Refractivity virial coefficients of gaseous CH4, C2H4, C2H6, CO2, SF6, H2, N2, He, and Ar

Path-integral calculation of the third dielectric virial coefficient of noble gases

We present a rigorous framework for fully quantum calculation of the third dielectric virial coefficient C_ɛ(T) of noble gases, including exchange effects. The quantum effects are taken into account with the path-integral Monte Carlo method. Calculations employing state-of-the-art pair and three-body potentials and pair polarizabilities yield results generally consistent with the few scattered experimental data available for helium, neon, and argon, but rigorous calculations with well-described uncertainties will require the development of surfaces for the three-body nonadditive polarizability and the three-body dipole moment. The framework, developed here for the first time, will enable new approaches to primary temperature and pressure metrology based on first-principles calculations of gas properties.

The Short-Term Performances of Two Independent Gas Modulated Refractometers for Pressure Assessments

Refractometry is a powerful technique for pressure assessments that, due to the recent redefinition of the SI system, also offers a new route to realizing the SI unit of pressure, the Pascal. Gas modulation refractometry (GAMOR) is a methodology that has demonstrated an outstanding ability to mitigate the influences of drifts and fluctuations, leading to long-term precision in the 10−7 region. However, its short-term performance, which is of importance for a variety of applications, has not yet been scrutinized. To assess this, we investigated the short-term performance (in terms of precision) of two similar, but independent, dual Fabry–Perot cavity refractometers utilizing the GAMOR methodology. Both systems assessed the same pressure produced by a dead weight piston gauge. That way, their short-term responses were assessed without being compromised by any pressure fluctuations produced by the piston gauge or the gas delivery system. We found that the two refractometer systems have a significantly higher degree of concordance (in the 10−8 range at 1 s) than what either of them has with the piston gauge. This shows that the refractometry systems under scrutiny are capable of assessing rapidly varying pressures (with bandwidths up to 2 Hz) with precision in the 10−8 range.

Path-Integral Calculation of the Second Dielectric and Refractivity Virial Coefficients of Helium, Neon, and Argon

We present a method to calculate dielectric and refractivity virial coefficients using the path-integral Monte Carlo formulation of quantum statistical mechanics and validate it by comparing our results with equivalent calculations in the literature and with more traditional quantum calculations based on wavefunctions. We use state-of-the-art pair potentials and polarizabilities to calculate the second dielectric and refractivity virial coefficients of helium (both 3He and 4He), neon (both 20Ne and 22Ne), and argon. Our calculations extend to temperatures as low as 1 K for helium, 4 K for neon, and 50 K for argon. We estimate the contributions to the uncertainty of the calculated dielectric virial coefficients for helium and argon, finding that the uncertainty of the pair polarizability is by far the greatest contribution. Agreement with the limited experimental data available is generally good, but our results have smaller uncertainties, especially for helium. Our approach can be generalized in a straightforward manner to higher-order coefficients.

Invar-based refractometer for pressure assessments

Gas modulation refractometry (GAMOR) is a methodology that can mitigate fluctuations and drifts in refractometry. This can open up for the use of non-conventional cavity spacer materials. In this paper, we report a dual-cavity system based on Invar that shows better precision for assessment of pressure than a similar system based on Zerodur. This refractometer shows for empty cavity measurements, up to 10⁴ s, a white noise response (for N₂) of 3 mPa s^1/2. At 4303 Pa, the system has a minimum Allan deviation of 0.34 mPa (0.08 ppm) and a long-term stability (24 h) of 0.7 mPa. This shows that the GAMOR methodology allows for the use of alternative cavity materials.

Comparison measurements of low-pressure between a laser refractometer and ultrasonic manometer

We have developed a new low-pressure sensor which is based on the measurement of (nitrogen) gas refractivity inside a Fabry-Perot cavity. We compare pressure determinations via this laser refractometer to that of well-established ultrasonic manometers throughout the range 100 Pa to 180 000 Pa. The refractometer demonstrates 10(-6) ⋅ p reproducibility for p > 100 Pa, and this precision outperforms a manometer. We also claim the refractometer has an expanded uncertainty of U(pFP) = [(2.0 mPa)(2) + (8.8 × 10(-6) ⋅ p)(2)](1/2), as realized through the properties of nitrogen gas; we argue that a transfer of the pascal to p < 1 kPa using a laser refractometer is more accurate than the current primary realization.

Frequency-dependent polarizability of helium including relativistic effects with nuclear recoil terms

Future metrology standards will be partly based on physical quantities computed from first principles rather than measured. In particular, a new pressure standard can be established if the dynamic polarizability of helium can be determined from theory with an uncertainty smaller than 0.2 ppm. We present calculations of the frequency-dependent part of this quantity including relativistic effects with full account of leading nuclear recoil terms and using highly optimized explicitly correlated basis sets. A particular emphasis is put on uncertainty estimates. At the He-Ne laser wavelength of 632.9908 nm, the computed polarizability value of 1.39181141 a.u. has uncertainty of 0.1 ppm that is 2 orders of magnitude smaller than those of the most accurate polarizability measurements. We also obtained an accurate expansion of the helium refractive index in powers of density.

