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

Abstract

$\mathbf{Background}:$ 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. $\mathbf{Purpose}:$ 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). $\mathbf{Methods}:$ 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. $\mathbf{Results}:$ 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. $\mathbf{Conclusions}:$ 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.

10 pages, 8 figures

References in corpus (17)

• Evolution of shell structure in neutron-rich calcium isotopes
• Shell Model in the Complex Energy Plane
• A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states
• Shell Structure of Exotic Nuclei
• Two-proton radioactivity
• Generic strong coupling behavior of Cooper pairs in the surface of superfluid nuclei
• Two-proton radioactivity and three-body decay. III. Integral formulae for decay widths in a simplified semianalytical approach
• Three-body decay of ${}^6$Be
• Living on the edge of stability, the limits of the nuclear landscape
• Momentum distribution and correlation of two-nucleon relative motion in ${}^6$He and ${}^6$Li
• Role of diproton correlation in two-proton emission decay of the ${}^6$Be nucleus
• The nuclear force imprints revealed on the elastic scattering of protons with ${}^{10}$C
• Three-body model for the two-neutron decay of ${}^{16}$Be
• Precise comparison of the Gaussian expansion method and the Gamow shell model
• Numerical treatment of long-range Coulomb potential with Berggren bases
• Complex energy approaches for calculating isobaric analogue states
• Three-body model calculation of the 2${}^{+}$ state in ${}^{26}$O

Cited by in corpus (5)

• Quantified Gamow Shell Model interaction for $psd$-shell nuclei
• Fermion Pair Dynamics in Open Quantum Systems
• Structures and decay properties of extremely proton-rich nuclei ${}^{11,12}$O
• Gamow shell model description of ${}^4$He($d$,$d$) elastic scattering reactions
• Role of quadrupole deformation and continuum effects in the "island of inversion'' nuclei ${}^{28,29,31}$F