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

Abstract

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.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). 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. 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. 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 nucleonnucleon 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.

Structure and decay of the extremely proton-rich nuclei O11,12

“…To describe the energy spectra and 2p decay of 11,12 O, we use the three-body core+nucleon+nucleon GCC approach [49,50]. The core ( 9,10 C) is chosen as a deformed rigid rotor.…”

“…Beyond the potential barrier, the two emitted protons tend to gradually separate due to the repulsive Coulomb interaction. The behavior of the two protons below the barrier can be understood by the influence of pairing which favors low angular momentum amplitudes; hence, it effectively lowers the centrifugal barrier and increases the probability for the two protons to decay by tunnelling [49,[68][69][70].…”

Puzzling Two-Proton Decay of Kr67

“…So far, most of the theoretical models of 2p radioactivity divide the coordinate space into internal and asymptotic regions, where one can use the WKB approach [19][20][21], R-matrix theory [22,23], and current expression [24,25] to estimate the partial 2p decay width. In our previous work [26], we introduced the Gamow coupled-channel (GCC) framework. By utilizing the Berggren-ensemble expansion technique, the GCC model is capable of capturing structure and decay facets of three-cluster systems.…”

“…Theoretical framework-To describe 2p emission, we extend the previously introduced [26] three-body core+nucleon+nucleon Gamow coupled-channel (GCC) approach by considering core excitations. To this end, the wave function of the parent nucleus is written as Ψ Jπ = Φ Jpπp ⊗ φ jcπc Jπ , where Φ Jpπp and φ jcπc are the wave functions of the two valence protons and the core, respectively.…”

“…To this end, the wave function of the parent nucleus is written as Ψ Jπ = Φ Jpπp ⊗ φ jcπc Jπ , where Φ Jpπp and φ jcπc are the wave functions of the two valence protons and the core, respectively. Φ Jpπp is constructed in Jacobi coordinates with the hyperspherical harmonics expansion, of which the hyperradial part ψ γK (ρ) is expanded in the Berggren basis that includes bound, decaying, and scattering states [26,28]. K is the hyperspherical quantum number and γ = {s 1 , s 2 , S 12 , S, x , y , L, J p , j c }.…”