External Stationary Field Research Articles

Transition from a state with a certain momentum into a state with a certain parameter of spinless particle escape in the external field

A distribution function on the parameter of escape of particle B with the amplitude of process A → B in the external stationary field is investigated in this work. This distribution function is directly related to the form factor of the external-field source. By way of illustration consideration has been given to a hydrogen-like atom. It is shown that the distribution into the forward hemisphere comprises information on the spatial structure of an electron cloud, while the distribution into the backward hemisphere reproduces a spatial structure in the vicinity of a nucleus.

Collisional approach to dynamics of resonance atomic states in an external field

The following aspects of the dynamics of an atomic state in an external stationary field are assessed: (i) the rearrangement problem; (ii) the description of the appropriate final-channel wavefunctions; (iii) the analytical properties of the transition amplitude into the continuum. The rearrangement problem was solved by the introduction of the effective Hamiltonian, the eigenstates of which include both the initial state and final states ('modified states of continuum spectrum' MSCS) which describe the potential part of the exact wavefunction of the scattering problem. It is shown that the amplitude of decay and transition into MSCS as functions of time have an exact representation as a sum of resonance terms defined by a set of resonance states and the matrix elements of the shift R-matrix operator. Analysing the following expansion basis sets: stationary states, Volkov-Keldysh states and coherent states it is shown that the most appropriate one is a modified set of Volkov-Keldysh states.

On the exact evolution of the distribution functions

A manageable method to study the exact evolution of the distribution functions is presented. In it no use of the techniques of the Brussels group is made, the development of the method being based on the easier techniques of projection operators (Zwanzig’s method) and on an idea of Andrews. With this method an unified view for every kind of classical system with finite-range interactions is obtained. The momentum distribution function of a homogeneous system and the one-particle reduced distribution function of an inhomogeneous system are both studied in a general manner, both in the case of free systems as in the case of systems subjected to external stationary fields. For these distribution functions the same (in form) evolution equations are set up. Thus, the until now unsolved problem of the exact equations for inhomogeneous systems in an external stationary field is easily resolved. Finally, a method for calculating exact expressions for the density in phase-space and for the reduced distribution functions in every kind of system in terms of the distribution functions studied before is obtained in a simple manner.