VACUUM-ULTRAVIOLET EMISSION AND ABSORPTION SPECTRUM OF THE NO MOLECULE: THE 2Δ STATES AND THEIR INTERACTIONS

1966 ◽  
Vol 44 (12) ◽  
pp. 3197-3216 ◽  
Author(s):  
Ch. Jungen
Keyword(s):  
Absorption Spectrum ◽  
Excited States ◽  
Vacuum Ultraviolet ◽  
Order Approximation ◽  
Electronic Configuration ◽  
Zero Order ◽  
Matrix Elements ◽  
Ultraviolet Emission ◽  
Zero Order Approximation ◽  
The Matrix

The emission spectrum of NO between 1 600 and 1 400 Å has been studied with a 1-m vacuum spectrograph. It consists of the two types of mutually perturbing 2Δ–X2Π bands already known from the much more complex absorption spectrum: the Rydberg systems F2Δ–X2Π, N2Δ–X2Π and the non-Rydberg system B′ 2Δ–X2Π. The interactions between the excited states of different electron configurations are of special interest. The matrix elements H = Hvib ∙ He have been obtained from detailed rotational analyses, a "deperturbation" in two steps has been carried out, and constants for the deperturbed 2Δ states are given. With calculated overlap integrals Hvib, the electronic configuration interaction energy He is derived. "Crossing" potential energy curves have been shown to be the appropriate zero-order approximation when [Formula: see text]. The phase of the interaction, i.e. the sign of He, has been deduced from the perturbed intensities of the observed bands.

Simultaneous Determination of Several Elements by Spectrochemical Addition Method … (II) (Tabulation of Analytical Value)

1968 ◽  
Vol 22 (6) ◽  
pp. 749-752 ◽  
Author(s):  
Isoo Masuda ◽  
Tamon Inouye
Keyword(s):  
Simultaneous Determination ◽  
Order Approximation ◽  
Analytical Data ◽  
Zero Order ◽  
Dilution Factor ◽  
Improved Method ◽  
Addition Method ◽  
Zero Order Approximation ◽  
First Approximation

An improved method for the tabulation of analytical data, obtained by addition and successive dilution procedures for spectrochemical analysis, is presented. The author's previous work shows that the solution of the first approximation diverges at some dilution factor smaller than unity when the slope of the working curve of added series is greater than that of unadded series. By obtaining the distance between this position and the origin, and taking it as a correction factor for zero-order approximation, tabulation of the analytical value, in the case of β>α, is carried out. One parameter of the calculation is deleted by normalizing the spectral intensity; therefore, the tabulation can be simplified.

scholarly journals Терагерцовая спектроскопия магнитоэлектрика HoAl-=SUB=-3-=/SUB=-(BO-=SUB=-3-=/SUB=-)-=SUB=-4-=/SUB=-

2022 ◽  
Vol 130 (1) ◽  
pp. 59
Author(s):  
А.М. Кузьменко ◽  
В.Ю. Иванов ◽  
А.Ю. Тихановский ◽  
А.Г. Пименов ◽  
А.М. Шуваев ◽  
...  
Keyword(s):  
Crystal Field ◽  
Excited States ◽  
Ground State ◽  
Theoretical Study ◽  
Low Frequency ◽  
Local Symmetry ◽  
Matrix Elements ◽  
The Matrix ◽  
Excitation Conditions ◽  
Ground Multiplet

Experimental and theoretical study of submillimeter (terahertz) spectroscopic and magnetic properties of the rare-earth aluminum borate HoAl3(BO3)4 were performed at temperatures 3–300 K. In the transmittance spectra a number of resonance lines were detected at frequencies 2–35 cm–1 for different radiation polarizations. These modes were identified as transitions between the lower levels of the ground multiplet of the Ho3+ ion split by the crystal field, including both transitions from the ground state to the excited ones and transitions between the excited states. The established excitation conditions of the observed modes and the simulation of the spectra made it possible to separate the magnetic and electric dipole transitions and to determine the energies of the corresponding states, their symmetry, and the matrix elements of the transitions. Low-frequency lines that do not fit into the established picture of the electron states of Ho3+ were also found; these lines, apparently, correspond to the ions with the distorted by defects local symmetry of the crystal field.

