Doubly magic nuclei and their near neighbours serve as an ideal testing ground for the nuclear shell model, and, consequently, enable us to define effective nuclear interactions.
Collective states in nuclei near $^{56}$Ni can be attributed to multiparticle-multihole excitations from the $1f_{7/2}$ to the $2p_{3/2}$, $1f_{5/2}$ and $2p_{1/2}$ orbits across the $N$, $Z$ = 28 shell gap. These features are usually associated with shape coexistence.
Properties of excited $0^{+}$ states, as well as $E0$ and $E2$ transition
strengths are sensitive probes of the underlying nuclear structure. The aim of this work is to identify and characterize excited $0^{+}$ states and corresponding $E0$ transitions in $^{54,56,58}$Fe to search for shape coexistence around the $N$, $Z$ = 28 shell closure.
In order to obtain experimental information, $E0$ transitions between the lowest excited $0^{+}$ states and ground states were measured for the stable even-even iron isotopes using the superconducting electron spectrometer ,"Super-e", at the Australian National University. Additional information on angular distributions, angular correlations, and $\gamma - \gamma$ coincidences was obtained with the CAESAR detector array (at ANU) under the same experimental conditions. In order to deduce $E0$ strengths, the experimental data were evaluated with lifetime information from Doppler-shift attenuation measurements following inelastic neutron scattering, carried out at the University of Kentucky.