Sensitivity Coefficients of Atomic-Clock Transitions and the Reach of Future Comparisons for Alpha Drift

An atomic clock does not measure the fine-structure constant; it measures a frequency, whose response to a changing alpha is set by a relativistic sensitivity coefficient that ranges from near zero for the aluminium ion clock to about minus six for the octupole transition of ytterbium ion. A comparison's reach for alpha drift is its ratio precision divided by the difference of the two coefficients. For the aluminium-mercury pair that produced the classic bound, the coefficient difference is 2.95; for the two ytterbium transitions compared within one ion it is 6.98, and a ratio precision of one part in 10^18 per year would then reach an alpha drift of 1.43e-19 per year - deep enough to press below the microwave-background constraint on early alpha under logarithmic accumulation. The table of coefficients and reaches is computed from published values. Computed, not measured.