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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.

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We have investigated the transmission of the 5 keV proton beam through a graphene sheet containing monovacancy, adatom, and Stone–Wales defects. The proton–graphene interaction potential was constructed using the Doyle–Turner's proton–carbon interaction potential. The closed form of the scattering law was obtained using the momentum approximation. Angular distributions of the transmitted protons were analyzed using the morphological method based on the inspection of the rainbow patterns in the impact parameter and scattering angle planes generated by the rainbow scattering. We have demonstrated that rainbows in the impact parameter plane are attracted and repelled by the nearest saddles and maxima of the reduced proton–graphene interaction potential. This explains why the rainbow pattern is so sensitive to the redistribution of the potential extrema caused by defects. Each defect type produces its distinctive rainbow pattern that dominantly determines the shape of the angular distribution. The ridge maxima of the angular distributions were investigated and related to the spectrum of the Jacobian matrix of the map generated by the scattering law. In the end, it has been shown how observed rainbow patterns could be used to determine the unknown defect densities of the complicated sample containing a combination of the different defect types.

The goal of the study was to assess the relationship between rookie player's Pre-Draft Combine physical abilities and basketball performance in the first NBA season. In strictly homogenized sample of players (N = 58) who matched the inclusion criterion of average playing time and number games in the period 2012-2015, the results indicate that Pre-Draft Combine testing procedures show low to moderate correlations with only few observed basketball performance variables in the first NBA season. The highest correlation was found between upper body strength and number of rebounds (r = .403, p = .002) and blocked shots (r = .333, p = .011). Regression model of Combine performance explained 24.7% of basketball performance with three physical performance tests. Practical application might suggest that some parts of the Combine might be restructured in order to include some other tests more informative tests for the future player performance and player selection.