Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

The excitation energy of the $1/2^{-}$ isomer in ${}^{99}\mathrm{In}$ at $N=50$ is measured to be 671(37) keV and the mass uncertainty of the $9/2^{+}$ ground state is significantly reduced using the ISOLTRAP mass spectrometer at ISOLDE/CERN. The measurements exploit a major improvement in the resolution of the multireflection time-of-flight mass spectrometer. The results reveal an intriguing constancy of the $1/2^{-}$ isomer excitation energies in neutron-deficient indium that persists down to the $N=50$ shell closure, even when all neutrons are removed from the valence shell. This trend is used to test large-scale shell model, ab initio, and density functional theory calculations. The models have difficulties describing both the isomer excitation energies and ground-state electromagnetic moments along the indium chain.

Highly accurate and precise electronic structure calculations of heavy radioactive atoms and their molecules are important for several research areas, including chemical, nuclear, and particle physics. Ab initio quantum chemistry can elucidate structural details in these systems that emerge from the interplay of relativistic and electron correlation effects, but the large number of electrons complicates the calculations, and the scarcity of experiments prevents insightful theory-experiment comparisons. Here we report the spectroscopy of the 14 lowest excited electronic states in the radioactive molecule radium monofluoride (RaF), which is proposed as a sensitive probe for searches of new physics. The observed excitation energies are compared with state-of-the-art relativistic Fock-space coupled cluster calculations, which achieve an agreement of ≥99.64% (within ~12 meV) with experiment for all states. Guided by theory, a firm assignment of the angular momentum and term symbol is made for 10 states and a tentative assignment for 4 states. The role of high-order electron correlation and quantum electrodynamics effects in the excitation energies is studied and found to be important for all states.

A comparative vacuum ultraviolet spectroscopy study conducted at ISOLDE-CERN of the radiative decay of the Th 229 m nuclear clock isomer embedded in different host materials is reported. The ratio of the number of radiative decay photons and the number of Th 229 m embedded are determined for single crystalline CaF 2 , MgF 2 , LiSrAlF 6 , AlN, and amorphous SiO 2 . For the latter two materials, no radiative decay signal was observed and an upper limit of the ratio is reported. The radiative decay wavelength was determined in LiSrAlF 6 and CaF 2 , reducing its uncertainty by a factor of 2.5 relative to our previous measurement. This value is in agreement with the recently reported improved values from laser excitation.

Precise experimental control and interrogation of molecules and calculations of their structure are enriching the investigation of nuclear and particle physics phenomena. Molecules containing heavy, octupole-deformed nuclei, such as radium, are of particular interest. Here, we report precision laser spectroscopy measurements and theoretical calculations of the structure of the radioactive radium monofluoride molecule ²²⁵ Ra ¹⁹ F. Our results reveal fine details of the short-range electron-nucleus interaction, indicating the high sensitivity of this molecule to the distribution of magnetization, within the radium nucleus. These results provide a stringent test of the description of the electronic wave function inside the nuclear volume, highlighting the suitability of these molecules for investigating subatomic phenomena.