Two-potential approach to multi-dimensional tunneling
Abstract
We consider tunneling to the continuum in a multi-dimensional potential. It is demonstrate that this problem can be treated as two separate problems: a) a bound state and b) a non-resonance scattering problem, by a proper splitting of the potential into two components. Finally we obtain the resonance energy and the partial tunneling widths in terms of the bound and the scattering state wave functions. This result can be used in a variety of tunneling problems. As an application we consider the ionization of atomic states by an external field. We obtain very simple analytical expressions for the tunneling width and for the angular distribution of tunneling electrons. It is shown that the angular spread of electrons in the final state is determined by the semi-classical traversal tunneling time.
Cite
@article{arxiv.nucl-th/0111076,
title = {Two-potential approach to multi-dimensional tunneling},
author = {S. A. Gurvitz},
journal= {arXiv preprint arXiv:nucl-th/0111076},
year = {2016}
}
Comments
13 pages, 1 figure, corrected typos, to appear in ``Multiple Facets of Quantization and Supersymmetry/Michael Marinov Memorial Volume'', World Scientific