General classical and quantum-mechanical description of magnetic resonance: An application to electric-dipole-moment experiments

TL;DR

This paper develops a comprehensive classical and quantum framework for magnetic resonance, crucial for analyzing spin dynamics in electric-dipole-moment experiments, and derives exact formulas for resonance effects including electric dipole moments.

Contribution

It provides the first exact formulas for electric dipole moment effects and compares classical and quantum approaches for magnetic resonance in storage rings.

Findings

Exact formulas for electric dipole moment effects derived.

Quantum and classical approaches show full agreement.

Differences between rf electric-field flipper and rf Wien filter effects identified.

Abstract

A general theoretical description of a magnetic resonance is presented. This description is necessary for a detailed analysis of spin dynamics in electric-dipole-moment experiments in storage rings. General formulas describing a behavior of all components of the polarization vector at the magnetic resonance are obtained for an arbitrary initial polarization. These formulas are exact on condition that the nonresonance rotating field is neglected. The spin dynamics is also calculated at frequencies far from resonance with allowance for both rotating fields. A general quantum-mechanical analysis of the spin evolution at the magnetic resonance is fulfilled and the full agreement between the classical and quantum-mechanical approaches is shown. Quasimagnetic resonances for particles and nuclei moving in noncontinuous perturbing fields of accelerators and storage rings are considered. Distinguishing features of quasimagnetic resonances in storage ring electric-dipole-moment experiments are investigated in detail. The exact formulas for the effect caused by the electric dipole moment are derived. The difference between the resonance effects conditioned by the rf electric-field flipper and the rf Wien filter is found and is calculated for the first time. The existence of this difference is crucial for the establishment of a consent between analytical derivations and computer simulations and for checking spin tracking programs. Main systematical errors are considered.