  Isotope shift of atomic spectra is considered as a probe of new interaction
between electrons and neutrons in atoms. We employ the method of seeking a
breakdown of King's linearity in the isotope shifts of two atomic transitions.
In the present work, we evaluate the magnitudes of the nonlinearity using
relativistic wave functions and the result is compared with that of
nonrelativistic wave functions in our previous work. It turns out that the
nonrelativistic calculation underestimates the nonlinearity owing to the new
interaction in the mass range of the mediator greater than 1 MeV. Further, we
find that the nonlinearity within the standard model of particle physics is
significantly magnified by the relativistic effect in the $\text{p}_{1/2}$
state. To get rid of this obstacle in the new physics search, we suggest to
avoid $\text{p}_{1/2}$, and use $\text{p}_{3/2}$ instead for example.
