Channeling in Nanotubes and Fullerites

Carbon nanotubes and fullerites in high-energy and X-ray physics

“…In absence of the experimental values of u 2 r and u 2 it may be reasonable to assume that they are close to the corresponding values u ⊥ = 8.5 × 10 −3 nm and u = 3.8 × 10 −3 nm in graphite (at room temperature) [26]. As numerical calculations showed [17], the influence of thermal vibrations on the continuum potential happens to be relatively small. An other effect of thermal vibrations is the fluctuations of the actual potential around the continuum potential which cause incoherent scattering of channeled particles.…”

“…Here { a j }={0.35, 0.55, 0.1} and { b j }={0.3, 1.2, 6.0} are three pairs of universal empirical constants, a TF = 0.529 Z −1/3Å is the Thomas-Fermi atomic radius, Ze is the non-rationalized nuclear charge and r a is the distance from the nucleus. Calculations of the expansion coefficients (2.8) using (2.10) give us the following result [17]:…”

“…The concentric nanotubes of a MWNT are necessarily arranged in an incommensurate manner as they have different diameters and different helicities. It is easy to show [17] that the spatial symmetry of a SWNT along its axis is determined by the following translational vector:…”

“…Here r is the distance from the axis of the nanotube and is the azimuthal angle around this axis which is counted from one of the atomic rows. Using the above expansion we may represent the continuum potential of a nanotube with arbitrary indices (n, m) as [17] U(r, ) = 2N V 0 (r) + 2 (Note that the azimuthal period is no more 2 but 2 /N.) Thus, the task is reduced to the standard calculation of the continuum potential of a row, however the latter must be presented as a function of the distance r from the nanotube axis.…”

“…In absence of experimental values for u ⊥ , we may use the graphite value u ⊥ = 8.5 × 10 −3 nm at room temperature [26] as a rough estimate of atomic vibrations in a fullerite. The calculated continuum potential of a fullerite at room temperature for positron channeling along the [100] direction is presented in Fig. 6.…”