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What is a Schiff moment anyway?

Amar Vutha

TL;DR

This work provides a transparent electrostatic picture of the Schiff moment and its interaction with atomic electrons relevant to time-reversal violation searches. It builds a simple multipole expansion of the electron–nucleus potential up to third order, identifying the Schiff moment $\vec{\mathscr{S}}=\vec{\mathscr{S}}_0+\vec{\mathscr{S}}_1$ and the associated $\mathcal{F}$-field that couples to it. Schiff shielding is discussed, showing that the nuclear EDM is canceled by electron rearrangement and that observable effects arise from the Schiff moment rather than the EDM. A concrete charge-distribution example and a hydrogenic calculation of the $\mathcal{F}$-field illustrate how the Schiff interaction leads to a nuclear-spin dependent energy shift, with strong enhancement for heavy nuclei and requiring $s$–$p$ mixing. The analysis connects a foundational electrostatic picture to measurable spin-structure shifts in heavy-atom or heavy-nucleus systems, informing precision tests of time-reversal symmetry beyond the Standard Model.

Abstract

Schiff moments of atomic nuclei are of considerable interest to experiments searching for undiscovered new physics that breaks time-reversal symmetry. I develop a simple picture of the Schiff moment of a charge distribution, and discuss the interaction of the Schiff moment of a nucleus with the field produced by an electron in an atom.

What is a Schiff moment anyway?

TL;DR

This work provides a transparent electrostatic picture of the Schiff moment and its interaction with atomic electrons relevant to time-reversal violation searches. It builds a simple multipole expansion of the electron–nucleus potential up to third order, identifying the Schiff moment and the associated -field that couples to it. Schiff shielding is discussed, showing that the nuclear EDM is canceled by electron rearrangement and that observable effects arise from the Schiff moment rather than the EDM. A concrete charge-distribution example and a hydrogenic calculation of the -field illustrate how the Schiff interaction leads to a nuclear-spin dependent energy shift, with strong enhancement for heavy nuclei and requiring – mixing. The analysis connects a foundational electrostatic picture to measurable spin-structure shifts in heavy-atom or heavy-nucleus systems, informing precision tests of time-reversal symmetry beyond the Standard Model.

Abstract

Schiff moments of atomic nuclei are of considerable interest to experiments searching for undiscovered new physics that breaks time-reversal symmetry. I develop a simple picture of the Schiff moment of a charge distribution, and discuss the interaction of the Schiff moment of a nucleus with the field produced by an electron in an atom.
Paper Structure (4 sections, 22 equations, 1 figure)

This paper contains 4 sections, 22 equations, 1 figure.

Table of Contents

  1. Electron interaction with a nuclear charge distribution
  2. Shielding of the nuclear electric dipole moment in an atom
  3. Charge distribution with a Schiff moment
  4. The $\mathcal{F}$-field

Figures (1)

  • Figure 1: The $\mathcal{F}$-field produced by an electron in an atom. This field is localized within a sphere of radius $\sim a$ (which we take to be much smaller than the size of an electron orbit), and is directed opposite to the electron's position vector $\vec{r}$. The $\mathcal{F}$-field couples to the Schiff moment of the nucleus as described by Equation (\ref{['eq:schiff_moment_interaction']}).