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Field-shift factors and nuclear charge-radius difference in 3He and 4He
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DOI：10.1007/s41365-026-02037-7.png)
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Abstract
En 中文
Precise nuclear charge radii provide stringent constraints on nuclear structure and few-body nuclear calculations. Their extraction from isotope-shift measurements relies critically on an accurate evaluation of the atomic field-shift factors. In this work, we present high-precision calculations of the field-shift factors for the helium isotopes $$^{3}$$ He and $$^{4}$$ He, including second-order relativistic perturbative corrections. For the $$2\,^3\!S-2\,^3\!P$$ transition, we achieve ppm-level accuracy and obtain field-shift factors of $$-1212.291(1)\ {{\mathrm{kHz}}/{\mathrm{fm}}^{2}}$$ for $$^{3}$$ He and $$-1212.455(1)\, {{\mathrm {kHz}}/{\mathrm {fm}}^{2}}$$ for $$^{4}$$ He. Using these improved values, we re-evaluate the difference of the squared nuclear charge radii to $$\Delta R^{2}=1.0736(21)\, {{\mathrm {fm}}^{2}}$$ based on the latest electronic-helium isotope-shift measurement. The resulting value is currently limited mainly by experimental uncertainty and shows a $$2.7\sigma $$ tension with the determination from muonic-helium spectroscopy. Our results provide an improved nuclear-size benchmark for helium isotopes and highlight the importance of further high-precision nuclear and atomic studies to achieve a consistent determination of nuclear charge radii across different probes.
Keywords:
Nuclear charge radius
Field-shift factor
Isotope shift
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