Positron supercritical resonances and spontaneous positron creation in slow collisions of heavy nuclei

We present a theoretical and computational study of positron supercritical resonances in systems consisting of two highly-charged bare nuclei. The resonance positions and widths depending on the internuclear separation are calculated with the help of the complex-scaling generalized pseudospectral method in modified prolate spheroidal coordinates. The results are applied to estimate the probability of spontaneous positron creation in slow U${}^{92+}$–U${}^{92+}$ and Cm${}^{96+}$–Cm${}^{96+}$ collisions.