Values Of Transition Probabilities Research Articles

On the Relative Transition Probabilities of BeO (B^1∑^+−X^1∑^+) System

It was shown that some of the values of transition probabilities from previous research were in significant error. The discrepancies found were of physical significance, and their origin was discussed and noted for future guidance in such problems.

A method for calculating vibrational transition probabilities

Relative vibrational transition probabilities for diatomic molecules can be calculated by methods utilizing band intensity observations or by methods not requiring such data. To date the latter class has been represented solely by the linear dipole moment function approximation. In this paper a second such method is developed. It makes use of the wave function expansion technique of Trischka and Salwen. Its critical assumption is the approximate equivalence of the Morse and simple harmonic potentials in the region about the potential minimum. This assumption is sufficient to remove all ambiguity in the relative signs of the matrix elements of the dipole moment. Further, it provides a relation through which the relative magnitudes of the matrix elements can be calculated. It is shown that this method is equivalent to using Morse eigenfunctions with a dipole moment function which departs from linearity in a manner that is qualitatively correct, at least in the region of the equilibrium configuration. The method is compared extensively with the linear approximation and with experiment. Insofar as the limited intensity data now available can show, it is generally superior to the linear approximation. The method can be of use in deriving Taylor coefficients for the expansion of the dipole moment function and in obtaining vibration-rotation interaction parameters. It also provides a new method for obtaining absolute values of transition probabilities. The experimental data required for this are values of the permanent dipole moment in two different vibrational levels. The procedure is illustrated by the calculation of the fundamental band strength of lithium hydride. The linear approximation and the present method are compared briefly with two methods which require intensity data. These are the quadratic and cubic approximations to the dipole moment function. It is suggested that the extent and the accuracy of the intensity data presently available is not sufficient for these methods to be of general use. Relative transition probabilities calculated by the present method are tabulated for all bands with v′ ≦ 9 for OH, HCl, and CO. The computational procedure used is outlined. It is not suitable for hand calculation but can be programmed for a high-speed computing machine with relative ease. On a large machine about one minute is required to compute the entire contents of each table.

Theory of Saturation in Electron Spin Resonance Spectra

A theory of saturation in electron spin resonance spectra exhibiting hyperfine splitting is presented. This theory is used to study the saturation of free radical spectra in solution, and a variety of relaxation processes are investigated. It is shown that motional modulation of the intramolecular electron-nuclear anisotropic dipole—dipole interaction introduces a relation between the saturation parameters and the hyperfine components that varies symmetrically about the center of the spectrum and causes a smaller degree of relaxation for the components in the central portion of the spectrum than for those in the wings. This relaxation mechanism introduces a greater dependence on nuclear spin state for radicals with several magnetic nuclei than for radicals with only one such nucleus. It is also shown that a cross term between this intramolecular dipolar interaction and motional modulation of the anisotropic g tensor introduces a relaxation that varies linearly from one side of the spectrum to the other. Numerical values of the relaxation-induced transition probabilities are estimated for the benzene negative ion, and tables are given from which saturation factors can be computed for a variety of conditions for several different spin systems. The relation between the spin-lattice relaxation time T1 and the parameters which determine saturation is discussed, and it is pointed out that these quantities are not equivalent in systems exhibiting cross relaxation.

Measurement of “optical” transition probabilities in the silver atom

Synopsis For 22 spectral lines of the silver atom the probability of spontaneous transition has been derived from measurements of the emission intensity of the line and the population of the corresponding upper level. The medium of excitation was the column of a vertical arc discharge in air of atmospheric pressure. The upper electrode (cathode) was a vertical carbon rod; the lower electrode was either a carbon rod filled with a mixture containing silver, or a silver rod. The length of the are was 1 1/2 cm, the current ca. 5 A and the axial field strength ca. 30 V/cm. The spectrum of the arc showed cyanogen bands and silver lines, the intensities of which were measured photographically. The arc temperature was derived from intensity ratios of the CN bands; in most cases the temperature was 5000 to 6000°K. For every exposure the relative populations of the upper levels of the silver lines were derived from the temperature. From these populations and the measured intensities of the silver lines the relative transition probabilities of the lines were calculated. The results are compiled in table I. As the concentration of the silver vapour in the arc is not accurately known, reliable values of the absolute transition probabilities cannot be derived from our measurements; we have confined ourselves to a rough estimation. On the other hand it could be established that in the relative measurements there was no disturbing effect of ionization of the vapour in the arc, nor of self-absorption of the measured silver lines. The transition probabilities of the resonance lines have not been measured.

