The evolution of nuclear structure with changing proton and neutron number is of common interest across the nuclear science community. Within the shell model, protons and neutrons occupy collections of single-particle states separated by relatively large energy gaps, giving rise to the so called ``magic'' numbers. Analogous to the noble gases in chemistry, which have enhanced chemical inertness, unstable nuclei possessing closed-shell nucleon configurations are generally spherical in shape and exhibit increased stability. Closed shell nuclei exhibit larger nucleon separation energies, and when radioactive they have longer half-lives. The energy of the single-particle states also migrate with changing numbers of protons and neutrons due to strong proton-neutron residual interactions. The migration of single-particle energies leads to shell evolution and can drive nuclei from spherical to deformed shapes. Within a single nucleus, the redistribution of nucleons can give rise to intruder states possessing different shapes than that of the ground state configuration. These intruder states owe their existence to the delicate balance between the cost of exciting nucleons into the higher-lying single-particle states and the stabilizing effect of residual proton-neutron interactions. If the energy of the intruder state descends far enough, states with nucleon configurations associated with different nuclear shapes can coexist at similar excitation energy in a phenomenon called shape coexistence. In even-even nuclei, the hallmark of shape coexistence is multiple low-lying $0^+$ states. Recently, the Ni isotopic chain has been the focus of many experimental and theoretical investigations studying the evolution of nuclear structure away from stability. In particular, $^{68}$Ni has elicited significant attention due to the presence of both the $Z = 28$ proton shell closure and the $N = 40$ neutron subshell closure. In $^{68}$Ni, three $0^+$ states, with energies of 0, 1603, and 2511 keV have been identified. Advanced shell-model calculations, utilizing the full $fpg_{9/2}d_{5/2}$ model space for both protons and neutrons, predict a spherical $0_1^+$ ground state, oblate-deformed $0_2^+$ state, and prolate-deformed $0_3^+$ state. The configuration of the oblate-deformed $0_2^+$ state is predicted to be predominately the excitation of two neutrons across $N=40$ into the $0 \nu g_{9/2}$ orbit, while the the prolate-deformed $0_3^+$ state is expected to contain multiple particle-hole excitations dominated by the excitation of two protons across $Z=28$ into the $0 \pi f_{5/2}$ orbit.Transitioning to $^{70}$Ni, with the addition of only two neutrons, the same shell-model calculations predict the prolate deformed $0^+$ state to drop precipitously from the measured energy of 2511 keV in $^{68}$Ni down to a predicted energy of 1525 keV in $^{70}$Ni. This is explained by the reduction of the energy spacing between the $0 \pi f_{7/2}$ and $0 \pi f_{5/2}$ single-particle states due to the strengthening of the attractive $ 0 \nu g_{9/2}-0 \pi f_{5/2}$ and repulsive $0 \nu g_{9/2}-0 \pi f_{7/2}$ monopole interactions of the tensor force with increased occupancy of the $0 \nu g_{9/2}$ orbital. In order to validate these predictions and experimentally investigate shape coexistence in $^{68,70}$Ni, two complimentary experiments were performed at the National Superconducting Cyclotron Laboratory. As a result of these experiments, a new $(0_2^+)$ state was discovered at 1567-keV in $^{70}$Ni, in good agreement with theoretical predictions. Transition probabilities deduced from new lifetime and branching ratio measurements of $0^+$ states in $^{68,70}$Ni provide stringent tests for competing theoretical descriptions. These results constitute the first quantitative descriptions of these $0^+$ states and support the predictions of shape coexistence in $^{68,70}$Ni.
Read
