A team of researchers has presented new experimental and theoretical findings concerning the bound electron g-factor in lithium-like tin, boasting a substantially higher nuclear charge compared to previous measurements.The experiment reached an accuracy of 0.5 parts per billion, while the theoretical prediction achieved a precision of 6 parts per billion using an enhanced interelectronic Quantum Electrodynamics (QED) method.

Quantum Electrodynamics: Striving for Precision

Quantum electrodynamics (QED) stands as the fundamental theory illuminating all electromagnetic phenomena, including light, and is renowned as the most precisely tested theory in physics. It has undergone rigorous testing, achieving accuracy up to 0.1 parts per billion. The very strength of QED motivates physicists to subject it to even more stringent tests and explore its potential boundaries. Any notable discrepancy could indicate the presence of new physics.

QED elucidates the electromagnetic interaction between charged particles as the exchange of “virtual” photons, illustrating how electrons within an atom interact with each other and the nucleus.This also includes their interaction with themselves through the emission and reabsorption of a photon,a phenomenon termed “self energy.” Furthermore, the physical vacuum is not empty but filled with virtual particles like electron-positron pairs that constantly appear and disappear within the constraints of quantum physics’ uncertainty principle. This concept explains the physics underlying experiments performed in atomic physics as early as the 1940s.

A cutting-edge approach to accessing QED phenomena involves the electron’s g-factor, which describes the relationship between its mechanical (intrinsic angular momentum: spin) and magnetic properties.According to Dirac’s theory (relativistic quantum mechanics), the g-factor of a free electron should be exactly 2. Though, various QED interactions alter the g-factor, resulting in a small but precisely measurable deviation from 2. QED effects exhibit a strong nonlinear dependence on external fields. Electrons in heavy elements experience extremely high electric fields due to the high nuclear charge.The simplest systems to study are hydrogen-like highly charged ions, which have been investigated extensively both theoretically and experimentally [1].

Researchers at the Max Planck Institute for Nuclear Physics in HEIDELBERG, in a collaborative experimental-theoretical effort, have now examined the g-factor of the outermost bound electron in lithium-like tin. This system resembles hydrogen but includes the interaction with the two tightly-bound electrons of the inner atomic shell.

Theory: From the Begining QED Calculations

An from the beginning calculation considers all electromagnetic interactions among the constituents, such as a Lithium-like ion, on a fundamental level, incorporating QED effects up to a certain degree. electron structure effects, where electrons exchange photons, are included in the calculations, along with QED screening effects, where the electron interacts with other electrons, itself, and the vacuum. The from the beginning prediction was further refined using the two-loop QED contribution derived from a recent measurement in hydrogen-like tin [33], scaled to the lithium-like electron case. This results in an “experimentally enhanced” theoretical prediction of:

g_th = 1.980 354 797(12)

The uncertainty is indicated in parentheses, representing a 25-fold betterment compared to the hydrogen-like case.

“QED is the most precisely tested theory in physics… Any significant deviation would be a hint for new physics.”

Experiment: Counting Spin Flips

The g factor measurement of the bound electron was conducted using the cryogenic Penning trap ALPHATRAP. The strong magnetic field within the trap causes a characteristic motion of the confined ion and a precession of the outer electron’s spin, akin to a tiny magnetic spinning top. The g factor is derived from the ratio of the ion’s motional frequency and the precession frequency, eliminating the magnetic field from the calculation. The ion motion is detected via small induced electric signals in the trap electrodes of the “precision trap.” To determine the precession frequency, microwave radiation is directed into the trap, inducing a spin flip, which alters the spin’s orientation. the rate of spin flips peaks when the microwave resonates with the precession frequency.

Results and Outlook

The experimental value for the g factor of the lithium-like tin ion is:

g_exp = 1.980 354 799 750(84)_stat(54)_sys(944)_ext

the statistical, systematic, and external uncertainties are given in parentheses. The external uncertainties are primarily due to the ion mass uncertainty,which currently limits the experimental accuracy. The overall accuracy is 0.5 parts per billion. The experimental result aligns well with the theoretical prediction within the calculation’s uncertainty. Experimentally, improving the precision of the mass value by more than an order of magnitude is feasible, which would enhance the g factor’s precision if motivated by theoretical advancements.Future measurements of heavier lithium-like systems like ²⁰⁸Pb⁷⁹⁺ and anticipated progress in two-loop QED calculations will offer even more robust tests in the strong electric field regime using highly charged ions. The advanced theoretical methods developed here for interelectronic QED effects can be applied to g-factor calculations of more complex ions (boron- or carbon-like),parity non-conserving transitions in neutral atoms,and other effects.