Rotational Transition of Hydrogen Molecule by Collision

The previous calculation of rotational transition probability for para-hydrogen gas is improved by adding an attractive term to the intermolecular potential. Using the result of recent calculations by Evett and Margenau of intermolecular force, good agreement is obtained between the calculated and experimental values of transition probability. The transition probability is also calculated for H2-H collisions, because of its importance for the cooling of interstellar matter. According to our present knowledge of the intermolecular forces the H2-H potential shows much more appreciable anisotropy than does the H2-H2 potential, so that H2-H collisions are much more effective than H2-H2 collisions for the rotational transition, nearly 10 times for 100-1000°K.

Vibrational transition probabilities for the C2 Swan bands.

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Vibrational transition probabilities for the C2 Swan bands. Wyller, Arne A. Abstract Reliable values for the vibrational transition probabilities are of great importance in the determination of vibrational temperatures for late- type stars. The purpose of this investigation has been to obtain improved theoretical values pertaining to the C3 Swan bands. Dr. Ta-You Wu has recently adapted to this particular problem the WKB-approximation of wave mechanics. With this method it is possible to construct vibrational wave functions utilizing any potential function for the nuclei. The potential function of Hulburt and Hirschfelder was chosen, being more accurate than the commonly used Morse potential. J. G. Phillips' determination of the molecular constants for the electronic levels has been adopted throughout.1 Ten vibrational wave functions were constructed on the basis of the above method, two sets of five, with vibrational quantum numbers ranging from zero to four. The vibrational transition probability is proportional to the square of the integral over the wave functions for the levels involved in the transition. The integrals were evaluated by graphical methods with the aid of an IBM electronic computer. The wave functions are properly normalized decreasing the values of the transition probabilities by 1-10 per cent. The results give improved agreement with the experimental values of R. King2 notably in the $ I and - I sequences. 3.Ap. J. io8, 434, 3948. 2.Ap. J. io8, 429, 3948. Harvard College Observatory, Cambridge, Mass. Publication: The Astronomical Journal Pub Date: October 1952 DOI: 10.1086/106744 Bibcode: 1952AJ.....57..169W full text sources ADS |

De toepasselijkheid van de formule van saha in de electrische lichtboog

For a gas mixture in thermal equilibrium the degree of ionization of each component can be computed with the formula of Saha (§ 1). We have investigated the applicability of this formula for Sr and Ba vapour in the central part of the column of vertical arc discharges between carbon electrodes in air of atmospheric pressure. For that purpose we had to determine, for a small region in the arc, the concentration of the electrons, that of the ions and atoms in question, and also the temperature (§ 1). The former was found from the current, the electric field-strength, the mobility of the electrons and their radial distribution in the arc (arc diameter, § 5 and 6). The concentrations of the ions and atoms were derived from the intensities of some of their spectral lines, on the basis of the values of the corresponding transition probabilities (§ 4) and with the help of the formula of Boltzmann for the populations of the levels (§ 3) ; this formula had been checked previously. The temperature too was determined optically, namely from the intensity ratios in the CN bands which were also present in the spectrum (§ 2). Both sides of the checked eq. 3 are very sensitive to errors in the results and in the interpretation of the optical measurements; consequently no accurate agreement can be expected even if the formula of Saha is valid. The measurements were performed with a number of direct current arcs of different current-strengths and temperatures (§ 6 and table I), and also for the maximum phase of some alternating current arcs (50 cycles/sec) (§ 7 and table V). A comparison (method: § 8) of ths results (table II–IV and VII) shows a relatively good agreement (§ 9 and 10). Therefore we conclude that the formula of Saha is applicable to Sr and Ba in the arcs investigated, within an uncertainty margin of about 20% in the ionization.