Quantum modeling, beyond secularity, of the collisional dissipation of molecular alignment using the energy-corrected sudden approximation.

We propose a Markovian quantum model for the time dependence of the pressure-induced decoherence of rotational wave packets of gas-phase molecules beyond the secular approximation. It is based on a collisional relaxation matrix constructed using the energy-corrected sudden approximation, which improves the previously proposed infinite order sudden one by taking the molecule rotation during collisions into account. The model is tested by comparisons with time-domain measurements of the pressure-induced decays of molecular-axis alignment features (revivals and echoes) for HCl and CO2 gases, pure and diluted in He. For the Markovian systems HCl-He and CO2-He, the comparisons between computed and measured data demonstrate the robustness of our approach, even when the secular approximation largely breaks down. In contrast, significant differences are obtained in the cases of pure HCl and CO2, for which the model underestimates the decay rate of the alignment at short times. This result is attributed to the non-Markovianity of HCl-HCl and CO2-CO2 interactions and the important contribution of those collisions that are ongoing at the time when the system is excited by the aligning laser pulse.

Line shape parameters of PH3 transitions: Theoretical studies of self-broadened widths and line mixing effects.

Line mixing effects have been calculated in various parallel and perpendicular bands of self-broadened PH3 lines and compared with recent experimental data. The theoretical approach is an extension to symmetric tops with high inversion barrier of the formalism previously developed for NH3 [Q. Ma and C. Boulet, J. Chem. Phys. 144, 224303 (2016)]. The model takes into account the non-diagonality of the scattering operator within the line space as well as, in a correct way, the double degeneracy of the j, k levels when k ≠ 0. Transitions between such levels should be considered as doublets whose components may be coupled by the line mixing process. It has been shown that, at low pressure, the inversion of the experimental data will strongly depend on the splitting between the two components of a doublet. When it is significant, one can measure independently both the width of one component and the intra-doublet coupling matrix element. Otherwise, one can only measure the sum of these two elements. Comparisons with measurements show that the present formalism leads to accurate predictions of the experimental line shapes.

Collisional dissipation of the laser-induced alignment of ethane gas: Energy corrected sudden quantum model.

We present the first quantum mechanical model of the collisional dissipation of the alignment of a gas of symmetric-top molecules (ethane) impulsively induced by a linearly polarized non-resonant laser field. The approach is based on use of the Bloch model and of the Markov and secular approximations in which the effects of collisions are taken into account through the state-to-state rates associated with exchanges among the various rotational states. These rates are constructed using the Energy Corrected Sudden (ECS) approximation with (a few) input parameters obtained independently from fits of the pressure-broadening coefficients of ethane absorption lines. Based on knowledge of the laser pulse characteristics and on these rates, the time-dependent equation driving the evolution of the density matrix during and after the laser pulse is solved and the time dependence of the so-called "alignment factor" is computed. Comparisons with measurements, free of any adjusted parameter, show that the proposed approach leads to good agreement with measurements. The analysis of the ECS state-to-state collisional rates demonstrates that, as in the case of linear molecules, collision-induced changes of the rotational angular momentum orientation are slower than those of its magnitude. This explains why the collisional decay of the permanent component of the alignment is significantly slower than that of the amplitudes of the transient revivals in both experimental and computed results. It is also shown that, since intermolecular forces within C2H6 colliding pairs weakly depend on rotations of the molecules around their C-C bond, the dissipation mechanism of the alignment in pure ethane is close to that involved in linear molecules.

Collisional dissipation of the laser-induced alignment of ethane gas: A requantized classical model.

