scholarly journals A theory of some electron-levels in H 2

1932 ◽  
Vol 136 (830) ◽  
pp. 528-537 ◽  
Keyword(s):  
Stark Effect ◽  
Quantitative Agreement ◽  
Wave Functions ◽  
Variation Method ◽  
Quantum Electron ◽  
Quantum Wave ◽  
Approximate Wave ◽  
Experimental Values ◽  
Short Time ◽  
Good Agreement

§ 1. Introduction . —Preparatory to a theoretical investigation of the Stark-effect in the hydrogen molecule, it was found necessary to undertake the present study of some excited electron levels. Suitable approximate wave functions must be determined in order to calculate the Stark-effect perturbations associated with neighbouring states. The functions must be appropriate for certain integrations in which the equilibrium nuclear separations are used. Kemble and Zener have employed a method which gives wave functions suitable for great inter-atomic separation. Their calculations for “equili­brium” energies show rather poor quantitative agreement with experimental values for the 2 p ∏ states. In an unpublished study of the 2 p Ʃ states, using the method of Kemble and Zener, the writer also found great discrepancies. Guillemin and Zener used a variation method and obtained moderately good agreement with the experimental results for the 2 p 1 Ʃ state. A short time before the present paper was submitted for publication a paper by Hylleraas appeared. In it the energy curves for 2-quantum electron levels were determined. The results arrived at by Hylleraas agree well with the experimental data which he gives. In his paper Hylleraas does not discuss the methods by which his 2-quantum wave functions are constructed from the basic H 2 + -like functions which he uses.

Competitive reactions in the irradiation of anthracene + cyclohexane solutions

1959 ◽  
Vol 249 (1256) ◽  
pp. 51-64 ◽  
Keyword(s):  
Radiation Intensity ◽  
Quantitative Agreement ◽  
Radical Scavenger ◽  
Organic Systems ◽  
Low Concentrations ◽  
Radiation Induced ◽  
Experimental Values ◽  
Very High ◽  
Intensity Radiation ◽  
Good Agreement

Anthracene acts as a radical scavenger when present at low concentrations in irradiated hydrocarbons. A study has been made of the effect of radiation intensity and anthracene concentration on G( — A) , the number of anthracene molecules lost per 100 eV of energy absorbed. A theoretical calculation is made of the dependence of G( — A) on radiation intensity 1 and anthracene concentration ( A ), assuming that radiation-induced radicals (R.) are formed at random, and can either disappear by direct combination with one another, or with the anthracene to give RAR or RAAR bridges, or possibly some form of stabilized RA molecules. This theory is in good agreement with the experimental values of G( — A) measured at various low radiation intensities and anthracene concentrations. From the comparison estimates of the reactivity constants are derived. With very high intensity radiation quantitative agreement is less satisfactory, due to the non-steady conditions prevailing in a pulsed beam. The results obtained are compared with previous work on anthracene + hexane and iodine + cyclo hexane mixtures, in which the effect of radiation intensity was not investigated. The results reported here are of interest to the study of reaction kinetics in irradiated organic systems.

scholarly journals HYSTERESIS OF PERIODIC AND CHAOTIC PASSIVE Q-SWITCHING SELF-PULSATIONS IN A MOLECULAR LASER MODEL, AND THE STARK EFFECT AS A CODIMENSION-2 PARAMETER

2012 ◽  
Vol 22 (10) ◽  
pp. 1250238 ◽  
Author(s):  
EUSEBIUS J. DOEDEL ◽  
CARLOS L. PANDO L.
Keyword(s):  
Stark Effect ◽  
Molecular Model ◽  
Quantitative Agreement ◽  
Numerical Continuation ◽  
Necessary Condition ◽  
Bifurcation Structure ◽  
Small Shift ◽  
Q Switching ◽  
Laser Model ◽  
Good Agreement

We give a systematic comparison of a molecular model for a CO 2 laser with a fast saturable absorber and a reduced version of this model. Overall, we find that there is good agreement between these models. We use numerical continuation algorithms to analyze the bifurcation structure of the equations, and complement the results by numerical simulations to model possible experiments. Our study predicts the existence of isolas of periodic passive Q-switching self-pulsations and a rich structure of Q-intervals of stability for these periodic orbits, where Q represents the incoherent pump of the laser. These intervals correspond to the observed phenomenon known as period-adding cascades. Computed loci of codimension-1 bifurcations show that a small shift of a secondary parameter in the reduced model with respect to that of the complete model substantially improves their quantitative agreement. This parameter is associated with the action of the Stark effect in the absorber. We also discuss a necessary condition for chaotic windows to arise as Q changes.

