In this work, we use both Coupled-Cluster and Embedded Two-Body Random Ensemble (ETBRE) to diagnose quantum chaos in deep-hole states. Applying Equation of Motion Coupled Cluster method with singles and doubles to a Woods-Saxon potential plus the delta interaction, we compute spectral functions for neutron removal from 16 O. Valence 1 p 3/2 hole exhibits a quasiparticle peak with negligible spreading width (Γ ↓ ≈ 0), while deep 1 s 1/2 hole is strongly fragmented (Γ ↓ ≈ 2.58 MeV), hinting at chaotic dynamics. Mapping these microscopic widths onto an ETBRE establishes the spreading width Γ as an order parameter for level statistics. We find a transition in the Brody parameter ω from Poisson regularity ( ω → 0) to Gaussian orthogonal ensemble (GOE) ( ω → 1), the transitional point of the width at Γ c ≈ 0.55 MeV ( ω ≈ 0.5) and the 1 s 1/2 deep-hole state lies deep in the chaotic regime ( ω ≈ 0.95).
Wang et al. (Fri,) studied this question.