[Paper Review] The deuteron (nuclei) birefringence effect in a matter and in an electric field and the searches for an EDM of a deuteron (nucleus) rotating in a storage ring

V.G. Baryshevsky, A. R. Shirvel|ArXiv.org|Mar 22, 2005

Quantum, superfluid, helium dynamics1 references3 citations

TL;DR

This paper analyzes the deuteron birefringence effect in matter and electric fields as a critical systematic background in storage ring experiments searching for the deuteron electric dipole moment (EDM). It derives spin evolution equations including magnetic, electric dipole, and spin-dependent scattering interactions, showing that birefringence effects can mimic EDM-induced spin rotation and must be corrected. The key result is that birefringence in gas targets can produce spin rotation 100–1000× larger than the EDM signal, necessitating careful control and calibration in EDM experiments.

ABSTRACT

The phenomena of deuteron birefringence in a matter and an electric field should be accurately considered when preparing experiments for the EDM search with a storage ring, because they could imitate the spin rotation due to the EDM. Moreover, study of these effects in such experiments could provide to measure both the spin-dependent part of the amplitude of the coherent elastic scattering of a deuteron by a nucleus at the zero angle and the tensor electric polarizability of a deuteron.

Motivation & Objective

• To identify and quantify systematic effects from deuteron birefringence in matter and electric fields that could mimic a deuteron electric dipole moment (EDM) signal in storage ring experiments.
• To derive a comprehensive spin evolution equation including magnetic dipole, electric dipole, and spin-dependent scattering interactions for deuterons in a storage ring.
• To estimate the magnitude of spin rotation due to birefringence in residual gas, gas jet targets, and external electric fields, comparing them to the expected EDM signal.
• To demonstrate that birefringence effects can be exploited to measure the spin-dependent part of the forward elastic scattering amplitude and the deuteron's tensor electric polarizability.

Proposed method

• Derives the effective potential energy for a deuteron in a medium using the spin-dependent zero-angle coherent elastic scattering amplitude, expressed as $ \hat{V} = -\frac{2\pi\hbar^2}{M\gamma}N(d + d_1(\vec{S}\cdot\vec{n})^2) $.
• Models the interaction of the deuteron's tensor electric polarizability with an external electric field via $ \hat{V}_E = -\frac{1}{2}\hat{\alpha}_{ik}E_iE_k $, leading to spin-dependent energy splitting.
• Combines all spin-dependent interactions into a single time-dependent Schrödinger equation: $ i\hbar\frac{\partial\Psi(t)}{\partial t} = (\hat{H}_0 + \hat{V}_d + \hat{V} + \hat{V}_E)\Psi(t) $.
• Derives the spin rotation frequency due to birefringence in residual gas as $ \omega = \frac{2\pi N}{M\gamma}\hbar\,\texttt{Re}\,d_1 $.
• Calculates the effective spin rotation frequency in a gas jet polarimeter as $ \omega_{t\,\text{eff}} = \frac{2\pi j}{k}\,\texttt{Re}\,d_1\,\nu $, where $ j = N_t l $.
• Estimates the spin rotation due to the electric field using $ \omega_E \sim \alpha_T E^2 \cdot \text{Re}\,d_1 $, with $ \alpha_T \sim 10^{-37} \,\text{cm}^3 $.

Experimental results

Research questions

• RQ1 How do birefringence effects in residual gas and gas jet targets in a storage ring mimic the spin rotation expected from a deuteron electric dipole moment?
• RQ2 What is the magnitude of spin rotation due to deuteron birefringence in matter and in an external electric field, and how does it compare to the EDM signal?
• RQ3 Can the birefringence effect be used to measure the spin-dependent part of the forward elastic scattering amplitude of deuterons?
• RQ4 Can the tensor electric polarizability of the deuteron be extracted from birefringence measurements in an electric field?

Key findings

• The spin rotation frequency due to birefringence in a gas jet target is estimated at $ \omega_{t\,\text{eff}} \approx 10^{-5} - 10^{-4} \,\text{rad/s} $, which is two orders of magnitude larger than the expected EDM-induced rotation for $ d \sim 10^{-27} \, e\cdot\text{cm} $.
• The spin rotation due to residual gas at $ N \sim 10^9 \,\text{cm}^{-3} $ is $ \omega \approx 2 \times 10^{-7} \,\text{rad/s} $, comparable to the EDM signal for $ d \sim 10^{-27} \, e\cdot\text{cm} $.
• The spin rotation due to the electric field with $ E = 3.5 \,\text{MV/m} $ and $ \alpha_T \sim 10^{-37} \,\text{cm}^3 $ is $ \omega_E \sim 10^{-6} \,\text{rad/s} $, a significant background.
• The beam spin dichroism parameter $ \chi $ reaches $ \sim 3.4 \times 10^{-5} $ in the gas jet, indicating strong spin-dependent transmission differences.
• The birefringence effect in the gas jet is dominated by the spin-dependent scattering amplitude $ \texttt{Re}\,d_1 \sim 10^{-13} $, which can be extracted from data.
• The study shows that birefringence effects must be corrected in EDM experiments and can be used to measure the spin-dependent forward scattering amplitude and tensor electric polarizability.