Periodic table for highly charged ions

Abstract

Mendeleev's periodic table successfully groups atomic elements according to their chemical and spectroscopic properties. However, it becomes less sufficient in describing the electronic properties of highly charged ions (HCIs) in which many of the outermost electrons are ionized. In this work, we put forward a periodic table particularly suitable for HCIs. It is constructed purely based on the successive electron occupation of relativistic orbitals. While providing a much-simplified description of the level structure of highly charged isoelectronic ions -- essential for laboratory and astrophysical plasma spectroscopies, such a periodic table predicts a large family of highly forbidden transitions suitable for the development of next-generation optical atomic clocks. Furthermore, we also identify universal linear $Z$ scaling laws ($Z$ is the nuclear charge) in the so-called ``Coulomb splittings'' between angular momentum multiplets along isoelectronic sequences, complementing the physics of electron-electron interactions in multielectron atomic systems.

Figures (7)

• Figure 1: Periodic table for HCIs. It is arranged according to the number of electrons $N$, with each cell represents one isoelectronic sequence with a given $nl_{{}^{\pm}}^m$ configuration. The reference ions at the bottom of each cell indicate the elements in which $jj$ couplings become significant. As the energy of $6s$ is always lower than that of $5f_{{}^+}$, the two cells with $N=85,86$ at the bottom-left corner of the table shall be inserted between the $5f_{{}^-}^6$ ($N=84$) and $5f_{{}^+}^1$ ($N=87$) cells. The bottom row presents all allowed $J$s, ordered according to their increasing energies, of the ground-state $j^m$ multiplet in each column. This periodic table is created via Latex by modifying the pgf-PeriodicTable package pgf2.
• Figure 2: Clustered level structures in highly charged uranium ions: the upper and lower panels correspond to the ions from the second and fourth rows of the periodic table shown in Fig. \ref{['pd']}, respectively. Horizontal axis is the total angular momentum, with the first tick point being $0$ (or $1\!/\!2$) for integer (or half-integer) $J$s. The parity is colored in red (blue) for even (odd) states. In the lower panel, levels in blue color are the states formed by single excitation mainly from the $3p_{{}^+}$ subshell, with the level energy around 1.4 keV being the single excitation from the $3p_{{}^-}$ subshell.
• Figure 3: Superior clock properties of HCI clock candidates. The projected instability $\sigma_{\tau}$, differential magnetic- ($\Delta\alpha_{M1}$) and electric-dipole ($\Delta\alpha_{E1}$) polarizability of over 700 HCI clock candidates are plotted, with the grey lines and crosses being their projections in the $x-y$ plane. Each line corresponds to a relevant isoelectronic sequence denoted by the colored cells in the periodic table Fig. \ref{['pd']}. The values for state-of-the-art singly charged ion clocks ludlow2015opticalBBR2018, Ar$^{13+}$HCIclock-Ar13-2022, Pr$^{9+}$HCIclock-4f5p-2019, Cf$^{15+}$HCIclock-5f6p-2012, and nuclear clock $^{229}$Th$^{3+}$Th-2023-Beloy are presented for comparison.
• Figure 4: Universal linear scaling laws manifested by mutual-electron interactions. Energies of the low lying levels of the $nd_{{}^-}^2$, $nd_{{}^+}^2$, $nd_{{}^+}^3$, and $nd_{{}^+}^4$ ions are plotted as functions of the atomic number $Z$. The energies scale linearly with $Z$ are all from the ground-state multiplets listed at the bottom of the periodic table in Fig. \ref{['pd']}.
• Figure S1: Level structure of highly charged uranium ions: the seventh row of the periodic table shown in Fig. \ref{['pd']}.