A method for the evaluation of tunneling probabilities through a slowly varying potential barrier containing potential holes

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Abstract
A theory is proposed for the evaluation of electron tunneling probabilities through a slowly varying potential barrier containing potential holes. In particular a method is proposed for the evaluation of the multiple scattering between strongly interacting holes. The method utilizes the two stage interaction formalism of the T scattering matrix. The series describing in all orders the scattering of the tunneling electron by the potential holes is summed using a technique of Beeby (1968) modified accordingly. The theory is developed for both the one dimensional and the three dimensional case. A discussion of the qualitative correctness of one dimensional calculations, with particular reference to field emission, is included. No numerical results on specific cases are reported.

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