In $beta$-decay studies the determination of the decay probability to the ground state of the daughter nucleus often suffers from large systematic errors. The difficulty of the measurement is related to the absence of associated delayed $gamma$-ray emission. In this work we revisit the $4pigamma-beta$ method proposed by Greenwood and collaborators in the 1990s, which has the potential to overcome some of the experimental difficulties. Our interest is driven by the need to determine accurately the $beta$-intensity distributions of fission products that contribute significantly to the reactor decay heat and to the antineutrinos emitted by reactors. A number of such decays have large ground state branches. The method is relevant for nuclear structure studies as well. Pertinent formulae are revised and extended to the special case of $beta$-delayed neutron emitters, and the robustness of the method is demonstrated with synthetic data. We apply it to a number of measured decays that serve as test cases and discuss the features of the method. Finally, we obtain ground state feeding intensities with reduced uncertainty for four relevant decays that will allow future improvements in antineutrino spectrum and decay heat calculations using the summation method.
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