Coulomb excitation of the semi-magic nucleus 206Hg

Exploring nuclear structure in the region close to the doubly-magic $^{208}$Pb nucleus, presents a significant challenge for modern shell-model calculations. In addition, experimental data, particularly southward of the $Z=82$ shell closure, is scarce. To this end, the singly-magic, two proton-hole nucleus $^{206}$Hg, was Coulomb-excited for the first time at \ac{CERN}'s \ac{ISOLDE} facility. The radioactive beam was accelerated using the recently-commissioned \ac{HIE-ISOLDE} linear accelerator, to an energy of 4.195~MeV/u, and intensity of $7.75 \times 10^{5}$~pps. The $^{206}$Hg nucleus then underwent safe-energy Coulomb excitation in the centre of Miniball, using one of two 2~mg/cm$^{2}$ thick targets: either $^{94}$Mo, or $^{104}$Pd. De-excitation $\gamma$ rays were detected using 23 \ac{HPGe} detectors comprising the Miniball array, and recoiling particles using a \ac{DSSSD}, with the primary goal to investigate the structure, shape and collectivity of the nucleus, and compare experimental results with those obtained from theoretical calculations. The Coulomb-excitation least-squares search code, \path{GOSIA}, was employed in order to determine the set of matrix elements which reproduced the experimental yields and other spectroscopic information, which could then be converted into transition strengths and spectroscopic quadrupole moments. Two peaks were observed in the spectra, arising from de-excitations in the $^{206}$Hg nucleus: one from the known $2_{1}^{+}\rightarrow0_{1}^{+}$ transition at $1068$~keV, and the other in coincidence with this $\gamma$ ray, with an energy of $1637$~keV. The spin and parity of this previously-unobserved second excited state was also investigated.Based on the \path{GOSIA} calculations, the second strongest $\gamma$ ray observed at $1637$~keV was determined to have arisen from a collective octupole $3^{-}$ state. Analysis performed on the data, assuming this scenario, yields: $B(E2;2_{1}^{+} \rightarrow 0_{1}^{+})=4.4^{+0.6}_{-0.6}$~W.u., and $B(E3;3_{1}^{-} \rightarrow 0_{1})=30_{-13}^{+10}$~W.u. Although not conclusive due to lack of statisctics, the spectroscopic quadrupole moment of the first excited state was found to be approximately zero ($Q_{s}(2_{1}^{+})=0.0_{-0.6}^{+0.6}$~eb), indicating that the nucleus is spherical in shape. The results are in good agreement with theoretical predictions, which were obtained with large-scale shell-model and \ac{TDHF} calculations.A significant presence of $^{130}$Xe was found in the beam, resulting from a number of factors, such as insufficient purification of the \ac{REXTRAP} buffer gas, and the charge state chosen for the isotope of interest. This beam contaminant was present in sufficient quantities to perform a detailed analysis on the data produced. A range of transition probabilities were calculated, which were in line with previously-determined results, supporting the use of this data to obtain new spectroscopic information. The spectroscopic quadrupole moments were determined to be: $Q_{s}(2_{1}^{+})=-0.38_{-14}^{+17}$~eb, $Q_{s}(4_{1}^{+})=-0.41_{-0.12}^{+0.12}$~eb, and $Q_{s}(2_{2}^{+})=0.1_{-0.1}^{+0.1}$~eb. These results were compared with shell model, \ac{UNEDF0}, and simple phenomenological (\ac{D-F} and $\gamma$-soft) model calculations, in general finding good agreement between them. Finally, shape parameters were extracted, indicating triaxial-prolate ground state band deformation, although neither phenomenological model was found to adequately describe the low-lying structure of $^{130}$Xe