UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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Conference: Bucharest University Faculty of Physics 2007 Meeting


Section: Quantum Mechanics, Statistical Physics, Optics, Spectroscopy, Plasma and Lasers


Title:
Numerical solution of the one-dimensional Dirac equation for an atom in external laser field


Authors:
Madalina Boca, Viorica Florescu


Affiliation:
Department of Physics, University of Bucharest

MG11, Bucharest Magurele 077125, Romania


E-mail
boca@barutu.fizica.unibuc.ro


Keywords:
Dirac equation, Volkov solutions, laser pulse


Abstract:
For very high laser field intensity relativistic effects must be taken into account in the description of laser atom interaction [1]. We define the Volkov solutions as particular solutions of the 1D Dirac equation for the electron in a laser pulse which at the beginning of the pulse reduce to the free 1D Dirac solutions with given momentum. In the presence of a laser pulse, we numerically solve the Dirac equation for determining i) the Volkov solutions and ii) the state spinor of an electron in a Gaussian potential, which at the initial moment reduces to the ground state. The numerical method used is based on the split-operator algorithm. For a laser pulse of Gaussian shape, frequency 1 au and FWHM 1 cycle, we study the transfer of population between positive and negative energy states during the pulse and the dynamic of population on Volkov states originating from negative energy free solutions. Our conclusion is that if the potential is not too deep (the ground state energy less than about 20 au) the Volkov states originating from negative energy solutions are not populated during the pulse, such that the expansion of the system wave spinor in a basis set consisting only in Volkov spinors originating from positive energy states should be possible. The validity of this conclusion for the three dimensional case is qualitatively discussed. [1]Yousef I. Salamin, S.X. Hu, Karen Z. Hatsagortsyan, and Christoph H. Keitel, Physics Reports 427, 41 (2006).