A new approach to observe the radiative decay of the $^{229}$Th nuclear isomer, and to determine its energy and radiative lifetime, is presented. Situated at a uniquely low excitation energy, this nuclear state might be a key ingredient for the development of a nuclear clock, a nuclear laser and the search for time variations of the fundamental constants. The isomers $gamma$ decay towards the ground state will be studied with a high-resolution VUV spectrometer after its production by the $beta$ decay of $^{229}$Ac. The novel production method presents a number of advantages asserting its competitive nature with respect to the commonly used $^{233}$U $alpha$-decay recoil source. In this paper, a feasibility analysis of this new concept, and an experimental investigation of its key ingredients, using a pure $^{229}$Ac ion beam produced at the ISOLDE radioactive beam facility, is reported.
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