Quasibound

Quasibound refers to a quantum-mechanical state that is temporarily localized in a region of space while lying in or near the continuum of scattering states. It behaves like a bound state for a finite time but ultimately decays into open channels. In scattering theory such states appear as resonances, characterized by a complex energy E = E_R − iΓ/2, where E_R is the resonance energy and Γ is the total decay width. The lifetime of a quasibound state is τ = ħ/Γ. Mathematically, quasibound states can be described as poles of the S-matrix on the unphysical sheet or as solutions to the Schrödinger equation with outgoing-wave (Siegert) boundary conditions, or via non-Hermitian effective Hamiltonians.

Origins and examples: Quasibound states arise when a potential creates a temporary trapping region, such as a barrier or a centrifugal term in a multi-channel system, allowing tunneling or decay to open channels. They occur across physics disciplines, including nuclear, atomic, and molecular systems. Examples include shape resonances in nuclear reactions and metastable electronic or molecular states above a dissociation or ionization threshold, as well as Feshbach resonances in cold-atom systems.

Observables and interpretation: Quasibound states produce resonant features in scattering cross sections with a characteristic Breit–Wigner line shape around E_R, whose width Γ reflects the decay rate. In spectroscopy, finite lifetimes of these states are inferred from decay rates and resonance lifetimes.

Mathematical treatment: Practically, one identifies quasibound states by solving for complex energies or by methods such as complex scaling, stabilization, or R-matrix approaches. The total width Γ is the sum of partial widths to all open decay channels, Γ = ∑Γ_i.