the role of electron induced processing has been seen on such a body. Analysis of other emission features is handicapped by a lack of detailed knowledge of electron impact cross sections which highlights the need for a broad range of electron scattering data from the molecular systems detected on the comet. In this paper we present an overview of the needs for electron scattering data relevant for the understanding of observations in coma, the tenuous atmosphere and on the surface of 67P/Churyumov-Gerasimenko during the Rosetta mission. The relevant observations for elucidating the role of electrons come from optical spectra, particle analysis using the ion and electron sensors and mass spectrometry measurements. To model these processes electron impact data should be collated and reviewed in an electron scattering database and an example is given in the BEAMD, which is a part of a larger consortium of Virtual Atomic and Molecular Data Centre – VAMDC.

The emission of [O I] lines in the coma of Comet 67P/Churyumov-Gerasimenko during the Rosetta mission have been explained by electron impact dissociation of water rather than the process of photodissociation. This is the direct evidence for the role of electron induced processing has been seen on such a body. Analysis of other emission features is handicapped by a lack of detailed knowledge of electron impact cross sections which highlights the need for a broad range of electron scattering data from the molecular systems detected on the comet. In this paper we present an overview of the needs for electron scattering data relevant for the understanding of observations in coma, the tenuous atmosphere and on the surface of 67P/Churyumov-Gerasimenko during the Rosetta mission. The relevant observations for elucidating the role of electrons come from optical spectra, particle analysis using the ion and electron sensors and mass spectrometry measurements. To model these processes electron impact data should be collated and reviewed in an electron scattering database and an example is given in the BEAMD, which is a part of a larger consortium of Virtual Atomic and Molecular Data Centre – VAMDC.

Markov chain Monte Carlo sampling propagators, including numerical integrators for stochastic dynamics, are central to the calculation of thermodynamic quantities and determination of structure for molecular systems. Efficiency is paramount, and to a great extent, this is determined by the integrated autocorrelation time (IAcT). This quantity varies depending on the observable that is being estimated. It is suggested that it is the maximum of the IAcT over all observables that is the relevant metric. Reviewed here is a method for estimating this quantity. For reversible propagators (which are those that satisfy detailed balance), the maximum IAcT is determined by the spectral gap in the forward transfer operator, but for irreversible propagators, the maximum IAcT can be far less than or greater than what might be inferred from the spectral gap. This is consistent with recent theoretical results (not to mention past practical experience) suggesting that irreversible propagators generally perform better if not much better than reversible ones. Typical irreversible propagators involve a parameter controlling the mix of ballistic and diffusive movement. To gain insight into the effect of the damping parameter for Langevin dynamics, its optimal value is obtained here for a multidimensional quadratic potential energy function.