Computer analysis of the axial-to-planar channeling transition: Linkage with continuum theory

A systematic computer analysis of the transition between channeling along the $〈110〉$ axis and along the most important planes intersecting it ({111}, {110}, and {100}) of 1-MeV protons in silicon is carried out. It is shown that, as the tilt angle varies, the transition between the two channeling regimes does not take place gradually, but occurs by passing through an angular region in which dechanneling is maximum. An analysis of the ion trajectories in a four-dimensional reduced phase space shows that in this transition region the occupied volume is maximum, which explains the experimental effects observed by different authors. The transition is also clearly displayed when the incidence angle is tilted from the axis within the most open plane, which shows that axial and planar channeling cannot simply be reduced one to the other. An interpretation in terms of Lindhard's continuum theory is worked out, giving results in satisfactory agreement with computer simulations.