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

## TL;DR

This paper develops integral formulae for decay widths in three-body nuclear decays using a simplified semianalytical model, applied to specific isotopes, and analyzes convergence, uncertainties, and correlations.

## Contribution

It introduces a simplified Hamiltonian approach with integral formulae for three-body decay widths, enabling semianalytical calculations and detailed analysis of specific nuclear decays.

## Key findings

- Convergence of hyperspherical model calculations to exact decay widths.
- Updated decay width values for $^{17}$Ne and $^{45}$Fe.
- Analysis of decay correlations for $^{17}$Ne.

## Abstract

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 $3/2^{-}$ state of $^{17}$Ne and the $3/2^{-}$ 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 $3/2^-$ state are also studied.