We present the first theoretical study of collisional dissipation of the alignment of a symmetric-top molecule (ethane gas) impulsively induced by a linearly polarized non-resonant laser field. For this, Classical Molecular Dynamics Simulations (CMDSs) are carried out for an ensemble of C2H6 molecules based on knowledge of the laser-pulse characteristics and on an input intermolecular potential. These provide, for a given gas pressure and initial temperature, the orientations of all molecules at all times from which the alignment factor is directly obtained. Comparisons with measurements show that these CMDSs well predict the permanent alignment induced by the laser pulse and its decay with time but, as expected, fail in generating alignment revivals. However, it is shown that introducing a simple requantization procedure in the CMDS "creates" these revivals and that their predicted dissipation decay agrees very well with measured values. The calculations also confirm that, as for linear molecules, the permanent alignment of ethane decays more slowly than the transient revivals. The influence of the intermolecular potential is studied as well as that of the degree of freedom associated with the molecular rotation around the symmetry axis. This reveals that ethane practically behaves as a linear molecule because the intermolecular potential is only weakly sensitive to rotation around the C-C axis.

Relaxation matrix for symmetric tops with inversion symmetry: Line coupling and line mixing effects on NH3 lines in the 𝝂4 band.

Line shape parameters including the half-widths and the off-diagonal elements of the relaxation matrix have been calculated for self-broadened NH3 lines in the perpendicular ν4 band. As in the pure rotational and the parallel ν1 bands, the small inversion splitting in this band causes a complete failure of the isolated line approximation. As a result, one has to use formalisms not relying on this approximation. However, due to differences between parallel and perpendicular bands of NH3, the applicability of the formalism used in our previous studies of the ν1 band and other parallel bands must be carefully verified. We have found that, as long as potential models only contain components with K1 = K2 = 0, whose matrix elements require the selection rule Δk = 0, the formalism is applicable for the ν4 band with some minor adjustments. Based on both theoretical considerations and results from numerical calculations, the non-diagonality of the relaxation matrices in all the PP, RP, PQ, RQ, PR, and RR branches is discussed. Theoretically calculated self-broadened half-widths are compared with measurements and the values listed in HITRAN 2012. With respect to line coupling effects, we have compared our calculated intra-doublet off-diagonal elements of the relaxation matrix with reliable measurements carried out in the PP branch where the spectral environment is favorable. The agreement is rather good since our results do well reproduce the observed k and j dependences of these elements, thus validating our formalism.

VIBRATIONAL DEPENDENCE OF LINE COUPLING AND LINE MIXING IN SELF-BROADENED PARALLEL BANDS OF NH3.

Line coupling and line mixing effects have been calculated for several self-broadened NH3 lines in parallel bands involving an excited v 2 mode. It is well known that once the v 2 mode is excited, the inversion splitting quickly increases as this quantum number increases. In the present study, we have shown that the v 2 dependence of the inversion splitting plays a dominant role in the calculated line-shape parameters. For the v 2 band with a 36 cm-1 splitting, the intra-doublet couplings practically disappear and for the 2v 2 and 2v 2 - v 2 bands with much higher splitting values, they are completely absent. With respect to the inter-doublet coupling, it becomes the most efficient coupling mechanism for the v 2 band, but it is also completely absent for bands with higher v 2 quantum numbers. Because line mixing is caused by line coupling, the above conclusions on line coupling are also applicable for line mixing. Concerning the check of our calculated line mixing effects, while the present formalism has well explained the line mixing signatures observed in the v 1 band, there are large discrepancies between the measured Rosenkranz mixing parameters and our calculated results for the v 2 and 2v 2 bands. In order to clarify these discrepancies, we propose to make some new measurements. In addition, we have calculated self-broadened half-widths in the v 2 and 2v 2 bands and made comparisons with several measurements and with the values listed in HITRAN 2012. In general, the agreements with measurements are very good. In contrast, the agreement with HITRAN 2012 is poor, indicating that the empirical formula used to predict the HITRAN 2012 data has to be updated.

A rare presentation of histologically proven sarcoidosis of the knee: A case report and brief review of the literature.

