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

Collinear laser spectroscopy of the <math altimg="si1.svg"><mi>N</mi><mo linebreak="goodbreak" linebreakstyle="after">=</mo><mi>Z</mi><mo linebreak="goodbreak" linebreakstyle="after">=</mo><mn>21</mn></math> self-conjugate nucleus <sup loc="post">42</sup>Sc has been performed at the JYFL IGISOL IV facility in order to determine the change in nuclear mean-square charge radius between the <math altimg="si2.svg"><msup><mrow><mi>I</mi></mrow><mrow><mi>π</mi></mrow></msup><mo linebreak="goodbreak" linebreakstyle="after">=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">+</mo></mrow></msup></math> ground state and the <math altimg="si3.svg"><msup><mrow><mi>I</mi></mrow><mrow><mi>π</mi></mrow></msup><mo linebreak="goodbreak" linebreakstyle="after">=</mo><msup><mrow><mn>7</mn></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">+</mo></mrow></msup></math> isomer via the measurement of the <math altimg="si4.svg"><msup><mrow/><mrow><mn>42</mn><mi mathvariant="normal">g</mi><mo>,</mo><mn>42</mn><mi mathvariant="normal">m</mi></mrow></msup></math>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 <sup loc="post">42−46</sup>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. The measured nuclear magnetic dipole moment and electric quadruple moment, on the other hand, are in good agreement with simple empirical estimates and shell-model calculations.