SELECTIVE REFLECTION FROM THE VAPORS OF THE ALKALI METALS

1951 ◽  
Vol 29 (3) ◽  
pp. 217-226 ◽  
Author(s):  
A. C. Lauriston ◽  
H. L. Welsh
Keyword(s):  
Alkali Metals ◽  
Incident Light ◽  
Steel Tube ◽  
Oscillator Strengths ◽  
Vapor Pressures ◽  
Selective Reflection ◽  
Sodium Potassium ◽  
Square Roots ◽  
Resonance Doublet ◽  
Good Agreement

Selective reflection from sodium, potassium, rubidium, and caesium vapors in the neighborhood of the resonance lines was observed for vapor pressures between 10 mm. and 1 atm., using a steel tube with a window of transparent magnesium oxide. Reflecting power as a function of frequency was measured by using incident light of continuous spectral distribution. The reflection contour for pressures up to ½ atm. is in good agreement with the theory of reflection from an absorbing medium. For each line the damping constant in the dispersion equations varies as the square root of the number of atoms per cubic centimeter, as was found previously for mercury and cadmium. For the two members of the resonance doublet the damping constants are proportional to the square roots of the oscillator strengths. In a region about 5 cm.−1 wide about each resonance frequency the reflected intensity measured experimentally is greater than that calculated. These lines of residual intensity may be due to a second kind of selective reflection. At pressures above ½ atm. the observed reflection contour cannot be explained by the simple anomalous dispersion theory.

SELECTIVE REFLECTION FROM MERCURY AND CADMIUM VAPORS

1950 ◽  
Vol 28a (2) ◽  
pp. 93-112 ◽  
Author(s):  
H. L. Welsh ◽  
J. Kastner ◽  
A. C. Lauriston
Keyword(s):  
Resonance Frequency ◽  
Oscillator Strength ◽  
Large Range ◽  
Incident Light ◽  
Selective Reflection ◽  
Residual Intensity ◽  
Order Of Magnitude ◽  
Low Pressures ◽  
The Relationship ◽  
Good Agreement

Selective reflection from mercury and cadmium vapors in the neighborhood of the resonance lines was investigated quantitatively using incident light of continuous spectral distribution. For a given experimental arrangement the lowest vapor density (atoms per cubic centimeter) at which selective reflection could be detected at Hg 2537 Å, Cd 2288 Å, and Cd 3261 Å was inversely proportional to the oscillator strength (f-value) of the absorption line. Contours of the selective reflection of the Hg 2537 Å and Cd 2288 Å lines were obtained over a large range of vapor densities up to 80 × 1018 atoms per cc. At this density the cadmium reflection extended over several thousand cm.−1 compared to about a hundred cm.−1 for mercury. The general features of the reflection contours can be explained by the theory of reflection from an absorbing medium. Fitting a theoretical curve to the experimental reflection contour yields values of the oscillator strength and the damping constant. For Hg 2537 Å and Cd 2288 Å the f-values are 0.0268 and 1.40 respectively, in good agreement with those found by other methods. The damping constant, γ, varies as the square root of the number of atoms per cubic centimeter, indicating that the mechanism of selective reflection is not the same as that for absorption and emission. An empirical areal law for selective reflection confirms the relationship [Formula: see text]. A shift of the resonance frequency of the order of magnitude of the coupling shift calculated by Weisskopf was observed for Hg 2537 Å. Deviations from theory at both high and low pressures were observed for Cd 2288 Å. The low pressure deviation takes the form of a line of residual intensity at the resonance frequency, which may be due to a different kind of selective reflection.

Thermal and electrical conductivities of the alkali metals at low temperatures

1956 ◽  
Vol 235 (1202) ◽  
pp. 358-374 ◽  
Keyword(s):  
Alkali Metals ◽  
Current Theory ◽  
Thermal Resistivity ◽  
Free Electrons ◽  
Sodium Potassium ◽  
Electrical Conductivities ◽  
Semi Empirical ◽  
Thermal Vibrations ◽  
Temperature Resistivity ◽  
Good Agreement

Measurements of the thermal and electrical conductivities of very pure lithium, sodium, potassium, rubidium and caesium have been made down to temperatures as low as 2°K. The respective resistivities, W and ρ , may be written as the sum of an impurity resistance ( W 0 , ρ 0 ) and a so-called ‘ideal’ component ( W i , ρ i ) due to scattering by the thermal vibrations of the lattice. The terms in the thermal resistivity may be represented by W 0 = A / T and W 1 = B T n f o r T ≤ θ / 10 , where n ≃ 2 and A = ( ρ 0 /2⋅45) x 10 8 cm deg. 2 W -1 . Current theory predicts thatt he quantity C ≡ Bθ 2 / W ∞ N ⅔ should be constant, where N is the number of free electrons per atom and W is the measured high-temperature resistivity. Taking N = 1, the present experiments yield C ≃ 18 ± 4. The electrical resistance may be written ρ = ρ 0 + β T m f o r T < θ / 10 with m ≃ 5 except for sodium, where, below 8°K , m is found to increase to 6. The theoretical relationships which exist between the low-temperature ‘ideal’ resistivities and those at higher temperatures are discussed in conjunction with the measured values. It is concluded that with the existing theories, no common adjustment of θ can give satisfactory agreement of theory with experiment. A new simple semi-empirical expression is put forward for W i which provides rather good agreement with experiment.

