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We study the steady-state distribution function of a run-and-tumble particleevolving around a repulsive hard spherical obstacle. We show that thewell-documented activity-induced attraction translates into a delta peakaccumulation at the surface of the obstacle accompanied with an algebraicdivergence of the density profile close to the obstacle. We obtain the fullform of the distribution function in the regime where the typical distance runby the particle between two consecutive tumbles is much larger than the size ofthe obstacle. This provides an expression for the low-density pair distributionfunction of a fluid of highly persistent hard-core run-and-tumble particles.This also provides an expression for the steady-state probability distributionof highly-ballistic active Brownian particles and active Ornstein-Ulhenbeckparticles around hard spherical obstacles.

A run-and-tumble particle around a spherical obstacle: steady-state distribution far-from-equilibrium