We here report a patient with histologically proven sarcoidosis of the knee, a rare localization of sarcoidosis, which usually presents itself as a pulmonary disease. Case reports of radiological images that suggest osseous sarcoidosis of the appendicular skeleton are not so rare, however few are histologically proven. Since in our patient MRI could not distinguish between sarcoidosis and another (possibly malignant) disease, histological proof was obtained through a CT-guided biopsy. Imaging and treatment guidelines for extrapulmonary sarcoidosis are inexistent, due to lack of randomized trials.

The relaxation matrix for symmetric tops with inversion symmetry. I. Effects of line coupling on self-broadened ν1 and pure rotational bands of NH3.

The Robert-Bonamy formalism has been commonly used to calculate half-widths and shifts of spectral lines for decades. This formalism is based on several approximations. Among them, two have not been fully addressed: the isolated line approximation and the neglect of coupling between the translational and internal motions. Recently, we have shown that the isolated line approximation is not necessary in developing semi-classical line shape theories. Based on this progress, we have been able to develop a new formalism that enables not only to reduce uncertainties on calculated half-widths and shifts, but also to model line mixing effects on spectra starting from the knowledge of the intermolecular potential. In our previous studies, the new formalism had been applied to linear and asymmetric-top molecules. In the present study, the method has been extended to symmetric-top molecules with inversion symmetry. As expected, the inversion splitting induces a complete failure of the isolated line approximation. We have calculated the complex relaxation matrices of self-broadened NH3. The half-widths and shifts in the ν1 and the pure rotational bands are reported in the present paper. When compared with measurements, the calculated half-widths match the experimental data very well, since the inapplicable isolated line approximation has been removed. With respect to the shifts, only qualitative results are obtained and discussed. Calculated off-diagonal elements of the relaxation matrix and a comparison with the observed line mixing effects are reported in the companion paper (Paper II).

The relaxation matrix for symmetric tops with inversion symmetry. II. Line mixing effects in the ν1 band of NH3.

Line mixing effects have been calculated in the ν1 parallel band of self-broadened NH3. The theoretical approach is an extension of a semi-classical model to symmetric-top molecules with inversion symmetry developed in the companion paper [Q. Ma and C. Boulet, J. Chem. Phys. 144, 224303 (2016)]. This model takes into account line coupling effects and hence enables the calculation of the entire relaxation matrix. A detailed analysis of the various coupling mechanisms is carried out for Q and R inversion doublets. The model has been applied to the calculation of the shape of the Q branch and of some R manifolds for which an obvious signature of line mixing effects has been experimentally demonstrated. Comparisons with measurements show that the present formalism leads to an accurate prediction of the available experimental line shapes. Discrepancies between the experimental and theoretical sets of first order mixing parameters are discussed as well as some extensions of both theory and experiment.

Evidence of increased axillary blood flow velocity without increased handgrip strength and endurance in persons with a fibromuscular axillary arch.

BACKGROUND: The purpose of this in vivo study was to compare axillary artery blood flow velocity, and maximal handgrip strength and endurance performance in young subjects with and without an axillary arch (AA). MATERIALS AND METHODS: One hundred and fifty-six young adults were screened for the presence of an AA on their dominant arm side. After physical examination subjects were checked using diagnostic echography for the presence of an AA. Sixteen subjects with an AA and 15 without an AA had their axillary artery peak systolic velocity quantified in 3 different arm positions using Doppler ultrasound. Maximal handgrip strength and endurance performance was quantified in the same positions using a functional rehabilitation system. RESULTS: Mean peak systolic velocity was significantly higher in the AA group compared to controls in abduction/external rotation of the arm during muscle relaxation (p = 0.003) and contraction (p = 0.01). No significant differences between groups were found for maximal handgrip strength and endurance performance. CONCLUSIONS: This study provides evidence for a transient axillary artery compression by the AA in a throwing position. This is not reinforced by additional contraction of the shoulder muscles along with the AA. Axillary artery compression does not influence maximal handgrip strength and endurance performance in symptom-free young adults.

