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Thorium-229 possesses the lowest nuclear first excited state with an energyof about 8 eV. The extremely narrow linewidth of the nuclear first excitedstate with the uncertainty of 53 THz prevents the direct laser excitation andthe realization of the nuclear clock. We present a proposal using the Coulombcrystal of a linear chain formed by the $^{229}$Th$^{3+}$ ions, the nuclei of$^{229}$Th$^{3+}$ ions in the ion trap are excited by the electronic bridge(EB) process. The 7$P_{1/2}$ state of the thorium-229 nuclear ground state ischosen for the EB excitation. Using the two-level optical Bloch equation underexperimental conditions, we calculate that 2 out of 36 prepared thorium ions inthe Coulomb crystal can be excited to the nuclear first excited state, and ittakes about 2 hours to scan over the uncertainty of 0.22 eV. Taking theadvantage of transition enhancement of the EB and the long stability of theCoulomb crystal, the energy uncertainty of the first excited state can belimited to the order of 1 GHz.

A scheme for excitation of thorium-229 nuclei based on the electronic bridge excitaion