Splitting Isotope Shift in the $1s2p\,^3\!P_{0,1,2}$ Fine-Structure Triplet in $^{12,13,14}$C$^{4+}$: Experiment and Theory

TL;DR

This work measures and theory-calculates the splitting isotope shift (SIS) in the $1s2p\,^3P_J$ fine-structure triplet of heliumlike carbon ions across isotopes $^{12}$C, $^{13}$C, and $^{14}$C. Using COLA-based collinear-anticollinear laser spectroscopy on ions produced by an EBIS, transition frequencies are converted to absolute rest-frame values, enabling the SIS to be determined with high precision; the SIS benefits from cancellation of leading nonrelativistic terms, making it a sensitive test of relativistic recoil and QED effects. The theory combines NRQED with a unified approach to electron correlation across intermediate $Z$, treating singlet–triplet mixing (notably $2^3P_1$ with $^1P_1$) and higher-order corrections via exact diagonalization and perturbation theory, yielding SIS predictions with uncertainties at the 2 kHz level for the theoretical values. Agreement between experiment and theory, especially for $^{14}$C$^{4+}$, validates the experimental accuracy and the hyperfine-coupled corrections, and provides robust SIS coefficients for $2 \le Z \le 10$ that can benchmark future high-precision QED tests in light He-like ions.

Abstract

We report measurements and theoretical calculations of the fine-structure splittings in all three $1s2s\,^3\!S_1\rightarrow\,1s2p\,^3\!P_{0,1,2}$ transitions in the heliumlike systems of the isotopes $^{12,13,14}$C. The metastable triplet state was efficiently populated in an electron beam ion source and the C$^{4+}$ ions were electrostatically accelerated to 50\,keV to perform collinear laser spectroscopy. From the determined transition frequencies, the splitting isotope shift (SIS), i.e., the difference in fine-structure splittings between different isotopes of the same element, was extracted. In the SIS, theoretical uncertainties due to higher-order quantum electrodynamic corrections are strongly suppressed since they are independent of both nuclear mass and the fine-structure quantum number $J$ in lowest order. Comparison with theory provides an important test of experimental accuracy, particularly in the $^{13}$C$^{4+}$ case, for which the nuclear spin leads to hyperfine-induced fine-structure mixing. At the same time, the even-even isotopes $^{12,14}$C$^{4+}$ without nuclear spin can be used to confirm theory. Theoretical values of the SIS are given for all the heliumlike ions with $2\le Z\le 10$.

Figures (1)

• Figure 1: Typical spectra of the $1s2s\,^3\!S_1\rightarrow\,1s2p\,^3\!P_{0,1,2}$ transitions in $^{12,14}\text{C}^{4+}$. The $y$-axis was normalized and the $x$-axis centered to the respective transition frequency of $^{12}\text{C}^{4+}$. The resonance center of $^{14}\text{C}^{4+}$ is shifted by the SIS as defined in Eq. \ref{['Eq:CG_SIS']}. The width of the vertical bars at the line centers represents the total uncertainty (statistical + systematic) of each transition frequency after averaging over all measurements. At the top, a 10-MHz close-up depicts the experimentally and theoretically determined SIS. The total experimental uncertainty is depicted as error bar and the theoretical value (2 kHz uncertainty) as vertical line.