Electron-impact ionization of the hydrogen atom is the prototypical three-body Coulomb breakup problem in quantum mechanics. The combination of subtle correlation effects and the difficult boundary conditions required to describe two electrons in the continuum have made this one of the outstanding challenges of atomic physics. A complete solution of this problem in the form of a ‘reduction to computation’ of all aspects of the physics is given by the application of exterior complex scaling, a modern variant of the mathematical tool of analytic continuation of the electronic coordinates into the complex plane that was used historically to establish the formal analytic properties of the scattering matrix. This review first discusses the essential difficulties of the three-body Coulomb breakup problem in quantum mechanics. It then describes the formal basis of exterior complex scaling of electronic coordinates as well as the details of its numerical implementation using a variety of methods including finite difference, finite elements, discrete variable representations and B-splines. Given these numerical implementations of exterior complex scaling, the scattering wavefunction can be generated with arbitrary accuracy on any finite volume in the space of electronic coordinates, but there remains the fundamental problem of extracting the breakup amplitudes from it. Methods are described for evaluating these amplitudes. The question of the volume-dependent overall phase that appears in the formal theory of ionization is resolved. A summary is presented of accurate results that have been obtained for the case of electron-impact ionization of hydrogen as well as a discussion of applications to the double photoionization of helium.
Since the invention of quantum mechanics, even the simplest example of the collisional breakup of a system of charged particles, e(-) + H --> H(+) + e(-) + e(-) (where e(-) is an electron and H is hydrogen), has resisted solution and is now one of the last unsolved fundamental problems in atomic physics. A complete solution requires calculation of the energies and directions for a final state in which all three particles are moving away from each other. Even with supercomputers, the correct mathematical description of this state has proved difficult to apply. A framework for solving ionization problems in many areas of chemistry and physics is finally provided by a mathematical transformation of the Schrodinger equation that makes the final state tractable, providing the key to a numerical solution of this problem that reveals its full dynamics.
We demonstrate experimentally how the time-dependent phase modulation induced by molecular rotational wave packets can manipulate the phase and spectral content of ultrashort light pulses. Using impulsively excited rotational wave packets in CO2, we increase the bandwidth of a probe pulse by a factor of 9, while inducing a negative chirp. This chirp is removed by propagation through a fused silica window, without the use of a pulse compressor. This is a very general technique for optical phase modulation that can be applied over a broad spectral region from the IR to the UV.
We show that the ''two-potential'' formalism of conventional distorted-wave rearrangement theory, which is formally valid only for short-range interactions, can be used to evaluate amplitudes for the ionization of atomic hydrogen by electron impact. The triply differential cross sections calculated using this method validate earlier results obtained by extrapolating the quantum mechanical flux. Although it uses the same time-independent wave functions, this method offers significant advantages over flux extrapolation. It is more accurate, can be applied in practical calculations over a broader range of collision energies, and unlike the flux-extrapolation method, can be applied for arbitrary values of energy sharing between the ejected electrons. Since this rearrangement formalism provides the complete scattering amplitude for ionization, it can be used to calculate any differential cross section.
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