About multiple scattering of high energy protons in crystal deflectors

Abstract

a b s t r a c tThe process of multiple scattering of high energy protons in a silicon crystal at its amorphous orientation was studied by simulation of proton trajectories in the model of binary collisions and by a straight simulation of the sequences of proton collisions with atoms when their impact parameters are randomly and uniformly distributed on the symmetry cell for a given crystallography direction. The value of the RMS deflection of multiple scattering obtained by the simulation is in a good agreement with the experiment and more than 15% larger than it follows from the Moliere theory. The obtained RMS deflection used in the Gaussian approach of multiple scattering well describes dechanneling of protons in the frame of the planar potential model. Different number of proton collisions with atoms occurs along the same crystal length for different crystal orientations. However, the change of the collision number is compensated by the corresponding change of the mean square deflection in a single collision. Therefore, multiple scattering is the same for different crystal orientations. The generator of multiple scattering for amorphous crystal orientations was proposed.

Improved separation of soft and hard components in multiple Coulomb scattering

“…Effectively, it slows down the transition from a Gaussian to Rutherford regime, so that over a substantial angular interval it may mimic a law intermediate between Gaussian and Rutherford decrease, such as a simple exponential law (cf. [13]), or a power law with an index greater than that for the lowest Born approximation, as is the case, e.g., for hard scattering of hadrons (which are themselves composite objects) [14].…”

“…That is strictly justified in limits of either large or small θ x /χ c : If θ x /χ c ≪ 1, that becomes possible because the upper integration limit tends to zero, leaving 27), (24) (solid red curve). Dashed curve, Rutherford asymptotics (13). Dot-dashed, Rutherford asymptotics with the first power correction, Eq.…”

“…The sum of thus computed hard and soft component is virtually indistinguishable from the solid curve. The dotted curve shows the Rutherford asymptotics (13).…”

“…It is known that, in principle, it does not converge (see, e.g., [12]), and yet, is comprised of oscillatory functions of deflection angles, which do not admit independent probabilistic interpretation. At the same time, there were recent phenomenological indications that beyond the central Gaussian region, the distribution function does not immediately switch to the asymptotic power law corresponding to single scattering, but exhibits some transient behavior over a sizable range of angles [13,14].…”