Real-time decay dynamics of the low-lying $1/2^{+}$ state in ${}^9$Be: Signatures of virtual-state behavior

Abstract

The low-lying $1/2^{+}$ state of ${}^9$Be has been interpreted either as a near-threshold resonance or as an ${}^8$Be+$n$ virtual state. Because both pictures can produce a pronounced threshold enhancement, its nature is difficult to determine from energy-domain observables alone. We investigate the low-lying $1/2^{+}$ state through its real-time decay dynamics and compare its behavior with that of the well-established $5/2^{+}$ resonance. A wave packet produced by electric-dipole excitation of the ${}^9$Be ground state is propagated in an $\alpha +\alpha +n$ three-body model. We analyze the survival probability, the fit-window dependence of the effective decay width, and time-dependent densities in different Jacobi-coordinate representations. The $1/2^{+}$ survival dynamics are further compared with an $s$-wave effective-range description motivated by the dominant ${}^8$Be+$n$ component found in our previous three-body studies. The $5/2^{+}$ channel shows approximately exponential late-time decay, with an effective width of $0.264$ MeV, close to the complex-scaled pole width of $0.285$ MeV. In contrast, the $1/2^{+}$ effective width decreases as the fitting interval is shifted to later times, and no stationary decay width is obtained. Its late-time survival probability is well described by the effective-range spectral distribution. The density evolution develops an ${}^8$Be+$n$-like asymptotic configuration while retaining a localized $p_{3/2}$ $\alpha n$ component suggestive of a ${}^5$He+$\alpha$-like configuration in the internal region. The $1/2^{+}$ decay differs qualitatively from resonance-like exponential decay and is consistent with near-threshold virtual-state dynamics. The distinct internal and asymptotic configurations revealed by the time-dependent densities provide complementary structural information beyond that contained in a single decay width.

Comments: 8 pages, 6 figures