# Studies of quasiclassical approach applicability to true three-body decays

## TL;DR

This paper evaluates the quasiclassical method's effectiveness in modeling true three-body decays within the hyperspherical harmonics framework, highlighting its accuracy and limitations through specific nuclear decay examples.

## Contribution

It demonstrates the applicability and limitations of the quasiclassical approach in three-body decay calculations, especially when reducing to single-channel formalism.

## Key findings

- Quasiclassical approach is accurate for typical three-body potential profiles.
- Reduction to single-channel overestimates two-proton decay widths.
- Application to $^{17}$Ne decay questions the approximation's general validity.

## Abstract

Within the hyperspherical harmonics approach the three-body problem is reduced to a motion of one effective particle in a "strongly deformed" field, which is described in coupled-channel formalism. This method is especially suited to studies of phenomena characterized by genuine three-body dynamics, e.g. Borromean haloes and true three-body decays. The reduction of the hyperspherical equations set to a single-channel Schr\"odinger equation provides the basis for the use of the standard quasiclassical expression for calculations of widths for true three-body decays. We demonstrate that the quasiclassical approach by itself is quite precise in application to typical profiles of the three-body effective potentials. However, the reduction to single-channel formalism leads to significant overestimation of the two-proton width $\Gamma_{2p}$. This is demonstrated by the example of the $^{17}$Ne first excited $3/2^-$ state decay, questioning, however, the applicability of such an approximation in general.