Superfocusing of channeled protons and subatomic measurement resolution

Abstract

In this work we analyze the superfocusing of protons channeled in a LT 100 GT Si thin crystal using the theory of crystal rainbows. The initial proton energy is 68 MeV and the proton beam incident angle is increased gradually from zero up to 30% of the critical angle for proton channeling. The reduced crystal thickness is varied around 0.250, the corresponding crystal thickness being 481.8 nm. The spatial distributions of channeled protons, obtained by the numerical solution of the proton equations of motion in the transverse position plane and a Monte Carlo computer simulation code, are explored as functions of the beam incident angle and reduced crystal thickness. They are analyzed via the corresponding mappings of the impact parameter plane to the transverse position plane, which are characterized by the rainbow effect. The performed analysis shows that it is possible to focus the beam within the region of the radius considerably below the Bohr radius. The obtained results provide the theoretical basis for the possible development of a measurement technique with the picometer resolution-the rainbow subatomic microscopy.