Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling

Abstract Complex scaling enables one to associate the resonance phenomenon, as it appears in atomic, molecular, nuclear physics and in chemical reactions, with a single square integrable eigenfunction of the complex-scaled Hamiltonian, rather than with a collection of continuum eigenstates of the unscaled hermitian Hamiltonian. In this report, we illustrate the complex-scaling method by giving examples of simple analytically soluble models. We describe the computational algorithms which enable the use of complex scaling for the calculations of the energy positions lifetimes and partial widths of atomic and molecular autoionization resonance states, of small polyatomic molecules and van der Waals molecules in predissociation resonance states, of atoms and molecules which are temporarily trapped on a solid surface and of atoms and molecules which ionized/dissociate when they are exposed to high intensity laser field. We focus on the properties of the complex scaled Hamiltonian and on the extension of theorems and principles, which were originally proved in quantum mechanics for hermitian operators to non-hermitian operators and also on the development of the complex coordinate scattering theory.