Time-dependent approach to the continuum shell model

The continuum shell model represents a merger of the traditional shell model, the tool for understanding nuclear structure, with the physics of reactions. In this work a new time-dependent approach to the continuum shell model is presented, where construction and application of the time-dependent evolution operator culminate in an effective and successful strategy for tackling the nonstationary many-body dynamics. Details behind the technique and methods to overcome general problems associated with quantum many-body physics on the verge of stability are discussed. Topics presented include the construction of the time-dependent Green's function, the full propagator from the exact solution of Dyson's equation, a treatment of decays and virtual self-energy terms, the explicit time dependence and survival probability of states, the strength function and collective features of unstable systems, the center-of-mass problem, computation of the cross section and its Blatt-Biedenharn angular decomposition, Coulomb amplitudes, and interference. An extensive comparison with the R-matrix approach is offered. Realistic examples are used to demonstrate the techniques.