Scott Carmichael

The collective structure of low-lying states in the $N=50$ nucleus $^{92}\mathrm{Mo}$ $(Z=42)$ has been investigated through sub-barrier Coulomb excitation using the CHICO2 device coupled to the $\ensuremath{\gamma}$-ray energy tracking in-beam nuclear array (GRETINA). Quadrupole and octupole collective properties are measured for the ${2}_{1}^{+}$, ${2}_{2}^{+}$, ${2}_{3}^{+}$, ${2}_{4}^{+}$, and ${3}_{1}^{\ensuremath{-}}$ states. The spectroscopic quadrupole moment for the ${2}_{1}^{+}$ state is measured to be ${Q}_{s}=0.23(8)\phantom{\rule{0.28em}{0ex}}e\mathrm{b}$, showing a weakly deformed oblate nature in good agreement with recent state-of-the-art Shell-Model calculations. A modest reduced electric-octupole transition strength of $B(E3;{3}_{1}^{\ensuremath{-}}\ensuremath{\rightarrow}{0}_{1}^{+})=15(3)\phantom{\rule{0.28em}{0ex}}\mathrm{W}.\mathrm{u}.$ is obtained, in disagreement with the literature, revealing an emerging tension in the strength of octupole collectivity for the $N=50$ nuclei between historic $(e,{e}^{\ensuremath{'}})$ and $(p,{p}^{\ensuremath{'}})$ experiments and more recent experiments utilizing Coulomb excitation and lifetime plus branching-ratio data.

An yrast, ${J}^{\ensuremath{\pi}}={5}^{\ensuremath{-}}$, spin-trap isomer has been previously identified in $^{32}\mathrm{Si}$. The isomeric state decays predominantly via a hindered $E3$ transition [$B$($E3$) = 0.0841(10) W.u.], bypassing a nearby $E2$ decay path to the first excited ${3}^{\ensuremath{-}}$ level. The single-neutron aspects of these negative-parity levels were investigated via the $^{31}\mathrm{Si}(d,p)^{32}\mathrm{Si}$ reaction at 9.6 MeV/u using HELIOS and the ATLAS in-flight facility. The ${5}^{\ensuremath{-}}$ state appears as a dominant $\ensuremath{\ell}=3$ transfer with a relatively large spectroscopic factor, confirming its single-particle $\ensuremath{\nu}0{f}_{7/2}$ character. The yrast ${3}^{\ensuremath{-}}$ level had a reduced $\ensuremath{\ell}=3$ spectroscopic factor of approximately 0.44 compared with that of the ${5}_{1}^{\ensuremath{-}}$ level. This is similar to the situation observed in nearby $^{34}\mathrm{S}$, which by contrast has a measured $B$($E2,{5}^{\ensuremath{-}}\ensuremath{\rightarrow}{3}^{\ensuremath{-}}$) transition strength closer to 1 W.u. It has been concluded that the hindrance of the ${5}_{1}^{\ensuremath{-}}\ensuremath{\rightarrow}{3}_{1}^{\ensuremath{-}}$ transition in $^{32}\mathrm{Si}$ is not primarily due to the differing overlaps in the neutron structure. Instead, the lack of participation by both the protons and the neutrons in the transition is proposed as the transition-strength-reduction mechanism.

The electromagnetic properties of low-lying states in $^{70}$Ge were investigated via multi-step Coulomb excitation of a $^{70}$Ge beam impinging on a $^{208}$Pb target at the ATLAS facility of the Argonne National Laboratory. A total of 27 transitional elements and six diagonal matrix elements coupling 11 low-lying states, were extracted from the measured cross sections. These were used to calculate reduced transition probabilities, spectroscopic quadrupole moments, and rotational invariant shape parameters, providing enhanced precision and expanding on previous studies. The experimental data were compared within several theoretical frameworks, including the generalized triaxial rotor model, configuration interaction shell-model calculations, and computations within the combined frameworks of relativistic density functional theory and the five-dimensional collective Hamiltonian. The results demonstrate a good agreement with the experimental data and, in conjunction with calculations using a two-state mixing model, support significant triaxiality and strong mixing between the $0^+_1$ and $0^+_2$ states. This results in the magnitudes of their respective quadrupole deformations $[β_\text{rms}(0^+_1) = 0.228\,(3),\,β_\text{rms}(0^+_2) = 0.273\,(1)]$ being more similar than previously observed. The implications of these results for understanding the complex shape coexistence phenomena, the role of triaxiality, and shape evolution along the Ge isotopic chain are discussed.