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Physical Review

On Space Quantization in Time Varying Magnetic Fields

Lloyd Motz, M. E. Rose

Published Aug 15, 1936• 16 citations
Publisher

Abstract

The transitions between states of different space quantization which take place when an atom is passed through a weak inhomogeneous magnetic field are calculated by approximate methods taking into account the coupling between the nucleus and the orbital electrons. Two types of field are considered, namely, the field introduced by Majorana and the one introduced by G\"uttinger. For the Majorana field a discussion of the cases $I$ arbitrary $J=\frac{1}{2}$, $J$ arbitrary $I=\frac{1}{2}$, and $I$ and $J$ arbitrary with explicit application to the nitrogen atom is given. For the G\"uttinger field the general equations are set up for a field of any strength and are then applied to the case $I=J=\frac{1}{2}$.

DOI
10.1103/physrev.50.348

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The transitions between states of different space quantization which take place when an atom is passed through a weak inhomogeneous magnetic field are calculated by approximate methods taking into account the coupling between the nucleus and the orbital electrons. Two types of field are considered, namely, the field introduced by Majorana and the one introduced by G"uttinger. For the Majorana field a discussion of the cases III arbitrary J=12J=\frac{1}{2}J=21​, JJJ arbitrary I=12I=\frac{1}{2}I=21​, and III and JJJ arbitrary with explicit application to the nitrogen atom is given. For the G"uttinger field the general equations are set up for a field of any strength and are then applied to the case I=J=12I=J=\frac{1}{2}I=J=21​.
If a quantum mechanical particle passes a spatially finite region of a purely time-dependent potential, coherent emission and absorption of energy take place. Due to Zeeman interaction, this situation can be realized with neutrons crossing an oscillating magnetic field. We solve the corresponding Schr\"odinger equation for fields consisting of an arbitrary number of frequencies and measure the calculated transition amplitudes for the quantized energy transfer by means of time-dependent neutron interferometry. Investigating the interferometer contrast for magnetic signals consisting of a high number of modes whose phases are randomly distributed shows that noise fields and therefore decoherence processes can be modeled in this calculation as well.
This paper solves the problem of the interaction, via the field of virtual photon field with the emission or absorption of a real photon, of two atomic electrons located at arbitrary distances from one another. The interaction is interpreted as a third-order QED effect in the coordinate representation. The role of intermediate states with positive and negative frequencies is studied. A general expression is derived for the matrix elements of the operator of the effective electron-electron interaction energy for different types of quantum transitions. The expression makes it possible to calculate the probabilities of the corresponding transitions and to examine various patterns of induction of polarizing fields by one atom at the point occupied by the other atom. The exchange of virtual photons between the atoms located at arbitrary distances from one another is shown to lead to additional terms in the operators of spin-orbit and spin-spin coupling of the atomic electrons, over and above those in the corresponding Breit operators. It is shown that there is an important difference between the induction of polarizing fields and the transfer of optical photons. In particular, it is found that when polarizing fields are induced, a situation may arise in which the disappearance (production) of a photon takes place at the point occupied by one atom, while absorption (emission) of the same photon occurs at the place occupied by the other atom. A block diagram of an experimental device that could be used to study this property of polarizing fields is presented. Finally, a method of deriving integral field equations is proposed. The method is based on allowing for polarizing fields, and its effectiveness is demonstrated by the example of electric dipole and spin transitions in the spectrum of interacting atomic electrons.