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Abstract Proton radioactivity was discovered exactly 50 years ago. First, this nuclear decay mode sets the limit of existence on the nuclear landscape on the neutron-deficient side. Second, it comprises fundamental aspects of both quantum tunnelling as well as the coupling of (quasi)bound quantum states with the continuum in mesoscopic systems such as the atomic nucleus. Theoretical approaches can start either from bound-state nuclear shell-model theory or from resonance scattering. Thus, proton-radioactivity guides merging these types of theoretical approaches, which is of broader relevance for any few-body quantum system. Here, we report experimental measurements of proton-emission branches from an isomeric state in 54m Ni, which were visualized in four dimensions in a newly developed detector. We show that these decays, which carry an unusually high angular momentum, ℓ = 5 and ℓ = 7, respectively, can be approximated theoretically with a potential model for the proton barrier penetration and a shell-model calculation for the overlap of the initial and final wave functions. 

Asymptotic giant branch stars are responsible for the production of most of the heavy isotopes beyond Sr observed in the solar system. Among them, isotopes shielded from the $r$-process contribution by their stable isobars are defined as $s$-only nuclei. For a long time the abundance of ${}^{204}\mathrm{Pb}$, the heaviest $s$-only isotope, has been a topic of debate because state-of-the-art stellar models appeared to systematically underestimate its solar abundance. Besides the impact of uncertainties from stellar models and galactic chemical evolution simulations, this discrepancy was further obscured by rather divergent theoretical estimates for the neutron capture cross section of its radioactive precursor in the neutron-capture flow, ${}^{204}\mathrm{Tl}$( $t_{1/2}=3.78\mathrm{yr}$), and by the lack of experimental data on this reaction. We present the first ever neutron capture measurement on ${}^{204}\mathrm{Tl}$, conducted at the CERN neutron time-of-flight facility n_TOF, employing a sample of only 9 mg of ${}^{204}\mathrm{Tl}$produced at the Institute Laue Langevin high flux reactor. By complementing our new results with semiempirical calculations we obtained, at the $s$-process temperatures of $kT\approx 8\mathrm{keV}$and $kT\approx 30\mathrm{keV}$, Maxwellian-averaged cross sections (MACS) of 580(168) mb and 260(90) mb, respectively. These figures are about 3% lower and 20% higher than the corresponding values widely used in astrophysical calculations, which were based only on theoretical calculations. By using the new ${}^{204}\mathrm{Tl}$MACS, the uncertainty arising from the ${}^{204}\mathrm{Tl}(\mathrm{n},\gamma )$cross section on the $s$-process abundance of ${}^{204}\mathrm{Pb}$has been reduced from $\sim 30\%$down to $+8\%/-6\%$, and the $s$-process calculations are in agreement with the latest solar system abundance of ${}^{204}\mathrm{Pb}$reported by K. Lodders in 2021. Published by the American Physical Society2024