Microscopic structure of coexisting $0^+$ states in $^{68}$Ni probed via two-neutron transfer

The structure of low-spin states originating from shape-coexisting configurations in $^{68}_{40}$Ni$_{28}$ was directly probed via the two-neutron transfer reaction $^{66}$Ni$(t,p)^{68}$Ni in inverse kinematics using a radioactive ion beam on a radioactive target. The direct feeding to the first excited 0$^+$ state was measured for center-of-mass angles 4°–16° and amounts to an integral of 4.2(16)% relative to the ground state. The observed difference in feeding of the 0$^+$ states is explained by the transfer of neutrons, mainly in the $pf$ shell below $N=40$ for the ground state, and across $N=40$ in the $g_{9/2}$ orbital for the 0$_2^+$, based on second-order distorted-wave Born approximation calculations combined with state-of-the-art shell-model two-nucleon amplitudes. However, the direct feeding to the 2$_1^+$ state [29(3)%] is incompatible with these calculations.