Structure and decays of nuclear three-body systems: the Gamow coupled-channel method in Jacobi coordinates

TL;DR

The paper introduces a Gamow coupled-channel (GCC) method in Jacobi coordinates for accurately describing the structure and decay of three-body nuclear systems, validated against the Gamow Shell Model (GSM).

Contribution

It develops a new GCC framework in Jacobi coordinates, providing a precise and efficient tool for studying weakly bound and unbound nuclear states, with benchmarking against GSM results.

Findings

GCC results agree well with GSM for energies and decay widths.

Nucleon-nucleon angular correlations are sensitive to neutron interactions.

GCC is accurate, robust, and extendable to microscopic models.

Abstract

${\bf Background:}$ Weakly bound and unbound nuclear states appearing around particle thresholds are prototypical open quantum systems. Theories of such states must take into account configuration mixing effects in the presence of strong coupling to the particle continuum space. ${\bf Purpose:}$ To describe structure and decays of three-body systems, we developed a Gamow coupled-channel (GCC) approach in Jacobi coordinates by employing the complex-momentum formalism. We benchmarked the new framework against the complex-energy Gamow Shell Model (GSM). ${\bf Methods:}$ The GCC formalism is expressed in Jacobi coordinates, so that the center-of-mass motion is automatically eliminated. To solve the coupled-channel equations, we use hyperspherical harmonics to describe the angular wave functions while the radial wave functions are expanded in the Berggren ensemble, which includes bound, scattering and Gamow states. ${\bf Results:}$ We show that the GCC method is both accurate and robust. Its results for energies, decay widths, and nucleon-nucleon angular correlations are in good agreement with the GSM results. ${\bf Conclusions:}$ We have demonstrated that a three-body GSM formalism explicitly constructed in cluster-orbital shell model coordinates provides similar results to a GCC framework expressed in Jacobi coordinates, provided that a large configuration space is employed. Our calculations for $A=6$ systems and $^{26}$O show that nucleon-nucleon angular correlations are sensitive to the valence-neutron interaction. The new GCC technique has many attractive features when applied to bound and unbound states of three-body systems: it is precise, efficient, and can be extended by introducing a microscopic model of the core.