Combined high-resolution laser spectroscopy and nuclear decay spectroscopy for the study of the low-lying states in $^{206}$Fr, $^{202}$At, and $^{198}$Bi

High-resolution laser spectroscopy was performed on $^{206}$Fr with the collinear resonance ionization spectroscopy (CRIS) experiment at CERN-ISOLDE. The hyperfine structure and isotope shift of the ground, first isomeric and second isomeric states were measured. The hyperfine components were unambiguously assigned to each nuclear state by means of laser-assisted nuclear decay spectroscopy. The branching ratios in the α decay of $^{206}$Fr and $^{202}$At were also measured for the first time with isomerically purified beams. The extracted hindrance factors allow determination of the spin of the ground, first isomeric, and second isomeric states in $^{202}$At and $^{198}$Bi.