  Shear particle acceleration is a promising candidate for the origin of
extended high-energy emission in extra-galactic jets. In this paper, we explore
the applicability of a shear model to 24 X-ray knots in the large-scale jets of
FR II radio galaxies, and study the jet properties by modeling the
multi-wavelength spectral energy distributions (SEDs) in a leptonic framework
including synchrotron and inverse Compton - CMB processes. In order to improve
spectral modelling, we analyze Fermi-LAT data for five sources and reanalyzed
archival data of Chandra on 15 knots, exploring the radio to X-ray connection.
We show that the X-ray SEDs of these knots can be satisfactorily modelled by
synchrotron radiation from a second, shear-accelerated electron population
reaching multi-TeV energies. The inferred flow speeds are compatible with
large-scale jets being mildly relativistic. We explore two different shear flow
profiles (i.e., linearly decreasing and power-law) and find that the required
spine speeds differ only slightly, supporting the notion that for higher flow
speeds the variations in particle spectral indices are less dependent on the
presumed velocity profile. The derived magnetic field strengths are in the
range of a few to ten microGauss, and the required power in non-thermal
particles typically well below the Eddington constraint. Finally, the inferred
parameters are used to constrain the potential of FR II jets as possible UHECR
accelerators.
