TunnelingT h e q u a n t iz a t io n o f t h e t r a n s v e r s e m o t io n e n e r g y in t h e c o n tin u o u s p o t e n t ia ls o f a t o m ic s trin g s a n d p la n e s ca n ta k e p la c e u n d e r p a s s a g e o f fa s t c h a r g e d p a r tic le s th r o u g h c ry s ta ls . T h e e n e r g y le v e ls fo r e le c tr o n m o v in g in a x ia l c h a n n e lin g r e g im e in a s IntroductionThe motion o f a fast charged particle in a crystal near one of crystallographic axes or planes is determined mainly by the contin uous potential that is the potential o f a crystal lattice averaged along the axis or plane, near which the motion takes place. The longitudinal component o f the particle's momentum parallel to the crystallographic axis or plane is conserved in such field. So, the problem on the particle's motion in a crystal is reduced to the two-dimensional problem o f its motion in the transverse plane. The finite motion in the potential wells formed by the continuous potentials o f atomic axes or planes is known as axial or planar channeling, respectively (see [1][2][3][4][5][6][7] and references therein).The electron motion under axial channeling described by classical equation o f motion can be both regular and chaotic. A pronounced example o f chaotic behavior is axial channeling in a continuous potential created by two neighboring atomic strings [110] o f diamond-like crystal [3,4].On the other side, the quantum effects can manifest themselves during channeling. Particularly, the quantization o f the transverse motion energy can take place (see, e.g. [3, Ch. 7, Sec. 53],[5, Sec. II C]). Investigation o f the chaotic behavior on quantum level needs statistical analysis o f large massive o f energy levels (thousands or more) [8]. Many numerical methods for searching the transverse motion energy levels as well as other quantum characteristics o f a particle motion in channeling regime had been developed in the pioneering papers on quantum approach to channeling phenome non (a good review o f them could be found in the book [6]). E -m ail address: syshch@yandex.ru (V.V. Syshchenko). 0168-583X/S -see fron t m atter

TunnelingT h e q u a n t iz a t io n o f t h e t r a n s v e r s e m o t io n e n e r g y in t h e c o n tin u o u s p o t e n t ia ls o f a t o m ic s trin g s a n d p la n e s ca n ta k e p la c e u n d e r p a s s a g e o f fa s t c h a r g e d p a r tic le s th r o u g h c ry s ta ls . T h e e n e r g y le v e ls fo r e le c tr o n m o v in g in a x ia l c h a n n e lin g r e g im e in a s IntroductionThe motion o f a fast charged particle in a crystal near one of crystallographic axes or planes is determined mainly by the contin uous potential that is the potential o f a crystal lattice averaged along the axis or plane, near which the motion takes place. The longitudinal component o f the particle's momentum parallel to the crystallographic axis or plane is conserved in such field. So, the problem on the particle's motion in a crystal is reduced to the two-dimensional problem o f its motion in the transverse plane. The finite motion in the potential wells formed by the continuous potentials o f atomic axes or planes is known as axial or planar channeling, respectively (see [1][2][3][4][5][6][7] and references therein).The electron motion under axial channeling described by classical equation o f motion can be both regular and chaotic. A pronounced example o f chaotic behavior is axial channeling in a continuous potential created by two neighboring atomic strings [110] o f diamond-like crystal [3,4].On the other side, the quantum effects can manifest themselves during channeling. Particularly, the quantization o f the transverse motion energy can take place (see, e.g. [3, Ch. 7, Sec. 53],[5, Sec. II C]). Investigation o f the chaotic behavior on quantum level needs statistical analysis o f large massive o f energy levels (thousands or more) [8]. Many numerical methods for searching the transverse motion energy levels as well as other quantum characteristics o f a particle motion in channeling regime had been developed in the pioneering papers on quantum approach to channeling phenome non (a good review o f them could be found in the book [6]). E -m ail address: syshch@yandex.ru (V.V. Syshchenko). 0168-583X/S -see fron t m atter

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