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Dr. Milena Majkic

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Faculty of Technical Sciences, University of Pristina in Kosovska Mitrovica, Knjaza Milosa 7, Kosovska Mitrovica, Serbia
Interests: highly charged ions; atomic physics

Special Issue Information

Dear Colleagues,

Over the past decades, the physics of highly charged ions (HCIs) has advanced remarkably, yielding significant achievements in both fundamental and applied research. As exotic atomic systems with extremely strong electromagnetic fields, HCIs amplify relativistic and quantum electrodynamic (QED) effects, providing exceptional platforms for precision tests of fundamental theories and for exploring atomic structure under extreme conditions. Accurate atomic data on their electronic structure and spectroscopy remain central to atomic physics, both theoretically and experimentally.

Owing to their narrow optical transitions and reduced susceptibility to external perturbations, arising from the strong binding of their outer electrons, HCI are promising candidates for next-generation ultra-high-precision optical clocks and powerful tools for fundamental frequency metrology. Moreover, their exceptional sensitivity to possible variations in the fine-structure constant opens new avenues for probing physics beyond the Standard Model.

Beyond fundamental studies, HCIs have become versatile tools in applied research, including interactions with electrons, photons, atoms, molecules, clusters and surfaces. Understanding the underlying physics of these collision processes through advanced quantum mechanical and semiclassical approaches remains a significant challenge. HCI research also plays a crucial role in astrophysical diagnostics, plasma and fusion science, accelerator physics, advanced nanolithography and the development of XUV and X-ray light sources.

This Special Issue seeks contributions presenting state-of-the-art experimental results, innovative theoretical developments and advanced simulations, as well as studies exploring applications of HCI in precision spectroscopy, fundamental physics and next-generation optical clocks.

Dr. Milena Majkic
Guest Editor

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Research

14 pages, 551 KB

Open AccessArticle

Thresholded Zipf Scaling Across 14 Highly-Charged-Ion Isoelectronic Sequences: Identification of an nd⁶⁵D₀ jj-Coupling Pair

by André F. F. da Silva, Sergio Da Silva, Raul Matsushita and Giovanni F. Caramori

Atoms 2026, 14(7), 60; https://doi.org/10.3390/atoms14070060 - 18 Jul 2026

Viewed by 321

Abstract

Earlier work by some of the present authors identified power-law statistical regularities across the periodic table: a near-Zipf relationship

W \propto Z^{1.09}

between atomic weight and atomic number in neutral atoms, and a fine-structure splitting scaling

Δ E \propto Z^{1.78}

in [...] Read more.

Earlier work by some of the present authors identified power-law statistical regularities across the periodic table: a near-Zipf relationship

W \propto Z^{1.09}

between atomic weight and atomic number in neutral atoms, and a fine-structure splitting scaling

Δ E \propto Z^{1.78}

in the

3 d^{2 +}

(Cr-like) isoelectronic sequence of highly charged ions (HCIs). The apparent tension between this superlinear empirical exponent and the linear-in-Z scaling derived analytically by Lyu, Keitel, and Harman for relativistic clock-state transitions in

n d^{6}

ions is resolved by writing the scaling law in the form

Δ E = A {(Z - Z^{*})}^{γ}

, which gives

γ = 1.03

and

Z^{*} = 25.83

for the

3 d^{2 +}

data and restores a near-Zipf interpretation. We extend the thresholded model from the single

3 d^{2 +}

sequence to fourteen isoelectronic sequences spanning C-like (

Z \geq 6

) through Mo-like (

Z \geq 42

), drawing on the NIST Atomic Spectra Database, evaluated compilations of strontium, copper, and tungsten ion data, and digitization of GRASP MCDHF Mo-like results. Comparing the fitted threshold

Z^{*}

against the classical Slater shielding

σ_{Slater}

of the valence shell reveals three regimes: (i) Coulomb-LS sequences (C/N/O/Ne-like) with

Z^{*}

fixed at zero by construction; (ii) a mainstream cluster of nine sequences (a mix of spin–orbit fine-structure and, for the

d^{2}

Ca-/Sr-like members, Coulomb term separations) for which

Z^{*}

tracks

σ_{Slater}

within

\pm 1.5

units; (iii) a pair of

n d^{6} {}^{5}D_{0}

sequences (Cr-like

3 d^{6}

and Mo-like

4 d^{6}

) with

Z^{*} - σ_{Slater} = + 7.20

and

+ 10.36

, scaling linearly with Z in the jj regime (after resolving a low-Z LS–jj crossover for the Mo-like member). The slope ratio

A_{Mo} / A_{Cr} \approx 0.48

is of the order of the hydrogenoid radial-extent ratio

⟨ r^{2} ⟩ (3 d) / ⟨ r^{2} ⟩ (4 d) \approx 0.32

, exceeding it by ∼50% as expected from relativistic

4 d

contraction. A falsifiable extrapolation for the W-like

5 d^{6} {}^{5}D_{0}

sequence is offered:

Δ \in [+ 7, + 11]

A_{W} \in [0.12, 0.18]

eV/Z, with explicit failure modes specified for an independent GRASP MCDHF test. Full article

(This article belongs to the Special Issue Research in Highly Charged Ions)

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