scholarly journals On the Dynamics of Canyon–Flow Interactions

2018 ◽  
Vol 6 (4) ◽  
pp. 129 ◽  
Author(s):  
Jochen Kämpf
Keyword(s):  
Rossby Waves ◽  
Order Approximation ◽  
Zero Order ◽  
Submarine Canyons ◽  
Zero Order Approximation ◽  
Flow Disturbances ◽  
Flow Interactions ◽  
Direction Dependence ◽  
Topographic Rossby Waves ◽  
Fundamental Physical

This paper explores the dynamical origin and physical characteristics of flow disturbances induced by ocean currents in interaction with shelf-incised submarine canyons. To this end, a process-oriented hydrodynamic model is applied in a series of case studies. The focus of studies is the canyon-upwelling process in which seawater is moved from the upper continental slope onto the shelf within a shelf-break canyon. Results reveal that the generation of canyon upwelling, to zero-order approximation, is a barotropic and friction-independent quasi-geostrophic process. Hence, the principle of conservation of potential vorticity for such flows is sufficient to explain the fundamental physical properties of the canyon-upwelling process. For instance, this principle explains the direction-dependence of the canyon-upwelling process. This principle also explains the formation of stationary topographic Rossby waves downstream from the canyon that can lead to far-field effects. Density effects, being of secondary influence to the canyon-upwelling process, result in the intensification of canyon-upwelling flows via the formation of narrow near-bottom density fronts and associated baroclinic geostrophic frontal flows. Findings of this work reveal that the apparently complex canyon-upwelling process is much more basic than previously thought.

Absorption spectrum of the NO molecule. VIII. The heterogeneous (2Σ–2Π) interactions between excited states

1968 ◽  
Vol 46 (8) ◽  
pp. 987-1003 ◽  
Author(s):  
Ch. Jungen ◽  
E. Miescher
Keyword(s):  
Absorption Spectrum ◽  
High Resolution ◽  
Excited States ◽  
Rydberg State ◽  
Vacuum Ultraviolet ◽  
Principal Quantum Number ◽  
Rydberg States ◽  
Infrared Emission ◽  
Strong Interactions ◽  
Rydberg Series

Heterogeneous perturbations 2E+ ~ 2Π of largely different magnitudes are observed with high resolution in the vacuum-ultraviolet absorption and in the infrared emission spectrum of the NO molecule. The rotational interactions between 2Σ+ Rydberg states and levels of the B2Π non-Rydberg state are shown to be "configurationally forbidden", but produced by the configuration interaction between the non-Rydberg levels and 2Π Rydberg states. The latter together with the 2Σ+ Rydberg states form p complexes. In this way the interactions display the l uncoupling in the complexes; they can be evaluated theoretically and can be analyzed fully. The cases of the strong interactions D2Σ+(v = 3) ~ B2Π(v = 16)and D2Σ+(v = 5) ~ B2Π(v = 21) and of the weaker D2Σ+(v = 1) ~ B2Π(v = 11), all three observed as perturbations in ε bands crossing 3 bands, are discussed in detail. It is further shown that perturbations between γ bands and β bands as well as perturbations between analogous bands of higher principal quantum number are absent, and thus the assignment of the A2Σ+ and E2Σ+ states to the s Rydberg series is confirmed.

A perturbation method for Dirac’s new electrodynamics

1952 ◽  
Vol 213 (1115) ◽  
pp. 520-529 ◽  
Keyword(s):  
General Solution ◽  
Perturbation Method ◽  
Order Approximation ◽  
Zero Order ◽  
Classical Electrodynamics ◽  
Coupling Constant ◽  
Irrotational Flow ◽  
Zero Order Approximation ◽  
Fundamental Equations

The fundamental equations of Dirac’s new classical electrodynamics cannot be solved with the conventional perturbation method because there is no possibility of setting the coupling constant e equal to zero to start with. A perturbation method is worked out under the assumption that the charge is small, which means that the field created by the charge is neglected in the zero-order approximation. A general solution for the case of irrotational flow and another one for small vorticity are given. The equations derived are not easily soluble for large vorticity.

