Searching for the first excited nuclear state of $^{\mathrm{229}}$Th

The first excitation energy of $^{\mathrm{229}}$Th (Thorium) is only 7.8±0.5 eV and can be excited directly using lasers. Which makes the design of a nuclear clock based on the first excited nuclear state of $^{\mathrm{229}}$Th becomes possible. We are proposed to measure the energy of this first excited nuclear state of $^{\mathrm{229}}$Th based on $^{\mathrm{229}}$Th$^{\mathrm{3+}}$ coulomb crystals in vacuum chamber. The procedure includes 1) Preparation of $^{\mathrm{229}}$Th$^{\mathrm{3+}}$; 2) Confinement of $^{\mathrm{229}}$Th$^{\mathrm{3+}}$ using radio frequency quadrupole ion trap, together with Doppler laser cooling and high vacuum technology. Obtaining long lifetime and stabilized confined $^{\mathrm{229}}$Th$^{\mathrm{3+}}$ coulomb crystals; 3) Illuminating the $^{\mathrm{229}}$Th$^{\mathrm{3+}}$ Coulomb crystal with tunable lasers. Determine the energy range and lifetime of the first excited nuclear state of $^{\mathrm{229}}$Th. The probability of first excited nuclear state of $^{\mathrm{229}}$Th is small, makes it difficult to observe and measure directly. Alternate method is to measure the electron bridge to obtain information of the first excited nuclear state of $^{\mathrm{229}}$Th indirectly.