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High-energy particle transport in pulsar wind nebulae (PWNe) plays anessential role in explaining the characteristics revealed in multiwavelengthobservations. In this paper, the TeV-gamma-ray-emitting electrons in the Vela XPWN are approximated to be injected impulsively when the cocoon is formed dueto the interaction between the SNR reverse shock and the PWN. By solving thediffusion-loss equation analytically, we reproduce the broadband spectralenergy distribution and surface brightness profile simultaneously. Thediffusion coefficient of TeV electrons and positrons, which is well constrainedby the spectral and spatial properties of the TeV nebula, is thus determined tobe $1 \times 10^{26}$\,cm$^{2}$\,s$^{-1}$ for 10\,TeV electrons and positrons.This coefficient is more than three orders of magnitude lower than that in theinterstellar medium, in agreement with a constraint recently obtained from HAWCobservations of a TeV nebula associated with the Geminga pulsar. These resultssuggest that slow diffusion of high-energy particles might be common in PWNe.

On the Gamma-Ray Nebula of Vela Pulsar. I. Very Slow Diffusion of Energetic Electrons within the TeV Nebula