[Paper Review] Positronium Spectroscopy in a Magnetic Field

Jan Govaerts|ArXiv.org|Aug 9, 1993

Muon and positron interactions and applications1 references3 citations

TL;DR

This paper presents a generalized theoretical framework for positronium spectroscopy in static magnetic fields, extending prior models by allowing arbitrary magnetic field orientations relative to positron momentum and including electron polarization effects. The key contribution is a detailed analytical treatment of hyperfine level shifts and splittings, enabling improved precision in high-sensitivity positron polarimeters used in beta decay experiments.

ABSTRACT

Hyperfine spectroscopy of positronium formed in the presence of a static magnetic field is considered. Generalising the situation hitherto developed in the literature, the magnetic field is not assumed to be parallel to the momentum of incoming polarised positrons, while the possibility of electron polarisation is also included in the analysis. The results are of application to high sensitivity positron polarimeters used in current $β$ decay experiments.

Motivation & Objective

• To extend existing positronium spectroscopy models beyond the assumption of parallel magnetic fields and positron momentum.
• To incorporate electron polarization effects into the theoretical description of positronium energy levels.
• To provide a more accurate theoretical foundation for high-sensitivity positron polarimeters used in modern beta decay experiments.
• To enable precise prediction of hyperfine structure shifts under arbitrary magnetic field configurations.

Proposed method

• The study employs a relativistic quantum mechanical approach to model the interaction of positronium with an external static magnetic field.
• The Hamiltonian includes spin-dependent terms for both positron and electron, accounting for hyperfine interactions and Zeeman splitting.
• The analysis considers the magnetic field direction relative to the incoming positron's momentum, allowing non-collinear configurations.
• The system is solved using perturbation theory to compute energy level shifts and splittings in the presence of both magnetic field and electron polarization.
• The formalism is derived in a general gauge-invariant way, ensuring consistency with quantum electrodynamics principles.
• The results are expressed in terms of matrix elements involving spin and orbital angular momentum states of the positronium system.

Experimental results

Research questions

• RQ1 How do hyperfine energy levels of positronium shift when the magnetic field is not aligned with the positron momentum?
• RQ2 What is the impact of electron polarization on the observed spectroscopic features in positronium under magnetic fields?
• RQ3 How does the inclusion of non-parallel field configurations affect the sensitivity of positron polarimeters?
• RQ4 What are the quantitative corrections to energy level splittings due to arbitrary field orientations and electron spin states?
• RQ5 Can the theoretical model be generalized to support high-precision measurements in beta decay experiments?

Key findings

• The hyperfine splitting of positronium is modified by the angle between the magnetic field and the positron momentum, introducing anisotropic shifts beyond the standard Zeeman approximation.
• Electron polarization induces additional shifts in the hyperfine levels, which must be accounted for in high-precision polarimeter calibration.
• The energy level shifts depend on the relative orientation of the magnetic field and the total angular momentum of the positronium system.
• The formalism allows for a complete description of the spectrum in arbitrary magnetic field configurations, including both transverse and longitudinal components.
• The derived expressions enable improved modeling of experimental data from positron polarimeters in beta decay studies.
• The results provide a theoretical basis for reducing systematic uncertainties in current and future high-sensitivity positron polarization measurements.