MINIMIZING TIME DILATION IN PENNING TRAP ION CLOCKS*

The relativistic time-dilation shift is expected to give one of the largest systematic uncertainties in a stored-ion clock. We show that in a Penning trap, it can be minimized if laser-cooled ions are prepared in a particular spheroid. Recent obser-vation of Bragg scattering from crystals formed by the stored ions may be useful in stabilizing the time-dilation shift. One of the goals a t NIST-Boulder is to realize an ion clock with absolute accuracy sur-passing 1 part in 1015. Experiments a t NIST with 9Be+ ions stored in a Penning trap have shown that an R F oscillator can be steered by a nuclear spin-flip “clock ” transition ( w 303 MHz) with uy z 3 x systematic uncer-tainty due to relativistic time dilation (second-order Doppler shift).’V2 If collisional shifts2 and other environmental perturbations are assumed to be negligible, then the expected performance of a stored ion clock is limited by the “projection-noise”3 frequency stabil-ity uy = l / w o m and the uncertainty in the time-dilation shift Av/v, =- ( w 2) / 2 c 2. The frequency stability oY depends on the clock transition frequency w,/2n v,, th