Oscillator Strength Measurements in the Vacuum-Ultraviolet by the Emission Method

1988 ◽  
Vol 102 ◽  
pp. 353-356
Author(s):  
C. Goldbach ◽  
G. Nollez
Keyword(s):  
Oscillator Strength ◽  
Vacuum Ultraviolet ◽  
Oscillator Strengths ◽  
Emission Method ◽  
Absolute Scale ◽  
Good Agreement

AbstractThe principles and the realization of an experiment devoted to oscillator strength measurements in the vacuum-ultraviolet by the emission method are briefly presented. The results obtained for the strong multiplets of neutral nitrogen and carbon in the 1200-2000 Å range yield an absolute scale of oscillator strengths in good agreement with the most recent calculations.

Systematic calculations of energy levels and transitions rates in Mo XXVIII

2020 ◽  
Vol 75 (8) ◽  
pp. 739-747
Author(s):  
Feng Hu ◽  
Yan Sun ◽  
Maofei Mei
Keyword(s):  
Energy Levels ◽  
Oscillator Strengths ◽  
Atomic Data ◽  
Data Sets ◽  
Electron Systems ◽  
Excitation Energies ◽  
Experimental Values ◽  
Qed Effects ◽  
Hyperfine Structures ◽  
Good Agreement

AbstractComplete and consistent atomic data, including excitation energies, lifetimes, wavelengths, hyperfine structures, Landé gJ-factors and E1, E2, M1, and M2 line strengths, oscillator strengths, transitions rates are reported for the low-lying 41 levels of Mo XXVIII, belonging to the n = 3 states (1s22s22p6)3s23p3, 3s3p4, and 3s23p23d. High-accuracy calculations have been performed as benchmarks in the request for accurate treatments of relativity, electron correlation, and quantum electrodynamic (QED) effects in multi-valence-electron systems. Comparisons are made between the present two data sets, as well as with the experimental results and the experimentally compiled energy values of the National Institute for Standards and Technology wherever available. The calculated values including core-valence correction are found to be in a good agreement with other theoretical and experimental values. The present results are accurate enough for identification and deblending of emission lines involving the n = 3 levels, and are also useful for modeling and diagnosing plasmas.

A Convenient Method of Distillation of the Alkali Metals

1927 ◽  
Vol 23 (8) ◽  
pp. 953-955 ◽  
Author(s):  
R. J. Clark
Keyword(s):  
Convenient Method ◽  
Alkali Metals ◽  
Mercury Vapour ◽  
Sodium Potassium

The alkali metals, sodium, potassium and rubidium can be distilled easily in a good vacuum and obtained reasonably free from occluded gas in the following way. As potassium is now used for the absorption of mercury vapour and many experiments are being done on the others, an account of a convenient way of preparing pure specimens may be of some service to experimenters.

Furan and Thiophene Analogs of Phenanthrene A Theoretical Study of the Absorption Spectra of Benzodifurans, Benzodithiophenes and Thienobenzofurans

1971 ◽  
Vol 26 (12) ◽  
pp. 1235-1240 ◽  
Author(s):  
L. Klasinc ◽  
J. V. Knop
Keyword(s):  
Absorption Spectra ◽  
Theoretical Study ◽  
Oscillator Strengths ◽  
Electron Transitions ◽  
Good Agreement ◽  
Lcao Mo

The LCAO -MO -SCF -CI method was applied to benzo(1,2-b : 4,3-b′) -difuran and -dithiophene, benzo (2,1-b : 3,4-b′) -difuran and -dithiophene, benzo (1,2-b : 3,4-b′) -difuran and -dithiophene, thieno (2,3-e) benzofuran, thieno (3,2-e) benzofuran, thieno (3,2-g) benzofuran, thieno (2,3-g) benzofuran, benzofuran, benzothiophene and phenanthrene. The calculated π-electron transitions and their oscillator strengths are in good agreement with known absorption spectra. The resemblance of these spectra to the absorption spectra of phenanthrene and phenanthrolines is discussed.

The continuous absorption of light in alkali-metal vapours

1953 ◽  
Vol 219 (1136) ◽  
pp. 89-101 ◽  
Keyword(s):  
Cross Section ◽  
Alkali Metals ◽  
Theoretical Calculations ◽  
Wave Length ◽  
Energy Difference ◽  
Continuous Absorption ◽  
Absorption Of Light ◽  
Sodium Vapour ◽  
Good Agreement ◽  
Dipole Length

The first section of this paper is an account of some experiments on the absorption of light in sodium vapour from the series limit at 2412 Å to about 1600 Å (an energy difference of 2·6 eV). The absorption cross-section at the limit is 11·6 ± 1·2 x 10 -20 cm 2 . The cross-section decreases giving a minimum of 1·3 ± 0·6 x 10 -20 cm 2 at 1900 Å and then increases to 1600 Å. A theoretical calculation by Seaton based on the dipole-length formula gives good agreement with the experiments at the series limit and also correctly predicts the wave-length for the minimum, but it predicts a significantly lower absorption at the minimum. The experiments described in the first section of the paper conclude a series on the absorption of light in the alkali metals. The second section consists of a general discussion of the results of these experiments and of their relation to theoretical calculations. There is good agreement between theory and experiment except in regard to the magnitude of the absorption at the minimum.