The absorption and emission spectra of HD in the vacuum ultraviolet

1976 ◽  
Vol 54 (5) ◽  
pp. 525-567 ◽  
Author(s):  
I. Dabrowski ◽  
G. Herzberg
Keyword(s):  
Absorption Spectrum ◽  
Ab Initio ◽  
Excited States ◽  
Vacuum Ultraviolet ◽  
Emission Spectra ◽  
Dissociation Limit ◽  
Infinite Mass ◽  
Ab Initio Theory ◽  
Vibrational Constants ◽  
Weak Transitions

The absorption spectrum of HD has been studied under high resolution in the vacuum ultraviolet to 840 Å, the emission spectrum to 1000 Å. The analysis of the latter gives accurate rotational constants and vibrational intervals of the ground state right up to the dissociation limit. Comparing these experimental data with calculations from ab initio theory, agreement to the same extent as was previously found for H2 and D2 is obtained. Extrapolation of the obs. – calc. values from H2 and D2 to infinite mass yields agreement with the recently revised theoretical values to within less than 0.1 for v < 7 and less than 0.5 cm−1 for the whole range of observed v values. The deviations for finite mass (H2 and D2) are clearly due to the non-adiabatic corrections neglected in the ab initio calculations. The results for HD are not halfway between H2 and D2 but are closer to H2. This apparent anomaly can be quantitatively accounted for, on the basis of recent calculations of Wolniewicz, by the effect of additional nonadiabatic corrections caused by the excited Σu states which in HD, unlike H2 and D2, can interact with the ground state.The rotational and vibrational constants of the excited states B1Σu+, C1Πu, and B′1Σu+ show somewhat larger deviations from ab initio values ranging for v0v from 5 to 120 cm−1, just as for H2 and D2. The electronic isotope shift of HD lies approximately half-way between the values of H2 and D2 as expected. In addition to the B–X, C–X, and B′–X systems the absorption spectrum of HD, unlike that of H2 and D2, shows an extensive progression of weak transitions to the double minimum state EF1Σg+ and a few very weak transitions to the G1Σg+ and I1Πg states. For the EF state both levels in the outer minimum (F) and levels above the maximum are observed. The correlation of the six excited states B, C, B′, EF, G, and I to the two close-lying dissociation limits corresponding to H + D* and H* + D is briefly discussed.

QUANTUM PHASE TRANSITIONAL BEHAVIOR IN THE EXTENDED CASTEN TRIANGLE OF THE INTERACTING BOSON MODEL

2006 ◽  
Vol 15 (08) ◽  
pp. 1723-1733 ◽  
Author(s):  
FENG PAN ◽  
TAO WANG ◽  
Y.-S. HUO ◽  
J. P. DRAAYER
Keyword(s):  
Excited States ◽  
Quantum Phase ◽  
Interacting Boson Model ◽  
Matrix Elements ◽  
Fortran Code ◽  
Model Hamiltonian ◽  
Transitional Behavior ◽  
The Matrix ◽  
Boson Model ◽  
Shape Phase Transition

Quantum phase transitional patterns in the whole parameter space of the consistent-Q Hamiltonian in the Interacting Boson Model are studied based on an implemented Fortran code for numerical computation of the matrix elements in the SU (3) Draayer-Akiyama basis. Results with respect to both ground and some excited states of the model Hamiltonian are discussed. Quantum phase transitional behavior under a variety of parameter situations is shown. It is found that transitional behavior of excited states is more complicated. Pt isotopes are taken as examples in illustrating the prolate-oblate shape phase transition.

Sign in / Sign up

Export Citation Format

Share Document