Nuclear Charge Radii of Sr Isotopes: Reevaluation based on Transition Frequency Measurements in the $5s-5p-4d$ manifold in Sr$^+$

Abstract

High-precision quasi-simultaneous collinear/anticollinear laser spectroscopy was performed to measure the $5s$ $^2S_{1/2}\rightarrow 5p$ $^2P_{1/2}$ (D1), the $5s$ $^2S_{1/2}\rightarrow 5p$ $^2P_{3/2}$ (D2), and the three $4d\rightarrow 5p$ transitions in naturally abundant Sr$^+$ isotopes. For absolute transition frequencies, an accuracy of up to 600 kHz was achieved, while common-mode rejection allowed us to extract isotope shifts with uncertainties down to a level of 200 kHz, one order of magnitude better than previously achieved. The uncertainties of the hyperfine-structure coefficients for $^{87}$Sr of the $5p$ states and the $4d$ $^2D_{3/2}$ levels are also improved. A King plot analysis yielded a field-shift ratio of the D2 and D1 lines of $F_\text{D2}/F_\text{D1}=1.004(5)$, 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.