Measured Line Positions Research Articles

A direct approach for the reduction of diatomic spectra to molecular constants for the construction of RKR potentials

A nonlinear fitting procedure is presented that employs all measured line positions and iteratively compares their values with those calculated from numerically diagonalized model Hamiltonians with adjustable molecular constants. Case (a) wavefunctions with definite parity are introduced as a convenient basis set, and the effects of spin-orbit, spin-spin, spin-rotation, and centrifugal distortion interactions neglected in the Born-Oppenheimer separation are included simultaneously using the Van Vleck transformation. The spectroscopic constants found by this procedure represent the minimum-variance, unbiased set and maintain, to a high degree of accuracy, the separate mechanical and magnetic meanings of the molecular constants. Arguments are presented that such spectroscopic constants with mechanical meaning allow the most accurate construction of potential energy functions using the Rydberg-Klein-Rees (RKR) procedure. Residual mechanical and magnetic ambiguities, such as engendered by Λ-type doubling, are discussed.

The effect of absorber thickness in measurement of quadrupole splitting in a Mössbauer experiment

It is shown that the procedure of fitting two Lorentzian lines to an experimental Mössbauer spectrum consisting of a quardupole doublet of overlapping resonances leads to error in the measurement of line positions, and hence of quadrupole splitting, if the absorber is not thin. Two basic methods have been used to obtain accurate values of quadrupole splitting from thick absorber Mössbauer spectra. The first, calculation of correction factors to the results of Lorentzian fitting the thick absorber spectra, has itself been carried out in two ways. 1. 1. Thick absorber spectra have been simulated by computer and fitted by Lorentzian lines. Families of curves of ▪ have been plotted, using which the results of an experiment can be corrected assuming that the thin absorber linewidth is known. 2. 2. A simple formula for correcting thick absorber data has been derived, based on the assumption that a thick absorber spectrum approximates to the sum of two Lorentzian lines, but with parameters differing from those of a thin absorber spectrum. In the second basic method, a thick absorber lineshape function is fitted directly to the experimental spectrum. In addition to values of quadrupole splitting, this method is shown to give an estimate of the recoil free fraction of Mössbauer nuclei in the absorber. The methods have been applied to thick absorber quadrupole spectra of 119mSn in Y 2Sn 2O 7 and give results for quadrupole splitting which are in good agreement with a thin absorber measurement. A value for the recoil-free-fraction of 119mSn in Y 2Sn 2O 7 is also obtained.

Optical Spectroscopic Determination of the Zero-Field Splitting in Vibronic Levels of the Triplet State of Nitrite

We have used conventional high resolution optical spectroscopic methods to determine the principal values of the fine structure tensor for the lowest triplet state (B31 at 18 959 cm−1) of NO2− in Na NO2 single crystals. From the intensities in the Zeeman spectrum we find D − E = 0.86 ± 0.04 cm−1, D + E = 0.40 ± 0.04 cm−1, where the z axis is taken as the twofold axis and E = (Z − X) / 2. From the measurement of line positions in the high-field Zeeman spectrum we find D − E = 0.84 ± 0.05 cm−1, D + E = 0.41 ± 0.05 cm−1. The values of D and E calculated for one-center spin–spin interaction are D − E = 0.42 cm−1 and D + E = 0.24 cm−1. The calculated ordering of the spin states is the same as that observed, but we suggest that there is significant second-order spin–orbit energy associated with the real splittings. Roughly the same splittings are seen for different vibronic levels of B31 associated with ν2′.

Laboratory Studies of the Visible NH3Bands with Applications to Jupiter

Ammonia red and green bands measured line positions, strengths and half widths applied to Jupiter atmospheric pressure determination

Temperature dependence of the crystal-field splittings and hyperfine structure in Eu2+:CaWO4 and evidence for nuclear quadrupole interactions

The crystal-field splittings and hyperfine-structure constants of Eu2+ in CaWO4 have been accurately measured at 4.2 °K and at 78 °K using the method of electron paramagnetic resonance. These measurements were intended to provide liquid-helium temperature parameters for ENDOR experiments presently in progress but showed significant differences from the earlier measurements of Bronstein and Volterra. Because of these differences and the considerable current interest in the values of these parameters for S-state ions, z-axis measurements were extended to cover the temperature range from 1.8 °K to room temperature.A very good fit to the measured line positions has been obtained by carrying out an exact diagonalization of the spin Hamiltonian within the 8S7/2 manifold. The parameters fitted are [Formula: see text], [Formula: see text], b20, b40, b44, b60, b44, A, and B. Residual discrepancies, of the order of a tenth of a line width, are shown to be consistent with the presence of a purely ionic quadrupole interaction and an interaction between the nuclear quadrupole moment and the crystalline electric field. The temperature variation of the dipolar hyperfine-coupling constant is shown to be consistent with the theory of Šimánek and Orbach as extended to rare earth ions in cubic lattices by Menne, Ames, and Lee if a Θ of 150 °K is assumed. Within the restrictions imposed by the lack of thermodynamic data and the assumption of a point-charge lattice, it is shown that the temperature dependence of the fourth- and sixth-order crystal-field parameters is consistent with the predominance of a splitting mechanism at least quadratic and more probably of fourth power in the crystalline potential. The second-order axial parameter is found to have a temperature dependence which can not be explained in terms of a single mechanism.