The β+ Decay of 234Np and Other Isospin-Forbidden 0+→ 0+ Fermi Transitions

1984 ◽  
Vol 39 (12) ◽  
pp. 1168-1171
Author(s):  
C. T. Yap ◽  
E. L. Saw
Keyword(s):  
Nuclear Matrix ◽  
Coulomb Potential ◽  
Deformation Parameter ◽  
Theoretical Calculations ◽  
Wave Functions ◽  
Matrix Elements ◽  
Β Decay ◽  
A Value ◽  
Experimental Values ◽  
Good Agreement

Although experimental values of the Fermi nuclear matrix elements vary widely from about 1 × 10-3 to 40 × 10-3 for isospin-forbidden 0+→0+ β transitions, theoretical calculations using the Coulomb potential and Nilsson wave functions yielded values of MF in reasonably good agreement, except that of 234Np. However, our calculation of MF for this decay as a function of the deformation parameter β yielded a value of MF in good agreement with experiment for values of β between 0.1 and 0.2.

scholarly journals Multiconfiguration Dirac-Hartree-Fock calculations of Landé g-factors for ions of astrophysical interest: B II, C I−IV, Al I−II, Si I−IV, P II, S II, Cl III, Ar IV, Ca I, Ti II, Zr III, and Sn II

2020 ◽  
Vol 639 ◽  
pp. A25 ◽  
Author(s):  
W. Li ◽  
P. Rynkun ◽  
L. Radžiūtė ◽  
G. Gaigalas ◽  
B. Atalay ◽  
...  
Keyword(s):  
General Purpose ◽  
Wave Functions ◽  
Excitation Energies ◽  
Hartree Fock ◽  
Relativistic Configuration ◽  
Experimental Values ◽  
Relativistic Configuration Interaction ◽  
Relative Differences ◽  
Average Uncertainty ◽  
Good Agreement

Aims. The Landé g-factor is an important parameter in astrophysical spectropolarimetry, used to characterize the response of a line to a given value of the magnetic field. The purpose of this paper is to present accurate Landé g-factors for states in B II, C I−IV, Al I−II, Si I−IV, P II, S II, Cl III, Ar IV, Ca I, Ti II, Zr III, and Sn II. Methods. The multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2K, are employed in the present work to compute the Landé g-factors for states in B II, C I−IV, Al I−II, Si I−IV, P II, S II, Cl III, Ar IV, Ca I, Ti II, Zr III, and Sn II. The accuracy of the wave functions for the states, and thus the accuracy of the resulting Landé g-factors, is evaluated by comparing the computed excitation energies and energy separations with the National Institute of Standards and Technology (NIST) recommended data. Results. All excitation energies are in very good agreement with the NIST values except for Ti II, which has an average difference of 1.06%. The average uncertainty of the energy separations is well below 1% except for the even states of Al I; odd states of Si I, Ca I, Ti II, Zr III; and even states of Sn II for which the relative differences range between 1% and 2%. Comparisons of the computed Landé g-factors are made with available NIST data and experimental values. Analysing the LS-composition of the wave functions, we quantify the departures from LS-coupling and summarize the states for which there is a difference of more than 10% between the computed Landé g-factor and the Landé g-factor in pure LS-coupling. Finally, we compare the computed Landé g-factors with values from the Kurucz database.

scholarly journals Self-consistent field, including exchange and superposition of configurations, with some results for oxygen

1939 ◽  
Vol 238 (790) ◽  
pp. 229-247 ◽  
Keyword(s):  
Wave Functions ◽  
Radial Wave ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Approximate Wave ◽  
The One ◽  
The Individual ◽  
Single Configuration ◽  
Good Agreement

The calculation of approximate wave functions for the normal configurations of the ions O +++, O ++, O +, and neutral O, and the calculation of energy values from the wave functions, was carried out some years ago by Hartree and Black (1933)- In this work, the one-electron radial wave functions were calculated by the method of the selfconsistent field without exchange, but exchange terms were included in the calculation of the energy from these radial wave functions. In the energy calculations, the same radial wave functions were taken for each of the spectral terms arising from a single configuration; * consequently the ratios between the calculated intermultiplet separations were exactly those given by Slater’s (1929) theory of complex spectra, f The ratios between the observed intermultiplet separations, however, depart considerably from these theoretical values (for example, we have for 0 ++ ( 1 D - 1 S) / ( 3 P - 1 D), calc. 3 : 2, obs. 1.04 :1), although the energies of the individual terms, and particularly the intermultiplet separation between the lower terms, show quite a good agreement with the observed values.

