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Journal of Guizhou Normal University

Simple treatment of Paschen-Back effect

Feng Jing

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

In a strong magnetic field, the single electron's (valence's) atom overlooks electronic interaction of the spin track. Electronic spin and track vector make Larmor spin around the outer magnetic field respectively and can split energy level. The paper discusses the fission of atom spectrum and puts forward the frequency formula after spectrum splitting.

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In a strong magnetic field, the single electron's (valence's) atom overlooks electronic interaction of the spin track. Electronic spin and track vector make Larmor spin around the outer magnetic field respectively and can split energy level. The paper discusses the fission of atom spectrum and puts forward the frequency formula after spectrum splitting.
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.
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,
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.
A Rydberg atom has a highly excited valence electron which is weakly bound and far from the nucleus. These atoms have exaggerated properties that make them attractive candidates for quantum computation and studies of fundamental quantum mechanics. The discrete energy levels of Rydberg atoms are shifted in the presence of an electric field by the Stark effect and are similarly shifted due to a magnetic field by the Zeeman effect. These effects couple the energy levels together, creating avoiding crossings. At these avoided crossings, an electron in one energy level can jump to the other. Our goal is to be able to use these avoided crossings to put the electron in a superposition state of both energy levels. In order to achieve this we created new software that enables us to calculate the energy levels of an electron in both a magnetic and an electric field. We present energy level maps visualizing the results of the Stark and Zeeman effects.
Electron spin In our development of quantum mechanics to this point, the behavior of a particle, usually an electron, is governed by a wave function that is dependent only on the cartesian coordinates x, y, z or, equivalently, on the spherical coordinates r , θ, ϕ. There are, however, experimental observations that cannot be explained by a wave function which depends on cartesian coordinates alone. In a quantum-mechanical treatment of an alkali metal atom, the lone valence electron may be considered as moving in the combined field of the nucleus and the core electrons. In contrast to the hydrogen-like atom, the energy levels of this valence electron are found to depend on both the principal and the azimuthal quantum numbers. The experimental spectral line pattern corresponding to transitions between these energy levels, although more complex than the pattern for the hydrogen-like atom, is readily explained. However, in a highly resolved spectrum, an additional complexity is observed; most of the spectral lines are actually composed of two lines with nearly identical wave numbers. In an alkaline-earth metal atom, which has two valence electrons, many of the lines in a highly resolved spectrum are split into three closely spaced lines. The spectral lines for the hydrogen atom, as discussed in Section 6.5, are again observed to be composed of several very closely spaced lines, with equation (6.83) giving the average wave number of each grouping.