Two-proton radioactivity and three-body decay. III. Integral formulae for decay widths in a simplified semianalytical approach

Three-body decays of resonant states are studied using integral formulae for decay widths. Theoretical approach with a simplified Hamiltonian allows semianalytical treatment of the problem. The model is applied to decays of the first excited $3\mathrm{/}{2}^{-}$ state of ${}^{17}$Ne and the $3\mathrm{/}{2}^{-}$ ground state of ${}^{45}$Fe. The convergence of three-body hyperspherical model calculations to the exact result for widths and energy distributions are studied. The theoretical results for ${}^{17}$Ne and ${}^{45}$Fe decays are updated and uncertainties of the derived values are discussed in detail. Correlations for the decay of ${}^{17}$Ne $3\mathrm{/}{2}^{-}$ state are also studied.