Superfocusing of channeled protons and subatomic measurement resolution

Abstract

In this work we analyze the superfocusing of protons channeled in a 100 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.

Quantum Entanglement and Spin Control in Silicon Nanocrystal

“…Further calculations take into account the proton beam divergence before its interaction with the crystal [24] , [25] .…”

“…Figure 1 ( a (1, 2), b (1, 2), c (1, 2)) gives 3-d representation of channeled protons contour plots for 92 nm Si nanocrystal, Λ = 0.5 [24] , [25] , for tilt angles: φ = 0.05 ψ c , φ = 0.15 ψ c and φ = 0.20 ψ c , is the angle of external field relative to symmetry axis of the spin transformation tensor. The external field of 1 MeV is chosen to match the limits of Bohr radius with initial CP peak separation at 20% of the critical angle (relative to tensor principal axis).…”

“…The channeled proton distributions are mapped in configuration space and angular space in two steps: to transverse position phase plane, and to scattering angle phase plane, [24], [25] in accordance with the chosen value of reduced crystal thickness, Λ and the tilt angle, φ .…”

“…Simulation model considers cubic unit cell representation of the isotopically pure 29 Si nanocrystal. It includes atomic strings on three nearest square coordination lines of the axial channel [24] , [25] . According to diamond lattice symmetry, the orthogonal mesh is projected across the channel, mapping two layers of 2×2 triangular areas of unit cell.…”

Quantum Rainbows in Positron Transmission through Carbon Nanotubes

“…Besides its theoretical significance, the rainbow effect has a number of practical uses. It was used to extract the correct proton-Si interaction potential [19], and there is also suggestion to be employed for production of the ion beams focused to the subatomic precision [20]. A new method for characterization of the short SWCNTs proposed in the Refs.…”