One of the most important global properties of the atomic nucleus is its size. Experimentally determined nuclear charge radii carry unique information on the nuclear force and complex dynamics of protons and neutrons moving inside the nucleus. The intricate behaviour of charge radii along the chain of Ca isotopes, including the unexpectedly large charge radius of neutron-rich ⁵²Ca, poses a daunting challenge for nuclear theory¹. Here we present the measurements of the charge radii of proton-rich isotopes ^36,37,38Ca, whose properties are impacted by the interplay between nuclear superfluidity and weak binding. Calculations carried out within nuclear density functional theory show that the combination of a novel interaction² and a state-of-the-art theoretical method can successfully explain the behaviour of charge radii from the lightest to the heaviest Ca isotopes. Through this model, we show how the new data on ^36,37,38Ca elucidate the nature of nucleonic pairing in weakly bound proton-rich isotopes.

Mid-infrared femtosecond optical frequency combs were produced by difference frequency generation of the spectral components of a near-infrared comb in a 3-mm-long MgO:PPLN crystal. We observe strong pump depletion and 9.3 dB parametric gain in the 1.5 μm signal, which yields powers above 500 mW (3 μW/mode) in the idler with spectra covering 2.8 μm to 3.5 μm. Potential for broadband, high-resolution molecular spectroscopy is demonstrated by absorption spectra and interferograms obtained by heterodyning two combs.

We describe a dual-comb spectrometer that can operate independently of laboratory-based rf and optical frequency references but is nevertheless capable of ultra-high spectral resolution, high SNR, and frequency-accurate spectral measurements. The instrument is based on a “bootstrapped” frequency referencing scheme in which short-term optical phase coherence between combs is attained by referencing each to a free-running diode laser, whilst high frequency resolution and long-term accuracy is derived from a stable quartz oscillator. The sensitivity, stability and accuracy of this spectrometer were characterized using a multipass cell. We demonstrate comb-resolved spectra spanning from 140 THz (2.14 µm, 4670 cm⁻¹) to 184 THz (1.63 µm, 6140 cm⁻¹) in the near infrared with a frequency sampling of 200 MHz (0.0067 cm⁻¹) and ~1 MHz frequency accuracy. High resolution spectra of water and carbon dioxide transitions at 1.77 µm, 1.96 µm and 2.06 µm show that the molecular transmission acquired with this system operating in the field-mode did not deviate from those measured when it was referenced to a maser and cavity-stabilized laser to within 5.6 × 10⁻⁴. When optimized for carbon dioxide quantification at 1.60 µm, a sensitivity of 2.8 ppm-km at 1 s integration time, improving to 0.10 ppm-km at 13 minutes of integration time was achieved.

Charge radii of the unstable ${}^{36}\mathrm{Ca}$ and ${}^{38}\mathrm{Ca}$ nuclei were recently determined and used to compute differences in charge radii between mirror nuclei $\mathrm{\Delta }{R}_{\mathrm{ch}}$ for the ${}^{36}\mathrm{Ca}-{}^{36}\mathrm{S}$ and ${}^{38}\mathrm{Ca}-{}^{38}\mathrm{Ar}$ mirror pairs. Given the correlation between $\mathrm{\Delta }{R}_{\mathrm{ch}}$ and the slope of the symmetry energy $L$ at the nuclear saturation density, we deduce $L=5–70$ MeV, which rules out a large fraction of models that predict a “stiff” equation of state. This is the most precise determination of $L$ in this model based on electromagnetic probes of nuclear ground states. The determined range is consistent with earlier analyses from both laboratory experiments and astrophysical observations, including the recent detection of gravitational waves from the merger of two neutron stars.

Bunched-beam collinear laser spectroscopy is performed on neutron deficient ${}^{52,53}\mathrm{Fe}$ prepared through in-flight separation followed by a gas stopping. This novel scheme is a major step to reach nuclides far from the stability line in laser spectroscopy. Differential mean-square charge radii $\delta ⟨r^2⟩$ of ${}^{52,53}\mathrm{Fe}$ are determined relative to stable ${}^{56}\mathrm{Fe}$ as $\delta ⟨r^2{⟩}^{56,52}=-0.034(13){\mathrm{fm}}^2$ and $\delta ⟨r^2{⟩}^{56,53}=-0.218(13){\mathrm{fm}}^2$, respectively, from the isotope shift of atomic hyperfine structures. The multiconfiguration Dirac-Fock method is used to calculate atomic factors to deduce $\delta ⟨r^2⟩$. The values of $\delta ⟨r^2⟩$ exhibit a minimum at the $N=28$ neutron shell closure. The nuclear density functional theory with Fayans and Skyrme energy density functionals is used to interpret the data. The trend of $\delta ⟨r^2⟩$ along the Fe isotopic chain results from an interplay between single-particle shell structure, pairing, and polarization effects and provides important data for understanding the intricate trend in the $\delta ⟨r^2⟩$ of closed-shell Ca isotopes.