Line mixing in parallel and perpendicular bands of CO2: A further test of the refined Robert-Bonamy formalism.

Starting from the refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)], we propose here an extension of line mixing studies to infrared absorptions of linear polyatomic molecules having stretching and bending modes. The present formalism does not neglect the internal degrees of freedom of the perturbing molecules, contrary to the energy corrected sudden (ECS) modelling, and enables one to calculate the whole relaxation matrix starting from the potential energy surface. Meanwhile, similar to the ECS modelling, the present formalism properly accounts for roles played by all the internal angular momenta in the coupling process, including the vibrational angular momentum. The formalism has been applied to the important case of CO2 broadened by N2. Applications to two kinds of vibrational bands (Σ â†’ Σ and Σ â†’ Π) have shown that the present results are in good agreement with both experimental data and results derived from the ECS model.

Effects on calculated half-widths and shifts from the line coupling for asymmetric-top molecules.

The refinement of the Robert-Bonamy formalism by considering the line coupling for linear molecules developed in our previous studies [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013); 140, 104304 (2014)] have been extended to asymmetric-top molecules. For H2O immersed in N2 bath, the line coupling selection rules applicable for the pure rotational band to determine whether two specified lines are coupled or not are established. Meanwhile, because the coupling strengths are determined by relative importance of off-diagonal matrix elements versus diagonal elements of the operator -iS1 - S2, quantitative tools are developed with which one is able to remove weakly coupled lines from consideration. By applying these tools, we have found that within reasonable tolerances, most of the H2O lines in the pure rotational band are not coupled. This reflects the fact that differences of energy levels of the H2O states are pretty large. But, there are several dozen strongly coupled lines and they can be categorized into different groups such that the line couplings occur only within the same groups. In practice, to identify those strongly coupled lines and to confine them into sub-linespaces are crucial steps in considering the line coupling. We have calculated half-widths and shifts for some groups, including the line coupling. Based on these calculations, one can conclude that for most of the H2O lines, it is unnecessary to consider the line coupling. However, for several dozens of lines, effects on the calculated half-widths from the line coupling are small, but remain noticeable and reductions of calculated half-widths due to including the line coupling could reach to 5%. Meanwhile, effects on the calculated shifts are very significant and variations of calculated shifts could be as large as 25%.

Two dimensional symmetric correlation functions of the S operator and two dimensional Fourier transforms: considering the line coupling for P and R lines of linear molecules.

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

Line broadening of confined CO gas: from molecule-wall to molecule-molecule collisions with pressure.

The infrared absorption in the fundamental band of CO gas confined in porous silica xerogel has been recorded at room temperature for pressures between about 5 and 920 hPa using a high resolution Fourier transform spectrometer. The widths of individual lines are determined from fits of measured spectra and compared with ab initio predictions obtained from requantized classical molecular dynamics simulations. Good agreement is obtained from the low pressure regime where the line shapes are governed by molecule-wall collisions to high pressures where the influence of molecule-molecule interactions dominates. These results, together with those obtained with a simple analytical model, indicate that both mechanisms contribute in a practically additive way to the observed linewidths. They also confirm that a single collision of a molecule with a wall changes its rotational state. These results are of interest for the determination of some characteristics of the opened porosity of porous materials through optical soundings.

Sonographic evaluation of the plantar fascia in asymptomatic subjects.

