A novel experiment has been commissioned at the Weizmann Institute of Science for the study of weak interactions via a high-precision measurement of the beta-neutrino angular correlation in the radioactive decay of short-lived $^{6}$He. The facility consists of a 14 MeV $d+t$ neutron generator to produce atomic $^{6}$He, followed by ionization and bunching in an electron beam ion source, and injection into an electrostatic ion beam trap. This ion trap has been designed for efficient detection of the decay products from trapped light ions. The storage time in the trap for different stable ions was found to be in the range of 0.6 to 1.2 s at the chamber pressure of $sim$7$times$10$^{-10}$ mbar. We present the initial test results of the facility, and also demonstrate an important upgrade of an existing method cite{stora} for production of light radioactive atoms, viz. $^{6}$He, for the precision measurement. The production rate of $^{6}$He atoms in the present setup has been estimated to be $sim 1.45times10^{-4}$ atoms per neutron, and the system efficiency was found to be 4.0$pm$0.6%. An improvement to this setup is also presented for the enhanced production and diffusion of radioactive atoms for future use.