The electromagnetic transition strengths between bound states in nuclei provide insight into nuclear structure. On one hand, from a single particle perspective the electromagnetic excitation and de-excitation of nuclei quantify the overlaps of nuclear wavefunctions, probing the internal configuration. On the other hand, in a collective model, the shape and dynamics of the nucleus are reflected in the electromagnetic transition strengths. For example, electric quadrupole transitions are sensitive to the deformation of a nucleus and distinguish between various pictures of collectivity, such as rotors and vibrators. In this work, electromagnetic transition strengths are studied through lifetime and Coulomb-excitation measurements. Nuclei across the contours of the valley of stability are studied to investigate features of nuclear structure and how they change near and far from stability.The first experiment discussed in this work investigates the effect of the $N=Z=28$ shell closure on collectivity in $^{58}$Ni. $^{58}$Ni has 28 protons and 30 neutrons, and therefore is not expected to exhibit enhanced collectivity compared to its neutron rich neighbors. However, a previous measurement of the lifetime of the $4_1^+$ state indicates an enhanced $B(E2;4_1^+\rightarrow2_1^+)$ transition strength, suggesting unexpectedly large collectivity. The present work revisits the lifetime of the $4_1^+$ state with a more sensitive technique, namely a Recoil Distance Method measurement at the National Superconducting Cyclotron Laboratory. The GRETINA detector array was employed with the S800 Spectrograph to measure the $4_1^+$ state lifetime. The model independent $B(E2;4_1^+\rightarrow2_{1}^+)$ from the present work supports an unenhanced transition strength, as expected near the shell closure.The second experiment discussed in this work is a study of the electromagnetic transition states in $^{27}$Ne. $^{27}$Ne is a loosely-bound neutron rich nucleus although it does not exhibit a halo structure in its ground state. This work investigates the excited states of $^{27}$Ne that lie closer to the particle threshold for features associated with a halo structure. The lifetimes of the $1/2^+$ and $3/2^-$ states in $^{27}$Ne and the branching ratio of the $1/2^+$ state decaying into the $3/2^-$ excited state and $3/2^+_{gs}$ ground state are measured. These values are used to determine the $B(E1;3/2^-\rightarrow3/2^+_{gs})$ and $B(E1;1/2^+\rightarrow3/2^-)$ values. It was found that the $B(E1)$ connecting the $1/2^+$ state to the $3/2^-$ state is at least 50 times larger than that between the $3/2^-$ and $3/2^+_{gs}$ states, indicating an extended radial component in the $1/2^+$ state wavefunction. Lifetime measurements of excited states in $^{28}$Ne are also presented. A new setup for performing Coulomb-excitation measurements based on heavy ion inelastic scattering with two targets is presented and employed to measure the $B(E2;3/2^+_{gs}\rightarrow1/2^+)$ strength in $^{27}$Ne. The method is demonstrated through a reference measurement of the $B(E2;0_{gs}^+\rightarrow2_1^+)$ of $^{30}$Mg. Combined with the lifetime measurement, the $B(M1;1/2^+\rightarrow3/2_{gs}^+)$ transition strength is extracted. The measured value is unhindered, indicating that the $1/2^+$ excited state of $^{27}$Ne is not dominated by an $s$-wave component. The electromagnetic transition strengths in $^{27}$Ne therefore indicate that the $1/2^+$ excited state may exhibit behaviors characteristic of deformed halos.In summary, this study of electromagnetic strengths demonstrates the features of nuclei in the valley of stability, and explores new aspects of nuclear structure that arise toward the edges of stability. Concurrently, Doppler-shift methods are shown to be powerful tools for investigating the structure of nuclei across the nuclear landscape.
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