Lifetime measurements of neutron-rich light isotopes ${}_{}{}^{14}{}_{}{}^{}\mathrm{Be}$ and ${}_{}{}^{17}{}_{}{}^{}\mathrm{C}$

β-decay half-lives have been measured for eight neutron-rich isotopes produced by bombardment of a ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$ target with an ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ beam at 30 MeV/nucleon. The previously unknown half-lives of ${}_{}{}^{14}{}_{}{}^{}\mathrm{Be}$ (4.2±0.7 ms) and ${}_{}{}^{17}{}_{}{}^{}\mathrm{C}$ (202±17 ms) have been obtained along with the half-lives of ${}_{}{}^9{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{B}$, and ${}_{}{}^{15}{}_{}{}^{}\mathrm{B}$. This experiment represents the first half-life measurements using the Michigan State reaction product mass separator.