  Collinear laser spectroscopy of the $N=Z=21$ self-conjugate nucleus $^{42}$Sc
has been performed at the JYFL IGISOL IV facility in order to determine the
change in nuclear mean-square charge radius between the $I^{\pi}=0^{+}$ ground
state and the $I^{\pi}=7^{+}$ isomer via the measurement of the
$^{42\mathrm{g},42\mathrm{m}}$Sc isomer shift. New multi-configurational
Dirac-Fock calculations for the atomic mass shift and field shift factors have
enabled a recalibration of the charge radii of the $^{42-46}$Sc isotopes which
were measured previously. While consistent with the treatment of
proton-neutron, proton-proton and neutron-neutron pairing on an equal footing,
the reduction in size for the isomer is observed to be of a significantly
larger magnitude than that expected from both shell model and ab-initio
calculations.
