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.

We report high-precision mass measurements of ${}^{50–55}\mathrm{Sc}$ isotopes performed at the LEBIT facility at NSCL and at the TITAN facility at TRIUMF. Our results provide a substantial reduction of their uncertainties and indicate significant deviations, up to 0.7 MeV, from the previously recommended mass values for ${}^{53–55}\mathrm{Sc}$. The results of this work provide an important update to the description of emerging closed-shell phenomena at neutron numbers $N=32$ and $N=34$ above proton-magic $Z=20$. In particular, they finally enable a complete and precise characterization of the trends in ground state binding energies along the $N=32$ isotone, confirming that the empirical neutron shell gap energies peak at the doubly magic ${}^{52}\mathrm{Ca}$. Moreover, our data, combined with other recent measurements, do not support the existence of a closed neutron shell in ${}^{55}\mathrm{Sc}$ at $N=34$. The results were compared to predictions from both ab initio and phenomenological nuclear theories, which all had success describing $N=32$ neutron shell gap energies but were highly disparate in the description of the $N=34$ isotone.

Background: The neutron-rich $A\approx 100, N\approx 62$ mass region is important for both nuclear structure and nuclear astrophysics. The neutron-rich segment of this region has been widely studied to investigate shape coexistence and sudden nuclear deformation. However, the absence of experimental data of more neutron-rich nuclei poses a challenge to further structure studies. The derivatives of the mass surface, namely, the two-neutron separation energy and neutron pairing gap, are sensitive to nuclear deformation and shed light on the stability against deformation in this region. This region also lies along the astrophysical $r$-process path, and hence precise mass values provide experimental input for improving the accuracy of the $r$-process models and the elemental abundances.

We report mass measurements of neutron-rich Ga isotopes ${}^{80-85}\mathrm{Ga}$ with TRIUMF's Ion Trap for Atomic and Nuclear science. The measurements determine the masses of ${}^{80-83}\mathrm{Ga}$ in good agreement with previous measurements. The masses of ${}^{84}\mathrm{Ga}$ and ${}^{85}\mathrm{Ga}$ were measured for the first time. Uncertainties between 25 and 48 keV were reached. The new mass values reduce the nuclear uncertainties associated with the production of $A\approx 84$ isotopes by the $r$-process for astrophysical conditions that might be consistent with a binary neutron star (BNS) merger producing a blue kilonova. Our nucleosynthesis simulations confirm that BNS merger may contribute to the first abundance peak under moderate neutron-rich conditions with electron fractions $Y_e=0.35-0.38$.

$\alpha$-, $\beta$-, and proton-decay energies have been combined with TITAN mass values for ${}^{150–157}\mathrm{Yb}$ to expand and refine the mass surface in the proton-rich $Z=70–82$ region. The calculations were performed using the Atomic Mass Evaluation (AME) algorithm, resulting in 11 new ground-state masses and uncertainty reductions of nine others. The new information allows the determination of the two-proton drip line for elements between Ir and Pb and provides indications of possible new candidates for two-proton emission. In addition, we examined binding energies in this region for Thomas-Ehrman shifts, so far only visible for light nuclides.