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Abstract Radioactive nuclei with lifetimes on the order of millions of years can reveal the formation history of the Sun and active nucleosynthesis occurring at the time and place of its birth^1,2. Among such nuclei whose decay signatures are found in the oldest meteorites,²⁰⁵Pb is a powerful example, as it is produced exclusively by slow neutron captures (thesprocess), with most being synthesized in asymptotic giant branch (AGB) stars^3–5. However, making accurate abundance predictions for²⁰⁵Pb has so far been impossible because the weak decay rates of²⁰⁵Pb and²⁰⁵Tl are very uncertain at stellar temperatures^6,7. To constrain these decay rates, we measured for the first time the bound-state β⁻decay of fully ionized²⁰⁵Tl⁸¹⁺, an exotic decay mode that only occurs in highly charged ions. The measured half-life is 4.7 times longer than the previous theoretical estimate⁸and our 10% experimental uncertainty has eliminated the main nuclear-physics limitation. With new, experimentally backed decay rates, we used AGB stellar models to calculate²⁰⁵Pb yields. Propagating those yields with basic galactic chemical evolution (GCE) and comparing with the²⁰⁵Pb/²⁰⁴Pb ratio from meteorites^9–11, we determined the isolation time of solar material inside its parent molecular cloud. We find positive isolation times that are consistent with the others-process short-lived radioactive nuclei found in the early Solar System. Our results reaffirm the site of the Sun’s birth as a long-lived, giant molecular cloud and support the use of the²⁰⁵Pb–²⁰⁵Tl decay system as a chronometer in the early Solar System. 

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.