Mössbauer six-line spectra position analysis for Fe57 in metallic iron

The formulae for evaluating the parameters of magnetically split Mossbauer six-line spectra with quadrupole splitting from measured line positions are derived. Some special cases are considered and the suitability of the centre of gravity rule for the shift determination as well as the case of the internal magnetic field measurement from the distance of the outermost lines of the Mossbauer sextet are discussed. From the measured spectra of metallic iron the ratio of magnitudes of the nuclear magnetic moments for Fe57 ¦μ1/μ0¦= 1·701±0·008 is derived by means of the proposed method. Further, the internal magnetic field intensity at the Fe57 nucleus in metallic ironH i =(329·4±1·2) kOe and other quantities are determined.

Crystal field spectra of rare earth salts in the far infrared (10–50 cm −1)

Measurements of line positions, widths and strengths are reported for transitions within the crystal field split ground state of some rare earth double-nitrates and ethyl-sulphates.

Alternating Linewidth Effect in the ESR Spectra of Anion Radicals of Dinitromesitylenes and -durenes

Accurate measurements of line positions in the ESR spectra of the aminodinitromesitylene, dinitroisodurene, dinitromesitylene, and dinitrodurene anion radicals have permitted calculation of the dynamic frequency shifts arising from modulation of the isotropic nitrogen hyperfine splittings. The results are in good agreement with the predictions of the ``two-jump'' model proposed by Freed and Fraenkel to explain the phenomenon of alternating linewidths observed in the spectra of such radicals. The effects of solvent composition on the ESR splitting constants and linewidths of the dinitrodurene and dinitroisodurene anions were studied in DMF—water mixtures. The observed increase in nitrogen splittings and decrease in methyl-proton splittings with increased water concentration is in agreement with previous theories, and the data may be fitted to a simple model assuming equilibrium between 1:1 solvent—solute complexes. The MI=±1 lines for both the dinitrodurene and dinitroisodurene anions were found to rapidly increase in width with increasing water concentration. The two-jump model was combined with the assumption of 1:1 solvent—solute complexes to develop a four-jump model for dinitro radical anions in mixed solvents. The four-jump model was found, however, to be incapable of explaining the rapid increase in linewidth observed. Possible sources of difficulty are discussed.

X-Ray Diffractometry of Polymers by a Transmission Method

AbstractThe practicability of using a symmetrical transmission method for accurate measurement of line positions and intensities for polymer samples was investigated. In comparison with the conventional symmetrical reflection method, the transmission method has some inherent advantages in the measurement of line positions. Very little extraneous line asymmetry is introduced by transmission, and errors due to sample misalignment can usually be corrected empirically. On the other hand, the reflection method introduces noticeable line asymmetry and a shift of the center of intensity toward smaller 2θ. Also, errors due to sample misalignment may be difficult to correct. Intensity measurements can usually be made with about the same accuracy by either method. However, the transmission method is less sensitive to misalignment errors, especially at the lower diffraction angles.

Electron nuclear double resonance of the divalent europium ion

The electron nuclear double resonance spectrum of both isotopes 151 Eu and 163 Eu has been measured in a single crystal of calcium fluoride containing about 0.01 % Eu 2+ . As the lines were narrow ( ~ 10kc/s) the hyperfine structure parameter and the nuclear g-value were measured to high precision giving the following values: A 151 = -102.9069±0.0013 Mc/s, A 153 = -45.6730±0.0025 Mc/s B 151 = -0.7855±0.0052 Mc/s, B 153 = -2.0294 ±0.0068 Mc/s, gI 151 = - 7.4969±0.0020 (x 10 -4 )β, gI 153 = - 3.3125±0.0030 (x 10 -4 )β. In order to fit the measured line positions to the spin Hamiltonian which is usually assumed for the system it was necessary to add small higher-order terms. The results of these measurements are compared with the precise atomic beam measurement on Eu.

Rapid and Accurate Measurement of Line Positions on X-Ray Diffraction Films with the Aid of a Cathode-Ray Oscillograph

An apparatus containing a cathode-ray oscillograph has been developed for the measurement of positions of x-ray diffraction lines. A small portion of the film is scanned by a moving slit. A trace of film transmission versus distance appears on the screen of the oscillograph. Lines are easily measured by centering their traces on the screen. Measurements are made very rapidly. Accuracy depends on the sharpness of the line measured. Ordinary back-reflection x-ray lines can be measured to better than 0.02 mm, sharper lines or points may be located much more accurately. The apparatus is compact and has no parts easily damaged. The cost is less than for a recording photo-densitometer. It can, no doubt, be used for intensity measurements and for the measurement of spectrographic and other types of lines on photographic plates or films.