$\beta$-delayed fission in proton-rich nuclei in the lead region

Nuclear fission is the breakup of an atomic nucleus into two (sometimes three) fragments, thereby releasing a large amount of energy. Soon after its discovery in the late 1930’s, the gross properties of the fission phenomenon were explained by macroscopic nuclear models. Certain features however, such as asymmetric fission-fragment mass distributions in the actinide region, require the inclusion of microscopic effects. This interplay of the microscopic motion of individual nucleons on this macroscopic process is, until today, not yet fully understood. The phenomenon of fission has therefore been of recurring interest for both theoretical and experimental studies. This thesis work focuses on the $\beta$-delayed fission ($\beta$DF) process, an excellent tool to study low-energy fission of exotic nuclei, which was discovered in 1966 in the actinide region. In this two-step process, a precursor nucleus first undergoes $\beta$-decay to an excited level in the daughter nucleus, which may subsequently fission. Recently, an unexpected asymmetric division of $^{180}$Hg nuclei was observed in a $\beta$DF study of $^{180}$Tl. This work presents the experimental investigation of $\beta$DF properties of $^{194,196}$At and $^{200,202}$Fr nuclei, also situated in this scarcely studied region (with respect to the fission process) of the nuclear chart. The experiments were performed at the ISOLDE facility in CERN (Geneva, Switzerland), where neutron-deficient francium (Fr) and astatine (At) isotopes are formed by bombarding a UCx target with energetic protons. A purified radioactive ion beam is created by element-selective ionization and subsequent mass separation. For francium, the surface ionization mode was employed, while resonant laser-ionization was used to ionize astatine. The beam was then implanted on one of ten thin carbon foils, mounted on a rotatable wheel. $\beta$-delayed fission fragments were recorded by silicon detectors placed on either side of this foil. Fission-fragment masses were extracted from the energy spectra employing mass and momentum conservation laws. A dedicated experimental campaign to calibrate the silicon detectors was performed at the Lohengrin spectrometer in ILL, where fission products from the neutron-induced fission of $^{235}$U are separated based on their mass and energy. Other systematic effects, such as energy loss in the carbon foil or the emission of prompt neutrons, were also investigated. Other physics observables, which can be extracted from the $\beta$DF data, are the $\beta$DF probability or partial decay half-life. For the studied isotopes $^{194,196}$At and $^{200,202}$Fr, $\beta$DF was observed and corresponding branching ratios could be extracted. Fission-fragment mass distributions of daughter products $^{194,196}$Po and $^{202}$Rn were measured for the first time and showed a triple-humped structure, marking the transition between asymmetric fission observed in $^{178,180}$Hg and a more symmetric split of $^{204}$Rn nuclei, observed in previous studies. A comparison with contemporary fission models, namely the macroscopic-microscopic finite-range liquid-drop model and the self-consistent approach employing the Gogny D1S energy density functional, yields discrepancies. These differences hint to the need for dynamical fission calculations, because for both models the potential-energy surfaces (PES) lack pronounced structures. This is in contrast to the actinide region, where deep valleys in the PES determine the most probable path from ground state to fission. This work, together with other recent experimental campaigns at ISOLDE- CERN and SHIP-GSI (Darmstadt, Germany), has significantly extended the experimental $\beta$DF data in the neutron-deficient lead region. When combined with earlier experimental work in the uranium region, a systematic comparison of $\beta$DF-branching ratios became possible for a wide variety of isotopes across the nuclear chart. From basic assumptions and simplified considerations, a simple exponential dependence of the $\beta$DF partial half-life on the difference between the Q value for $\beta$-decay of the precursor and the fission-barrier height of the daughter is expected. This systematic trend, described with only two free parameters, was confirmed for experimental $\beta$DF partial half-lives spanning over seven orders of magnitude. Also for $\beta$-delayed fission probabilities, a similar dependence could be inferred and was verified using the available experimental data. These considerations could also be applied to other regions of the nuclear chart where $\beta$DF is expected to occur.