  We measured the isotope shift in the $^2$S$_{1/2}$-$^2$P$_{3/2}$ (D2)
transition in singly-ionized calcium ions using photon recoil spectroscopy. The
high accuracy of the technique enables us to resolve the difference between the
isotope shifts of this transition to the previously measured isotopic shifts of
the $^2$S$_{1/2}$-$^2$P$_{1/2}$ (D1) line. This so-called splitting isotope
shift is extracted and exhibits a clear signature of field shift contributions.
From the data we were able to extract the small difference of the field shift
coefficient and mass shifts between the two transitions with high accuracy.
This J-dependence is of relativistic origin and can be used to benchmark atomic
structure calculations. As a first step, we use several ab initio atomic
structure calculation methods to provide more accurate values for the field
shift constants and their ratio. Remarkably, the high-accuracy value for the
ratio of the field shift constants extracted from the experimental data is
larger than all available theoretical predictions.
