Fig. 2: Experimental charge radii of ³⁶⁻⁵²K and three-point filters of binding energies and charge radii.

a, Changes in the mean-square charge radii of potassium isotopes. The results marked with squares are calculated using the newly calculated F and K_SMS factors, whereas those with circle markers are obtained using the values from ref. ¹⁹. Error bars indicate statistical uncertainties, which in most cases are too small to be seen. In cases where multiple measurements were reported, the weighted mean of these values was used (Methods and Extended Data Table 1). The red and grey bands indicate the systematic error due to the uncertainty on these atomic parameters. The inset shows the changes in the mean-square charge radii of neighbouring elements (all relative to the radius of the isotope with neutron number N = 28). The agreement of the data for different isotopic chains above N = 28 is striking. b, The energy gaps obtained from the measured binding energies^23,24 using the three-point filter²⁵ for potassium (bottom), calcium (middle) and lead (top). Magic shell closures are shown at N = 28 and N = 126 and a subshell effect at N = 32. c, The odd–even staggering of the charge radii (Δ⁽³⁾r)¹⁴ of the potassium (bottom), calcium (middle) and lead (top) isotopes exhibit an inversion at the neutron magic numbers N = 28 and 126. No such an effect appears at N = 32. The error bars in b and c indicate statistical uncertainties. The neutron magic numbers of N = 28, 32 and 126 are indicated with the vertical grey solid and dotted lines in a–c.

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