Absolute refractometry of dry gas to ±3 parts in 10⁹

We present a method of measuring the refractive index of dry gases absolutely at 632.8 nm wavelength using a Fabry-Perot cavity with an expanded uncertainty of <3×10⁻⁹ (coverage factor k=2). The main contribution to this uncertainty is how well vacuum-to-atmosphere compression effects (physical length variation) in the cavities can be corrected. This paper describes the technique and reports reference values for the refractive indices of nitrogen and argon gases at 100 kPa and 20 °C with an expanded uncertainty of <9×10⁻⁹ (coverage factor k=2), with the additional and larger part of this uncertainty coming from the pressure and temperature measurement.

Precision measurement of the refractive index of carbon dioxide with a frequency comb

We report a higher precision measurement of the refractive index of carbon dioxide using a frequency comb as the light source in a Mach-Zehnder interferometer setup. The experimental sensitivity can reach the level of 8.8x10(-9). Taking into account the measurement accuracy of temperature and pressure, the experimental accuracy has a value of 1.2x10(-8). The measurement result has a deviation from the commonly quoted result [Old , J. Opt. Soc. Am.61, 89 (1971)] by 6.4x10(-7) at 800 nm.

The collision-induced polarizability of a pair of hydrogen molecules

Collision-induced light scattering, impulsive stimulated scattering, and subpicosecond-induced birefringence all depend on the transient changes Deltaalpha in molecular polarizabilities that occur when molecules collide. Ab initio results for Deltaalpha are needed to permit comparisons with accurate experimental results for these spectra and for refractive index virial coefficients and dielectric virial coefficients. In this work, we provide results for Deltaalpha for a pair of hydrogen molecules, treated at CCSD(T) level, with an aug-cc-pV5Z (spdf) basis set. Our values replace the best previous ab initio results for the variation of Deltaalpha with intermolecular separation, the self-consistent-field results obtained by Bounds [Mol. Phys. 38, 2099 (1979)] with a relatively small (3s2p) basis set for H2. For the six geometrical configurations studied by Bounds, the inclusion of correlation and improvements in the basis tend to increase both the trace Deltaalpha(0)0 and the anisotropy Deltaalpha2m of the pair polarizability. The change in the anisotropy is relatively small, but our values for the trace differ by factors of 2 or more from Bounds' results. For use in computing experimental line shapes, intensities, and virial coefficients, we have calculated Deltaalpha for 18 different relative orientations of a pair of H2 molecules, with the intermolecular separation R ranging from 2 a.u. (3 a.u. for a linear pair) to 10 a.u. The H2 bond length is fixed at the vibrationally averaged internuclear separation in the ground state r=1.449 a.u. Our results agree well with the CCSD(T) results for Deltaalpha obtained by Maroulis [J. Phys. Chem. A 104, 4772 (2000)] for two pair configurations of H2...H2 (linear and T-shaped) at a fixed internuclear distance of R=6.5 a.u. in a [6s4p1d] basis. As the intermolecular distance increases (for R>or=8 a.u.), the spherical-tensor components of Deltaalpha converge to the results from a long-range model that includes dipole-induced-dipole (DID) interactions, higher-multipole induction, nonuniformity of the local field, hyperpolarization, and van der Waals dispersion. Deviations from the first-order DID model are still evident for R between 8 and 10 a.u. in most orientations of the pair. At shorter range, overlap damping, exchange, and orbital distortion reduce both Deltaalpha0(0) and Deltaalpha(2)0 below their long-range limiting forms.

Refractive index of air: 3. The roles of CO2, H2O, and refractivity virials

The author's recent studies of the refractive index of air are extended, and several assumptions made therein are further examined. It is shown that the alternative dispersion equations for CO2, which are due to Edlen [Metrologia 2, 71 (1966)] and Old et al. [J. Opt. Soc. Am. 61, 89 (1971)] result in differences of less than 2 x 10(-9) in the phase refractive index and less than 3 x 10(-9) in the group refractive index for current and predicted concentrations of CO2. However, because the dispersion equation given by Old et al. is consistent with experimental data in the near infrared, it is preferable to the equation used by Edlen, which is valid only in the ultraviolet and the visible. The classical measurement by Barrell and Sears [Philos. Trans. R. Soc. London Ser. A 238, 1 (1939)] on the refractivity of moist air is shown to have some procedural errors in addition to the one discussed by Birch and Downs [Metrologia 30, 155 (1993)]. It is shown that for normal atmospheric conditions the higher refractivity virial coefficients related to the Lorentz-Lorenz relation are adequately incorporated into the empirically determined first refractivity virial. As a guide to users the practical limits to the calculation of the refractive index of the atmosphere that result from the uncertainties in the measurement of the various atmospheric parameters are summarized.