The de Haas–van Alphen effect in alkali metals

1964 ◽  
Vol 281 (1384) ◽  
pp. 62-91 ◽  
Keyword(s):  
Fermi Surface ◽  
Field Dependence ◽  
Alkali Metals ◽  
Spherical Shape ◽  
Orientation Dependence ◽  
Sodium Potassium ◽  
Fermi Surfaces ◽  
Fixed Orientation ◽  
Absolute Amplitude ◽  
Structure Calculations

A new method for studying the de Haas–van Alphen effect in steady magnetic fields has been developed in which the field is modulated at frequency ω and a signal at frequency 2 ω is generated in a pick-up coil round the specimen because of the non-linear field dependence of magnetization. The rectified 2 ω signal is proportional to d 2 M /dH 2 and so shows de Haas–van Alphen oscillations either when H is varied for fixed orientation or when the orientation is varied in fixed H if the Fermi surface is anisotropic. Because the phase of oscillation is very high (of order 10 4 π ) even very slight anisotropy will produce a few oscillations when the orientation is varied and the method is therefore particularly sensitive for studying very nearly spherical Fermi surfaces. From the oscillations with H , values of the frequency F were found for sodium, potassium, rubidium and caesium which were close to those predicted for a free-electron sphere containing 1 electron per atom, though some small systematic deviations of order ½ % were observed which may be significant. From detailed study of the oscillations produced by rotation of single crystals in fixed H it was found possible to describe the orientation dependence of F (proportional to the area of cross-section of the Fermi surface) for potassium and rubidium consistently by a series of cubic harmonics and hence to deduce the small departures of the Fermi surfaces from spherical shape. The deviations from a sphere were found to be of the order of 1 part in 10 3 for potassium and a little less than 1 part in 10 2 for rubidium; these deviations are compared with those predicted by band structure calculations. Preliminary results for sodium suggest that it is appreciably less anisotropic than potassium. Some results are also reported on the temperature and field dependence and the absolute amplitude of the de Haas-van Alphen effect, and it is also shown how the effect can be used to measure very small variations of field with position.

scholarly journals Metalenses Based on Symmetric Slab Waveguide and c-TiO2: Efficient Polarization-Insensitive Focusing at Visible Wavelengths

Nanomaterials ◽  
2018 ◽  
Vol 8 (9) ◽  
pp. 699 ◽  
Author(s):  
Yaoyao Liang ◽  
Zhongchao Wei ◽  
Jianping Guo ◽  
Faqiang Wang ◽  
Hongyun Meng ◽  
...  
Keyword(s):  
Berry Phase ◽  
Incident Light ◽  
Visible Spectrum ◽  
Slab Waveguide ◽  
Optical Elements ◽  
Polarization Insensitive ◽  
Wavefront Shaping ◽  
Visible Wavelengths ◽  
532 Nm ◽  
Good Agreement

A key goal of metalens research is to achieve wavefront shaping of light using optical elements with thicknesses on the order of the wavelength. Here we demonstrate ultrathin highly efficient crystalline titanium dioxide metalenses at blue, green, and red wavelengths (λ0 = 453 nm, 532 nm, and 633 nm, respectively) based on symmetric slab waveguide theory. These metalenses are less than 488 nm-thick and capable of focusing incident light into very symmetric diffraction-limited spots with strehl ratio and efficiency as high as 0.96 and 83%, respectively. Further quantitative characterizations about metalenses’ peak focusing intensities and focal spot sizes show good agreement with theoretical calculation. Besides, the metalenses suffer only about 10% chromatic deviation from the ideal spots in visible spectrum. In contrast with Pancharatnam–Berry phase mechanism, which limit their incident light at circular polarization, the proposed method enables metalenses polarization-insensitive to incident light.

Calculation of Punch Force and Maximum Pressure for Tube Extrusion

2000 ◽  
Author(s):  
S.-H. Zhang ◽  
Y.-L. Shang
Keyword(s):  
Upper Bound ◽  
Physical Modeling ◽  
Steel Tube ◽  
Experimental Results ◽  
Maximum Pressure ◽  
Punch Force ◽  
Tube Extrusion ◽  
Tooling System ◽  
Very High ◽  
Good Agreement

Abstract Punch force and maximum pressure for tube extrusion can be predicted with an upper bound theory-based program POLSK. Experiments of steel tube extrusion and wax physical modeling were performed. The punch force and the maximum pressure values were obtained. Comparisons were made among the experimental results, physical modeling results and upper bound predictions. It was found that a medium extrusion coefficient causes the lowest pressure on the tooling system, very low and very high extrusion coefficients can both cause very high pressure. It is proved that the upper bound predictions are in good agreement with the experimental results and the upper bound program is suitable for use of steel tube extrusion design.

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