PURPOSE: To evaluate the appearance of the plantar fascia in asymptomatic subjects. MATERIALS AND METHODS: Thirty-one asymptomatic subjects were examined by 2 musculoskeletal radiologists. The plantar fascia was evaluated for thickness, echogenicity, vascularity on power Doppler, rupture, fluid adjacent to the fascia, andcalcifications. RESULTS: The study included 14 men and 17 women (age, 17-79 years; mean, 45 years). The mean thickness of the plantar fascia in men was 3.7 mm (range 2.5-7 mm), and in women 3.5 mm (range, 1.7-5.1 mm). The thickness was greater than 4 mm in 4 men (bilateral in 2). The mean thickness of fascias thicker than 4 mm in men was 5.4 mm (range, 4.3-7 mm). The thickness was greater than 4 mm in 5 women ( bilateral in 4). The mean thickness of fascias thicker than 4 mm in women was 4.7 mm (range, 4.2-5.1 mm). There was no statistically significant difference between men and women and between both heels. Hypoechogenicity was observed in 3 men (bilateral in 2), and in 5 women (bilateral in 6). Hypervascularity, rupture, fluid adjacent to the fascia, and calcifications were not observed. CONCLUSION: A thickness greater than 4 mm and hypoechogenicity, are common in the plantar fascia of asymptomatic subjects. Findings that were not seen in asymptomatic subjects include a thickness greater than 7 mm, hypervascularity on power Doppler, rupture, fluid adjacent to the fascia, and calcifications.

Dissipation of alignment in CO2 gas: A comparison between ab initio predictions and experiments.

We present comparisons between measurements and ab initio calculations of the dissipation of the nonadiabatic laser-induced alignment in pure CO2 and CO2-He gas mixtures. The experiments were made for pressures between 2 and 20 bars at 295 K by using short non-resonant linearly polarized laser pulses for alignment and probe. The calculations are carried, free of any adjusted parameter, using refined intermolecular potentials and a requantized Classical Molecular Dynamics Simulations approach presented previously but not yet confronted to experiments. The results demonstrate that the model accurately reproduces the decays with time of both the transient revivals and "permanent" component of the alignment. The significant differences observed between the behaviors resulting from CO2-CO2 and CO2-He collisions are also well predicted by the model.

Refinement of the Robert-Bonamy formalism: considering effects from the line coupling.

Since it was developed in 1979, the Robert-Bonamy (RB) formalism has been widely used in calculating pressure broadened half-widths and induced shifts for many molecular systems. However, this formalism contains several approximations whose applicability has not been thoroughly justified. One of them is that lines of interest are well isolated. When these authors developed the formalism, they have relied on this assumption twice. First, in calculating the spectral density F(ω), they have only considered the diagonal matrix elements of the relaxation operator. Due to this simplification, effects from the line mixing are ignored. Second, when they applied the linked cluster theorem to remove the cutoff, they have assumed the matrix elements of the operator exp(-iS1 - S2) can be replaced by the exponential of the matrix elements of -iS1 - S2. With this replacement, effects from the line coupling are also ignored. Although both these two simplifications relied on the same approximation, their validity criteria are completely different and the latter is more stringent than the former. As a result, in many cases where the line mixing becomes negligible, significant effects from the line coupling have been completely missed. In the present study, we have developed a new method to evaluate the matrix elements of exp(-iS1 - S2) and have refined the RB formalism such that line coupling can be taken into account. Our numerical calculations of the half-widths for Raman Q lines of the N2-N2 pair have demonstrated that effects from the line coupling are important. In comparison with values derived from the RB formalism, new calculated values for these lines are significantly reduced. A recent study has shown that in comparison with the measurements and the most accurate close coupling calculations, the RB formalism overestimates the half-widths by a large amount. As a result, the refinement of the RB formalism goes in the right direction and these new calculated half-widths become closer to the "true" values.

Erdheim-Chester disease detected with 99mTc MDP bone SPECT/CT.

Erdheim-Chester disease (ECD) is a rare non-Langerhans' cell histiocytosis. Mild but permanent juxta-articular bone pain in mainly knees and ankles is the most frequent associated symptom. Despite the pathognomonic radiographic findings, most cases are still diagnosed by the pathologist.The lesions consist of lipid-storing CD 68 +/CD 1a--non-Langerhans' cell histiocytes, most frequently localized in bone but also involving multiple organ systems in the body. We present a case report in which the diagnosis of ECD was established with 99mTc MDP bone SPECT/CT.