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Nuclear Physics and Atomic Energy

The time analysis of multiple internal reflections in tunneling description through the barrier

V. S. Olkhovsky, S. P. Maidanyuk

Published Dec 30, 2000• 0 citations
Publisher

Abstract

The problem of scattering of a nonrelativistic particle on a nucleus is considered, the interaction potential between which has a spherically symmetrical view. As the further development of the time analysis of processes of tunneling the non-stationary method of the solution of a problem is represented, due to which begins the possibility to describe in a time dependence the propagation (tunneling) of a particle and in details to study this process in an interesting instant or concerning a concrete point of space. At calculating the time parameters the method has shown itself simple and convenient. At finding the expressions for stationary wave functions for problems with an interaction potential, which radial part has more composite view than rectangular, this method is more effective than reference stationary approaches.

DOI
10.15407/jnpae2000.02.042

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The problem of scattering of a nonrelativistic particle on a nucleus is considered, the interaction potential between which has a spherically symmetrical view. As the further development of the time analysis of processes of tunneling the non-stationary method of the solution of a problem is represented, due to which begins the possibility to describe in a time dependence the propagation (tunneling) of a particle and in details to study this process in an interesting instant or concerning a concrete point of space. At calculating the time parameters the method has shown itself simple and convenient. At finding the expressions for stationary wave functions for problems with an interaction potential, which radial part has more composite view than rectangular, this method is more effective than reference stationary approaches.
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A method of a non-stationary description of tunneling of a particle through the one-dimensional and spherically symmetric rectangular barriers on the basis of analisis of multiple internal reflections of wave packets in relation on the barrier boundaries, named as the Method of multiple internal reflections, is presented at the first time. For the one-dimensional problem the applicability of this method is proved, its specific features are analyzed. For the spherically symmetric problem the amplitudes of the transmitted and reflected wave packets, times of tunneling and reflection in relation to the barrier are calculated using this method. The effect of Hartman-Fletcher is analyzed.
Using a recently developed procedure---multiple wave packet decomposition---here we study the phase time formulation for tunneling or reflecting particles colliding with a potential barrier. To partially overcome the analytical difficulties which frequently arise when the stationary phase method is employed for deriving phase (tunneling) time expressions, we present a theoretical exercise involving a symmetrical collision between two identical wave packets and an one-dimensional rectangular potential barrier. Summing the amplitudes of the reflected and transmitted waves---using a method we call multiple peak decomposition---is shown to allow reconstruction of the scattered wave packets in a way which allows the stationary phase principle to be recovered.
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