Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1707.08954

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

S. M. Wang·N. Michel·W. Nazarewicz·F. R. Xu
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

nucl-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

S. M. Wang, N. Michel, W. Nazarewicz, F. R. Xu. 2017-07-27. Structure and decays of nuclear three-body systems: the Gamow coupled-channel method in Jacobi coordinates. https://doi.org/10.1103/physrevc.96.044307

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Three-dimensional orbital-free density functional theory description of nuclear pasta in the inner crust of neutron stars

Background: In the bottom layer of the inner crust of neutron stars, various crystalline structures are expected to emerge that are collectively called ``nuclear pasta.'' It is desirable to know properties of nuclear pasta in a wide variety of conditions for astrophysical applications. However, three-dimensional fully-microscopic calculations require huge computational effort that makes it still challenging to carry out systematic calculations. Purpose: In this paper, we propose an efficient method to calculate various nuclear pasta configurations in a non-empirical manner, based on three-dimensional orbital-free density functional theory (OF-DFT). We demonstrate the feasibility of the proposed approach by applying it to densities across the inner crust of neutron stars. Methods: As a first application of OF-DFT for nuclear pasta, we employ the second-order extended Thomas-Fermi (ETF) expansion of Skyrme energy density functional (EDF) to construct an EDF that depends only on neutron and proton number densities. Based on the variational principle, we derive Euler-Lagrange equations to determine optimal neutron and proton density distributions and solve them self-consistently. In this work, we call this approach the self-consistent ETF (SC-ETF) method. Results: We perform three-dimensional SC-ETF calculations with various box sizes. We successfully obtain various pasta structures, depending on given average nucleon number densities, consistent with earlier studies. Moreover, we find other exotic structures, such as bending and/or connected rods, slabs with a hole, etc., underlining the advantage of the self-consistent formalism. Conclusions: We demonstrate that the SC-ETF method proposed in this study, which can be regarded as a realization of OF-DFT, is a promising tool that can efficiently describe complex pasta structures without empirical assumptions on geometric shapes.

nucl-th↗
arXiv2026

Microscopic analysis of M1 scissors mode in $^{254}$No

The low-energy $M1$ orbital scissors mode (SM) was recently observed by Oslo group in deformed nucleus $^{254}$No. This is the heaviest nucleus where SM was ever experimentally found. We propose the analysis of SM, together with the spin-flip $M1$ resonance, within fully self-consistent Quasiparticle Random-Phase Approximation (QRPA) with Skyrme forces SG2, SLy4 and SLy5. The impact of "tensor" $J^2$-term, introduced by perturbative (on the base of SG2) and consistent (SLy5) ways, is analyzed and shown to be noticeable but not decisive. The deformation-induced coupling of $M1$ and $E2$ states is inspected. The calculations reasonably describe Oslo's experimental data. The best agreement is obtained for SLy5. A fine structure of SM in $^{254}$No is predicted. A significant constructive interference of the dominant orbital and minor spin-flip contributions to $M1$ strength at SM energy region is found. What is remarkable, our analysis of distributions of the convective nuclear currents challenges the scissors-like flow usually assumed for SM.

nucl-th↗
arXiv2026

Systematic Study of Proton, Two-Proton, Alpha, and Cluster Radioactivity Half-Lives based on the Deformed Gamow-like Model and Tabular Prior-data Fitted Network ($\mathrm{TabPFN}$)

A hybrid framework combining the deformed Gamow-like model ($\mathrm{DGLM}$) with the Tabular Prior-data Fitted Network ($\mathrm{TabPFN}$) is developed to improve half-life predictions for two-proton emission, proton emission, $α$ decay, and cluster radioactivity. A total of 583 radioactive nuclei are investigated, including 17 two-proton emitters, 42 proton emitters, 498 $α$ emitters, and 26 cluster emitters. Among the four considered models, $\mathrm{DGLM}^{b}+\mathrm{TabPFN}$ achieves the best overall performance, with $σ_{\mathrm{RMS}}=0.423$, corresponding to an improvement of approximately $82.2\%$ over $\mathrm{DGLM}^{b}$. The model parameters are optimized for each decay mode using the least-squares method. After introducing $\mathrm{TabPFN}$, the prediction errors for proton emission and $α$ decay are reduced by approximately $80.6\%$ and $87.6\%$, respectively. For $α$ decay, the training, test, and overall RMSEs are 0.208, 0.305, and 0.240, indicating good generalization capability without evident overfitting. The model also reproduces the systematic evolution of $α$-decay half-lives and the shell-closure effect around $N=126$. These results demonstrate that combining $\mathrm{DGLM}$ with $\mathrm{TabPFN}$ significantly improves the accuracy and robustness of radioactive-decay half-life predictions while retaining the physical interpretability of the original model.

nucl-th↗