Open Access

Nuclear charge radii of Sr isotopes: Reevaluation based on transition frequency measurements in the $5 s − 5 p − 4 d$ manifold in ${Sr}^{+}$

J. Palmes ^1,*, K. König ^1,2, B. K. Sahoo ³, H. Bodnar ¹, A. Candiello ⁴, A. Dorne ^4,†, R. de Groote ⁴, P. Imgram ^1,4,‡, I. Lopp ¹ et al.

P. Müller ¹, W. Nörtershäuser ^1,2, B. Ohayon ⁵, and R. Van Duyse ⁴

¹Institut für Kernphysik, Technische Universität Darmstadt, Darmstadt, Germany
²Helmholtz Forschungsakademie Hessen für FAIR, GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
³Atomic, Molecular and Optical Physics Division, Physical Research Laboratory, Navrangpura, Ahmedabad 380058, Gujarat, India
⁴Instituut voor Kern- en Stralingsfysica, KU Leuven, Leuven, Belgium
⁵Technion—Israel Institute of Technology, Haifa, Israel

^*Contact author: jpalmes@ikp.tu-darmstadt.de
^†Present address: Department of Physics, University of Strathclyde, Glasgow, United Kingdom.
^‡Present address: GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany.

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Phys. Rev. Research 8, 033362 – Published 24 September, 2026

DOI: https://doi.org/10.1103/th38-y1t9

Abstract

High-precision quasisimultaneous collinear/anticollinear laser spectroscopy was performed to measure the $5 s^{2} S_{1 / 2} \to 5 p^{2} P_{1 / 2}$ ( $D 1$ ), the $5 s^{2} S_{1 / 2} \to 5 p^{2} P_{3 / 2}$ ( $D 2$ ), and the three $4 d \to 5 p$ transitions in naturally abundant ${Sr}^{+}$ isotopes. For absolute transition frequencies, an uncertainty as low as $600 k Hz$ was achieved, while common-mode rejection allowed us to extract isotope shifts with uncertainties down to a level of $200 k Hz$ , 1 order of magnitude better than previously achieved. Similarly, the uncertainties of the hyperfine-structure coefficients for ${}^{87}{Sr}$ of the $5 p$ states and the $4 d^{2} D_{3 / 2}$ levels are improved. A King-plot analysis yielded a field-shift ratio of the $D 2$ and $D 1$ lines of $F_{D 2} / F_{D 1} = 1.004 (5)$ , which lies within the theoretically allowed region and can be used as a benchmark for atomic structure theory calculations. We use the information from all stable isotopes in the investigated transitions to compare field-shift and mass-shift constants obtained by various techniques regularly used in the literature, ranging from King plots with purely experimental input to ab initio atomic structure calculations by state-of-the-art theory. We show that in the region above $N = 50$ , the charge radii are strongly dependent on the approach being used.

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Phys. Rev. Research 8, 033362– Published 24 September, 2026

Vol. 8, Iss. 3 — September - November 2026

Received 30 May 2026
Accepted 6 August 2026

DOI: https://doi.org/10.1103/th38-y1t9

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Nuclear charge radii of Sr isotopes: Reevaluation based on transition frequency measurements in the $5 s − 5 p − 4 d$ manifold in ${Sr}^{+}$

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Nuclear charge radii of Sr isotopes: Reevaluation based on transition frequency measurements in the 5s−5p−4d manifold in Sr+

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Nuclear charge radii of Sr isotopes: Reevaluation based on transition frequency measurements in the $5 s − 5 p − 4 d$ manifold in ${Sr}^{+}$