Ian Lazarus

The $\beta$ decay of ${}^{207}\mathrm{Hg}$ into the single-proton-hole nucleus ${}^{207}\mathrm{Tl}$ has been studied through $\gamma$-ray spectroscopy at the ISOLDE Decay Station (IDS) with the aim of identifying states resulting from coupling of the $\pi s_{1/2}^{-1}$, $\pi d_{3/2}^{-1}$, and $\pi h_{11/2}^{-1}$ shell model orbitals to the collective octupole vibration. Twenty-two states were observed lying between 2.6 and 4.0 MeV, eleven of which were observed for the first time, and 78 new transitions were placed. Two octupole states ($s_{1/2}$-coupled) are identified and three more states ($d_{3/2}$-coupled) are tentatively assigned using spin-parity inferences, while further $h_{11/2}$-coupled states may also have been observed for the first time. Comparisons are made with state-of-the-art large-scale shell model calculations and previous observations made in this region, and systematic underestimation of the energy of the octupole vibrational states is noted. We suggest that in order to resolve the difference in predicted energies for collective and noncollective $t=1$ states ($t$ is the number of nucleons breaking the ${}^{208}\mathrm{Pb}$ core), the effect of $t=2$ mixing may be reduced for octupole-coupled states. The inclusion of mixing with $t=0,2,3$ excitations is necessary to replicate all $t=1$ state energies accurately.

The nuclei below lead but with more than 126 neutrons are crucial to an understanding of the astrophysical $r$ process in producing nuclei heavier than $A\sim 190$. Despite their importance, the structure and properties of these nuclei remain experimentally untested as they are difficult to produce in nuclear reactions with stable beams. In a first exploration of the shell structure of this region, neutron excitations in ${}^{207}\mathrm{Hg}$ have been probed using the neutron-adding ($d$,$p$) reaction in inverse kinematics. The radioactive beam of ${}^{206}\mathrm{Hg}$ was delivered to the new ISOLDE Solenoidal Spectrometer at an energy above the Coulomb barrier. The spectroscopy of ${}^{207}\mathrm{Hg}$ marks a first step in improving our understanding of the relevant structural properties of nuclei involved in a key part of the path of the $r$ process.

Using a hybrid Gammasphere array coupled to 25 ${\mathrm{LaBr}}_3\left(\text{Ce}\right)$ detectors, the lifetimes of the first three levels of the yrast band in ${}^{114}\mathrm{Pd}$, populated via ${}^{252}\mathrm{Cf}$ decay, have been measured. The measured lifetimes are ${\tau }_{2^{+}}=103\left(10\right)\mathrm{ps}, {\tau }_{4^{+}}=22\left(13\right)\mathrm{ps}$, and ${\tau }_{6^{+}}\le 10\mathrm{ps}$ for the $2_1^{+}, 4_1^{+}$, and $6_1^{+}$ levels, respectively. Palladium-114 was predicted to be the most deformed isotope of its isotopic chain, and spectroscopic studies have suggested it might also be a candidate nucleus for low-spin stable triaxiality. From the lifetimes measured in this work, reduced transition probabilities $B(E2;J\to J-2)$ are calculated and compared with interacting boson model, projected shell model, and collective model calculations from the literature. The experimental ratio $R_{B\left(E2\right)}=B(E2;4_1^{+}\to 2_1^{+})/B(E2;2_1^{+}\to 0_1^{+})=0.80\left(42\right)$ is measured for the first time in ${}^{114}\mathrm{Pd}$ and compared with the known values $R_{B\left(E2\right)}$ in the palladium isotopic chain: the systematics suggest that, for $N=68$, a transition from $\gamma$-unstable to a more rigid $\gamma$-deformed nuclear shape occurs.

$\beta$-delayed one-neutron and two-neutron branching ratios $(P_{1n}$ and $P_{2n})$ have been measured in the decay of $A=84$ to 87 Ga isotopes at the Radioactive-Isotope Beam Factory (RIBF) at the RIKEN Nishina Center using a high-efficiency array of ${}^3\mathrm{He}$ neutron counters (BRIKEN). Two-neutron emission was observed in the decay of ${}^{84,85,87}\mathrm{Ga}$ for the first time and the branching ratios were measured to be $P_{2n}=1.6\left(2\right)\%,1.3\left(2\right)\%$, and $10.2{\left(28\right)}_{\mathrm{stat}}{\left(5\right)}_{\mathrm{sys}}\%$, respectively. One-neutron branching ratio of ${}^{87}\mathrm{Ga}\left(P_{1n}=81{\left(9\right)}_{\mathrm{stat}}{\left(8\right)}_{\mathrm{sys}}\%\right)$ and half-life of 29(4) ms were measured for the first time. The branching ratios of ${}^{86}\mathrm{Ga}$ were also measured to be $P_{1n}=74{\left(2\right)}_{\mathrm{stat}}{\left(8\right)}_{\mathrm{sys}}\%$ and $16.2{\left(9\right)}_{\mathrm{stat}}{\left(6\right)}_{\mathrm{sys}}\%$ with better precision than a previous study. The observation that $P_{1n}>P_{2n}$ for both ${}^{86,87}\mathrm{Ga}$ was unexpected and is interpreted as a signature of dominating one-neutron emission from the two-neutron unbound excited states in ${}^{86,87}\mathrm{Ge}$. In order to interpret the experimental results, shell-model and Hauser-Feshbach statistical model calculations of delayed particle and $\gamma$-ray emission probabilities were performed. This model framework reproduces the experimental results. The shell model alone predicts $P_{2n}$ significantly larger than $P_{1n}$ for the ${}^{87}\mathrm{Ga}$ decay, and it is necessary to invoke a statistical description to successfully explain the observation that $P_{1n}>P_{2n}$. Our new results demonstrate the relevance and importance of a statistical description of neutron emission for the prediction of the decay properties of multineutron emitters and that it must be included in the $r$-process modeling.

The structure of ${}^{34}\mathrm{Si}$ was studied through $\gamma$ spectroscopy separately in the ${\beta }^{-}$ decays of ${}^{34}\mathrm{Mg}$ and ${}^{34}\mathrm{Al}$ at the ISOLDE facility of CERN. Different configurations in ${}^{34}\mathrm{Si}$ were populated independently from the two recently identified $\beta$-decaying states in ${}^{34}\mathrm{Al}$ having spin-parity assignments $J^{\pi }=4^{-}$ dominated by the normal configuration $\pi {\left(d_{5/2}\right)}^{-1}\otimes \nu \left(f_{7/2}\right)$ and $J^{\pi }=1^{+}$ by the intruder configuration $\pi {\left(d_{5/2}\right)}^{-1}\otimes \nu {\left(d_{3/2}\right)}^{-1}{\left(f_{7/2}\right)}^2$. The paper reports on spectroscopic properties of ${}^{34}\mathrm{Si}$ such as an extended level scheme, spin and parity assignments based on $log\left(ft\right)$ values and $\gamma$-ray branching ratios, absolute $\beta$ feeding intensities, and neutron emission probabilities. A total of 11 newly identified levels and 26 transitions were added to the previously known level scheme of ${}^{34}\mathrm{Si}$. Large scale shell-model calculations using the SDPF-U-MIX interaction, able to treat higher order intruder configurations, are compared with the new results and conclusions are drawn concerning the predictive power of SDPF-U-MIX, the $N=20$ shell gap, the level of mixing between normal and intruder configurations for the $0_1^{+}$, $0_2^{+}$, and $2_1^{+}$ states, and the absence of triaxial deformation in ${}^{34}\mathrm{Si}$.