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The $E0$ transition strength in the $2^+_2 \rightarrow 2^+_1$ transitions of$^{58,60,62}$Ni have been determined for the first time following a series ofmeasurements at the Australian National University (ANU) and the University ofKentucky (UK). The CAESAR Compton-suppressed HPGe array and the Super-esolenoid at ANU were used to measure the $\delta(E2/M1)$ mixing ratio andinternal conversion coefficient of each transition following inelastic protonscattering. Level half-lives, $\delta(E2/M1)$ mixing ratios and $\gamma$-raybranching ratios were measured at UK following inelastic neutron scattering.The new spectroscopic information was used to determine the $E0$ strengths.These are the first $2^+ \rightarrow 2^+$ $E0$ transition strengths measured innuclei with spherical ground states and the $E0$ component is found to beunexpectedly large; in fact, these are amongst the largest $E0$ transitionstrengths in medium and heavy nuclei reported to date.

Identification of significant $E0$ strength in the $2^+_2 \rightarrow 2^+_1$ transitions of $^{58, 60, 62}$Ni