Unfolding of exotic near-threshold structure and decay dynamics in $^{17}$B

TL;DR

The paper investigates a unique near-threshold situation in $^{17}$B where a 1640 keV γ ray from a $1/2^-$ state competes with two-neutron emission. Using both configuration-interaction shell-model (SM) approaches and the Gamow shell model (GSM), complemented by the Gamow coupled-channel (GCC) framework for decay, the authors treat $^{17}$B as a core plus two neutrons and include continuum coupling and near-threshold dynamics. They demonstrate that the observed competition arises from an $L=2$ two-neutron decay channel and a delicate interplay between $s$- and $d$-wave components, strongly modulated by the position of low-lying $0^-$ or $1^-$ resonances in $^{16}$B and nearby virtual $s$-wave states. The work provides predictions for neutron-neutron energy and angular correlations, offering experimental observables to map the internal structure and test open-quantum-system dynamics in near-threshold nuclei.

Abstract

Neutron-rich boron isotopes provide a valuable testing ground for threshold-driven structure and reaction phenomena, including halo formation and exotic decay modes. In particular, the structure of $^{17}\mathrm{B}$ and its relation to unbound $^{16}\mathrm{B}$ are of special interest. The $^{16}\mathrm{B}$ nucleus is slightly unbound by approximately $50~\mathrm{keV}$, while $^{17}\mathrm{B}$ is bound with a neutron separation energy of about $1.4-1.6~\mathrm{MeV}$. The observation of a $1640~\mathrm{keV}$ $γ$ ray in $^{17}\mathrm{B}$, which we argue originates from a $1/2^-$ excited state, points to a remarkable situation in which $γ$ decay and two-neutron decay can compete. We analyze and identify the main reasons for this competition: $L=2$ emission of the neutron pair, and structural realignment driven by the proximity of the one-body threshold, in particular the nearby $s$-wave neutron decay channel. The decay is a unique near-threshold $L=2$ process in which multiple structural components contribute, each with coexisting direct and virtual sequential amplitudes whose interference governs the observables. Because threshold dynamics, continuum coupling, and interference of multiple quantum pathways are universal, closely related scenarios arise in ultracold atoms near Feshbach resonances, few-body atomic and molecular breakups, mesoscopic and photonic open systems, and other areas where open-quantum-system effects impact observables. We employ advanced theoretical models to study this first-of-its-kind case and provide a coherent theoretical perspective based on configuration interaction and complex-energy formalisms that incorporate both reaction continuum and structural effects near threshold.

Figures (7)

• Figure 1: Energy levels and transitions in boron isotopes in the region $^{15}\mathrm{B}$--$^{17}\mathrm{B}$. All energies are shown in keV. Levels are displayed relative to the $^{17}\mathrm{B}$ ground state, illustrating the $^{16}\mathrm{B}$ and $^{15}\mathrm{B}$ excitation spectra relative to the one- and two-neutron thresholds, respectively. Energy labels in $^{17}\mathrm{B}$ indicate excitation energies of the levels. Two $\gamma$-ray energies from Ref. Mozumdar2025Searcha are indicated by dashed lines. For $^{17}\mathrm{B}$ and $^{16}\mathrm{B}$, spin assignments shown in parentheses are tentative from shell-model calculations and experiments; we present supporting evidence for these assignments in the text. The dashed $7/2^{-}$ state in $^{17}\mathrm{B}$ reflects theoretical expectations, remains unobserved, and is included for illustration and discussion. Low-lying states in $^{16}\mathrm{B}$ are taken from the combined experimental data of Refs. Mozumdar2025SearchaYang2021Quasifree. Energies shown for states in $^{16}\mathrm{B}$ are resonance energies relative to the $^{15}\mathrm{B}$ ground state. The two-neutron separation energy, $S_{2n}=1.38(21)\,\mathrm{MeV}$and2012Ame2012, is shown by a horizontal dotted line at the central value and corresponds to the $^{15}\mathrm{B}$ ground-state energy relative to $^{17}\mathrm{B}$; the comparatively large uncertainty is reflected in the quoted value.
• Figure 2: Momentum-space kinematics for the three-body system $^{15}\mathrm{B}+n+n$. The diagram shows the center of mass (c.m.) and the single-particle momenta $\boldsymbol{k}_1$, $\boldsymbol{k}_2$, and $\boldsymbol{k}_c$ of the two neutrons and the core, with labels $\boldsymbol{k}_i/A_i$ indicating velocities scaled by the mass numbers $A_1$, $A_2$, and $A_c$. Two Jacobi sets are indicated. In the $(^{15}\mathrm{B}+n)+n$ set (unprimed, Jacobi–Y), $\ell_x$ is the relative momentum of the core–neutron pair $(^{15}\mathrm{B}+n)$ with associated energy is $E_{\mathrm{core}\text{-}n}$ and reduced mass $\mu_{2c}$. $\ell_y$ is the momentum of the second spectator neutron relative to the c.m. of the $^{15}\mathrm{B}+n$ subsystem. In the $nn$-core set $^{15}\mathrm{B}+(n+n)$ (primed, Jacobi–T), $\ell'_{x}$, $E_{nn}$, and $\mu_{12}$ represent relative momentum, total energy, and reduced mass of the $n+n$ subsystem. $\ell'_{y}$ is the momentum of the $^{15}\mathrm{B}$ core relative to the $n+n$ c.m. The orbital angular momenta couple to the total as $L=\ell_x\otimes \ell_y=\ell'_x\otimes \ell'_y$.
• Figure 3: Calculated $2n$ (orange band), $1n$ (blue dash-dotted line), $M1$ (green dashed line), and total (black solid line) decay widths (half-lives) from the excited $^{17}$B as a function of $2n$ decay energy $Q_{2n}$. All the particle decays are through the $L = 2$ channel, and spectroscopic factors have been taken into account.
• Figure 4: Predicted weight of each relative components in the $1/2^-$ excited state of $^{17}$B, plotted as a function of the $s$‑wave virtual-state energy $E_s$ with respect to the threshold.
• Figure 5: (a) Energy and (b) angular correlations for individual configurations in the final state. Each configuration is labeled by $(K, \ell_x', \ell_y', L)$ in the Jacobi-T coordinate, where $K$ is the hyperspherical quantum number. The definitions of $\ell_x'$, $\ell_y'$, and $L$ are the same as in Fig. \ref{['fig:diagram']}. This plot should be read as a display of wave functions for given Jacobi configurations; the patterns do not depend on whether the $Y$ or $T$ set is used, although the interpretation of the quantum numbers and angles differs between the two.