Ion clock and search for the variation of the fine-structure constant using optical transitions in Nd13+ and Sm15+

We study ultranarrow 5s(1/2)-4f(5/2) transitions in Nd13+ and Sm15+ and demonstrate that they lie in the optical region. The transitions are insensitive to external perturbations. At the same time they are sensitive to the variation of the fine structure constant alpha. The fractional accuracy of the frequency of the transitions can be smaller than 10 (19), which may provide a basis for atomic clocks of superb accuracy. Sensitivity to the variation of alpha approaches 10(-20) per year.