A variational method for calculating nuclear spin-spin interactions in molecules

1957 ◽  
Vol 243 (1233) ◽  
pp. 274-280 ◽  
Keyword(s):  
Magnetic Field ◽  
Nuclear Spin ◽  
Valence Bond ◽  
Wave Functions ◽  
Zero Magnetic Field ◽  
Variation Method ◽  
Magnetic Shielding ◽  
Spin Interactions ◽  
General Variation ◽  
Good Agreement

A general variation method is developed for determining: ( a ) the magnetic shielding of nuclear spin-spin interactions in molecules; ( b ) the electron-coupled nuclear spin-spin interactions in molecules. Using simple valence-bond and molecular-orbital wave functions calculations have been made for the HD molecule. It is concluded that effect ( a ) is small compared with ( b ). Both wave functions lead to values for the zero magnetic field splitting of about 49 c/s, in good agreement with the observed value of 43 c/s.

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.

scholarly journals DFT calculation and assignment of vibrational spectra of aryl and alkyl chlorophosphates

2014 ◽  
Vol 12 (2) ◽  
pp. 153-163
Author(s):  
Viktor Anishchenko ◽  
Vladimir Rybachenko ◽  
Konstantin Chotiy ◽  
Andrey Redko
Keyword(s):  
Vibrational Spectra ◽  
Basis Sets ◽  
Heavy Atoms ◽  
Wide Range ◽  
Complete Assignment ◽  
Key Factor ◽  
Polarization Functions ◽  
Experimental Values ◽  
Semi Empirical ◽  
Good Agreement

AbstractDFT calculations of vibrational spectra of chlorophosphates using wide range of basis sets and hybrid functionals were performed. Good agreement between calculated and experimental vibrational spectra was reached by the combination of non-empirical functional PBE0 with both middle and large basis sets. The frequencies of the stretching vibrations of the phosphate group calculated using semi-empirical functional B3LYP for all basis sets deviate significantly from the experimental values. The number of polarization functions on heavy atoms was shown to be a key factor for the calculation of vibrational frequencies of organophosphates. The importance of consideration of all the stable rotamers for a complete assignment of fundamental modes was shown.

scholarly journals Algebraic Approach to Exact Solution of the (2 + 1)-Dimensional Dirac Oscillator in the Noncommutative Phase Space

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
H. Panahi ◽  
A. Savadi
Keyword(s):  
Exact Solution ◽  
Phase Space ◽  
Algebraic Approach ◽  
Wave Functions ◽  
Dirac Oscillator ◽  
Noncommutative Phase Space ◽  
Energy Eigenvalues ◽  
Good Agreement

We study the (2 + 1)-dimensional Dirac oscillator in the noncommutative phase space and the energy eigenvalues and the corresponding wave functions of the system are obtained through the sl(2) algebraization. It is shown that the results are in good agreement with those obtained previously via a different method.

scholarly journals Efficiency of immersion mode ice nucleation on surrogates of mineral dust

2007 ◽  
Vol 7 (19) ◽  
pp. 5081-5091 ◽  
Author(s):  
C. Marcolli ◽  
S. Gedamke ◽  
T. Peter ◽  
B. Zobrist
Keyword(s):  
Contact Angle ◽  
Active Sites ◽  
Quantitative Agreement ◽  
Ice Nucleation ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Aqueous Suspensions ◽  
Freezing Temperatures ◽  
Good Agreement ◽  
Heterogeneous Ice Nucleation

Abstract. A differential scanning calorimeter (DSC) was used to explore heterogeneous ice nucleation of emulsified aqueous suspensions of two Arizona test dust (ATD) samples with particle diameters of nominally 0–3 and 0–7 μm, respectively. Aqueous suspensions with ATD concentrations of 0.01–20 wt% have been investigated. The DSC thermograms exhibit a homogeneous and a heterogeneous freezing peak whose intensity ratios vary with the ATD concentration in the aqueous suspensions. Homogeneous freezing temperatures are in good agreement with recent measurements by other techniques. Depending on ATD concentration, heterogeneous ice nucleation occurred at temperatures as high as 256 K or down to the onset of homogeneous ice nucleation (237 K). For ATD-induced ice formation Classical Nucleation Theory (CNT) offers a suitable framework to parameterize nucleation rates as a function of temperature, experimentally determined ATD size, and emulsion droplet volume distributions. The latter two quantities serve to estimate the total heterogeneous surface area present in a droplet, whereas the suitability of an individual heterogeneous site to trigger nucleation is described by the compatibility function (or contact angle) in CNT. The intensity ratio of homogeneous to heterogeneous freezing peaks is in good agreement with the assumption that the ATD particles are randomly distributed amongst the emulsion droplets. The observed dependence of the heterogeneous freezing temperatures on ATD concentrations cannot be described by assuming a constant contact angle for all ATD particles, but requires the ice nucleation efficiency of ATD particles to be (log)normally distributed amongst the particles. Best quantitative agreement is reached when explicitly assuming that high-compatibility sites are rare and that therefore larger particles have on average more and better active sites than smaller ones. This analysis suggests that a particle has to have a diameter of at least 0.1 μm to exhibit on average one active site.

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