Proton-neutron pairing correlations in the self-conjugate nucleus ${}^{42}$Sc

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.