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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.
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