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Simulation of Anomalous Zeeman Effect and Paschen-Back Effect for Positronium Atom when Electron Spins Upward and Downward with s=+ 1/2

Hadi Dawyich Zirzur

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

The research aims are for studying and calculation spin - orbit energy correction and Darwin’s correction when

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The orbital ${\mathrm{\ensuremath{\mu}}}_{\mathit{L}}$\ensuremath{\cdot}B and diamagnetic A2{\mathit{A}}^{2}A2 interactions of electrons and positrons with an external magnetic field lead to a small quadratic Zeeman shift in the L=0, mS{\mathit{m}}_{\mathit{S}}mS​=\ifmmode\pm\else\textpm\fi{}1 states of positronium, which, unlike the mS{\mathit{m}}_{\mathit{S}}mS​=0 states, are not affected by the usual, spin-induced Zeeman shifts. For the n=1 states, this shift would be about 2 kHz in a field of 1000 G. These additional shifts are the same in all spin states for L=0 but do depend on n.
The linear Zeeman effect in the molecular positronium Ps2 (dipositronium) is predicted for some of S=1S=1S=1, M=±1M=\pm1M=±1 states. This result is opposite to the case of the positronium atom; the latter has only quadratic Zeeman effect.
Abstract In this chapter we review time-independent and time-dependent perturbation theory in quantum mechanics. We begin with Rayleigh-Schrödinger perturbation theory for small corrections to the Hamiltonian for non-degenerate and degenerate spectra, which leads us to a discussion of avoided crossings. We then apply these methods to calculate the fine-structure corrections for the energy levels of the hydrogen atom, including the relativistic correction to the kinetic energy, the spin-orbit correction, and the Darwin term. We then turn to the effect of weak constant magnetic fields: for the resulting Zeeman effect we distinguish between the anomalous Zeeman effect and the Paschen-Back effect. In the context of the corresponding Stark effect for electric fields we introduce the Wigner-Eckart theorem and calculate perturbations to first and second order. We then turn to time-independent problems and discuss the Born-von Neumann series for the propagator, time-ordered integrals, the interaction picture, before explaining Fermi’s golden rule.