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Theory of Doublet Spectra under Magnetic Perturbation

S. Sengupta

Published Jul 1, 1949• 0 citations
OpenAlex

Abstract

The problem of a spinning electron moving round the nudeu.s in the piesence of an external magnetic held ha.sbeen considered from the wave-statistical point of view.The general expressions for energies and wave functions in any held strength have l)een obtained.The problems of no field, weak field (Zeeman effect) and strong field (Paschen-Back effect) are considered as .specialcases.The resnlt.s for the no field case are identical with tho.se obtained in the earlier paper (Kar and Sengnpta.uj'ig).Other results also agree with the well-known spectro,scopic formulae,

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Abstract 1. The chief object of the present paper is to present a simple system of equations which are competent to determine the frequencies and intensities of the lines in the standard Zeeman effect. By the standard Zeeman effect is meant the type where the terms are given by Landé’s "g"and “γ” formulæ, and where the multiplicity of the two sets of terms is the same. It will probably be held that the theory of such multiplets has been fairly completely understood for the last two years owing to the works of Sommerfeld, Heisenberg, Landé and Pauli, and the main new contribution of the present work is that, whereas these writers gave formulæ valid only either in weak or strong field (except for doublets, where Heisenberg and Jordan give the value for any strength), here we have complete formulæ from which the intensity of any component in any strength of field can be obtained merely from the solution of rather simple algebraic equations. The proper attack on this problem would undoubtedly be by way of the recent work of Heisenberg on the helium spectrum, and his still more recent work on complex spectra; but this theory is still in the making, so that it has not been practicable to apply it here, and to this extent our results are unverified. Their validity rests firstly on a complete verification of all known facts connected with both weak and strong fields (and intermediate fields for doublets), and also on a conformity with the general features of wave mechanics. The work of Heisenberg and Jordan could readily have been adapted to give all the results of the present paper; but it would have been harder to follow because the matrix methods are not so easy for most readers as are spherical harmonics.

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Optics and Spectroscopy•Dec 1, 2000•2 citations
The problem of a spinning electron moving round the nudeu.s in the piesence of an external magnetic held ha.sbeen considered from the wave-statistical point of view.The general expressions for energies and wave functions in any held strength have l)een obtained.The problems of no field, weak field (Zeeman effect) and strong field (Paschen-Back effect) are considered as .specialcases.The resnlt.s for the no field case are identical with tho.se obtained in the earlier paper (Kar and Sengnpta.uj'ig).Other results also agree with the well-known spectro,scopic formulae,
Abstract 1. The chief object of the present paper is to present a simple system of equations which are competent to determine the frequencies and intensities of the lines in the standard Zeeman effect. By the standard Zeeman effect is meant the type where the terms are given by Landé’s "g"and “γ” formulæ, and where the multiplicity of the two sets of terms is the same. It will probably be held that the theory of such multiplets has been fairly completely understood for the last two years owing to the works of Sommerfeld, Heisenberg, Landé and Pauli, and the main new contribution of the present work is that, whereas these writers gave formulæ valid only either in weak or strong field (except for doublets, where Heisenberg and Jordan give the value for any strength), here we have complete formulæ from which the intensity of any component in any strength of field can be obtained merely from the solution of rather simple algebraic equations. The proper attack on this problem would undoubtedly be by way of the recent work of Heisenberg on the helium spectrum, and his still more recent work on complex spectra; but this theory is still in the making, so that it has not been practicable to apply it here, and to this extent our results are unverified. Their validity rests firstly on a complete verification of all known facts connected with both weak and strong fields (and intermediate fields for doublets), and also on a conformity with the general features of wave mechanics. The work of Heisenberg and Jordan could readily have been adapted to give all the results of the present paper; but it would have been harder to follow because the matrix methods are not so easy for most readers as are spherical harmonics.
Using a kind of potential model wave function for alkali metal atoms, we nonperturbatively study the effect of fine structure on the Rydberg spectra of Cs atom in a strong magnetic field. Our numerical results reveal spectral structure dramatically different from the well-established Paschen-Back effect, and we argue that the fine structure of the Rydberg Cs atom cannot be neglected even in a magnetic field as strong as several teslas. We also give an error estimate of our results and a word on possible experimental verification. \textcopyright{} 1996 The American Physical Society.
Abstract 1. As soon as it was appreciated that the phenomenon of the "spinning electron" was to be attributed to the existance of simultaneous wave functions, the question naturally arose as to how far there would be an analogy with the polarisation of light, and in particular whether in diffraction by a slit or grating or in reflexion from a mirror, electrons would be selected having a preferential direction of magnetisation. Dynamical conceptions suggest that it would require a magnetic force to produce a change in the polarisation, so that the general indication was rather strongly negative, and it seemed hardly worth while to verify the fact by direct soultion. I believe, however, that recently experiments have been undertaken to search for such an effect (by means of successive diffractions from two crystals), and in view of this I have examined the question more closely. The result, broadly speaking, bears out the first conjecture that no effect could be observed in practice, but in certain cases (of a rather hypothetical kind) an effect might be found and the whole problem is interesting as an example of the wave theory. The essence of the matter is sufficiently represented by taking a line grating instead of a crystal, and, furthermore, by limiting the electric and magnetic forces of the grating in such a way that there shall only be first order spectra on each side, two reflected and two transmitted. The grating is supposed made out of periodic distribution of electric or magnetic material. Actual crystals will consist of almost purely electric material, but the magnetic case is as easy to treat and, though unpractical, gives rise to interesting results. It will appear that when a polarised electron wave falls on such a grating, the direction of magnetisation may be changed in the diffracted rays. It is a true polarisation effect in that the change in direction is independent of the strength of the field in the grating, which only determines the total intensity.
Analytical expressions for the dependence of the intensity of Zeeman components of doublet lines on the magnetic field are obtained. Sharp changes of these function on passing from the anomalous Zeeman effect to the Paschen-Back effect lead to the disappearance of marginal lines and the equalization of intensities of remaining lines. In the region of the complete Paschen-Back effect, a strong influence on these dependences is produced by the dynamic atom-field interaction, which weakens the paramagnetic effect in the states with a positive magnetic quantum number m and enhances the effect in the states with a negative m . Simple analytical expressions are obtained that take into account the effect of the diamagnetic interaction on line intensities. The role of the diamagnetic interaction increases in Rydberg atomic states with a large spin-orbit splitting. For the states with m > 0, it can lead to the “diamagnetic reversal” of the Paschen-Back effect, i.e., the recovery of the anomalous Zeeman effect.