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Siegert-state expansion for nonstationary systems. III. Generalized Born-Fock equations and adiabatic approximation for transitions to the continuum

Oleg I. Tolstikhin

Phys. Rev. A: At. Mol. Opt. Phys., vol: 77, num: 3, 17 pages, published: 17 March 2008, 032711

Abstract: This paper presents a further development of the Siegert-state expansion approach [O. I. Tolstikhin, Phys. Rev. A 73, 062705 (2006)]. Here, we switch to the adiabatic representation. We introduce the adiabatic Siegert states and derive the generalized Born-Fock equations describing the time evolution of coefficients in the expansion of the solution to the time-dependent Schrödinger equation in their terms. By constructing the asymptotic solution to these equations, we develop an adiabatic approximation for transitions to the continuum. The leading-order asymptotic formulas for the spectra of ejected particles in the underbarrier (when the initial state remains bound during all the evolution) and overbarrier (when the initial state is temporarily promoted to the continuum) cases are obtained. These formulas are uniform in the momentum of ejected particles and thus give a complete solution to the problem in the adiabatic approximation. Their relation to previous studies of nonadiabatic transitions to the continuum is discussed. The results are illustrated by calculations for a model describing the dissociation of a diatomic molecule by an electric field pulse.

   Atoms and molecules.
      Interaction of atoms and molecules with external fields and radiation.
         Photoionisation and photodissociation.
            Dissociation and other transformations of molecules by action of light.

   Atoms and molecules.
      General problems of atomic and molecular physics.
         Methods of the quantum mechanics of atoms and molecules.