Simple mode on a highly excited background: Collective strength and damping in the continuum

Simple states, such as isobaric analog states or giant resonances, embedded into continuum are typical for mesoscopic many-body quantum systems. Due to the coupling to compound states in the same energy range, a simple mode acquires a damping width (“internal” dynamics). When studied experimentally with the aid of various reactions, such states reveal enhanced cross sections in specific channels at corresponding resonance energies (“external” dynamics which include direct decay of a simple mode and decays of intrinsic compound states through their own channels). We consider the interplay between internal and external dynamics using a general formalism of the effective non-Hermitian Hamiltonian and looking at the situation both from the “inside” (strength functions and spreading widths) and from the “outside” (S matrix, cross sections, and delay times). The restoration of isospin purity and the disappearance of the collective strength of giant resonances at high excitation energy are discussed as important particular manifestations of this complex interplay.