Present and future rare isotope accelerator facilities provide new opportunities to explore the structure of unstable nuclei. We report the measurements of the elastic scattering angular distributions of ²¹Na and ²²Na on the doubly magic ⁴⁰Ca above the Coulomb barrier energies, using high-purity post-accelerated ISOL beams from Beijing Radioactive Ion Beam Facility (BRIF). Angular distributions were measured with a silicon detector telescope array, and relative cross sections were determined with a CaF₂ target on Au backing. The data were well reproduced by optical model calculations with Woods–Saxon and USNP potentials, the latter giving better agreement. These results confirm the stable operation and performance of the BRIF ISOL production and post-acceleration system, demonstrate its capability to provide radioactive beams of useful intensity and purity for future investigations of reaction dynamics and astrophysically relevant processes involving proton-rich nuclei, and simultaneously extend proton-rich elastic scattering studies to heavier systems.

²⁰Na is a well-known $\beta$-delayed $\alpha$ emitter, owing to the large decay energy of ²⁰Na above the α + ¹⁶O threshold in the $A=5\alpha$ daughter nucleus ²⁰Ne. In this work, the decay property of ²⁰Na is investigated in detail via the β-γ β-α and β-γ-α coincidence spectroscopy. As the day-one experiment of the Beijing Rare Isotope Facility (BRIF), the intense ²⁰Na beam was produced using the Isotope Separator On Line (ISOL) technique through the 100 MeV proton bombarding a stack of MgO as a thick target. Specific interest was focused on the exotic decay mode of ²⁰Na; the previously reported low-energy α lines at 713 and 846 keV were confirmed, and several weak β-γ-α decay sequences were clearly identified for the first time, thanks to the strong resolving power of α-γ coincidence spectroscopy. The decay properties of ²⁰Na are compared to the shell model calculation, which agree reasonably well with the allowed β transition strengths and subsequent electro-magnetic transitions with the use of the sd shell-model space with the USDB interaction.