How the Pauli principle governs the decay of three-cluster systems

TL;DR

This paper introduces a new method for analyzing the continuum spectrum of three-cluster systems, emphasizing the Pauli principle's role in decay processes, with applications to the 5H nucleus.

Contribution

It proposes a discrete basis approach for three-cluster systems and establishes asymptotic boundary conditions consistent with the Pauli principle.

Findings

Eigenfunctions and eigenvalues of the three-cluster norm kernel analyzed

Classification of eigenvalues using two-body subsystem eigenvalues

Asymptotic boundary conditions favor subsequent decay over democratic decay

Abstract

New approach to the problem of multichannel continuum spectrum of three-cluster systems composed of an s-cluster and two neutrons is suggested based on the discrete representation of a complete basis of allowed states of the multiparticle harmonic oscillator. The structure of the eigenfunctions and behavior of the eigenvalues of the three-cluster norm kernel are analyzed. Classification of the eigenvalues of the three-cluster systems with the help of eigenvalues of the two-body subsystem is suggested. Asymptotic boundary conditions for a three-cluster wave function in the continuum consistent with the requirements of the Pauli principle are established. Such asymptotic behavior corresponds rather to subsequent decay of the three-cluster system than to the so-called "democratic decay" associated with the hyperspherical harmonics. The 3H+n+n configuration of the 5H nucleus is considered in detail.