Burnett-function solution of the steady-state Fokker-Planck equation near an absorbing sphere

The steady-state, spherically symmetric Fokker-Planck equation of Brownian motion is solved in an infinite homogeneous medium surrounding a perfectly absorbing sphere. The solution is obtained by expanding the distribution function in terms of Burnett functions. It is shown that the final solution consists of an asymptotic mode found earlier, and a set of transient modes that decrease exponentially with the distance from the center. Our numerical results in the so-called $L_1{P}_1$ approximation [S. Waldenstrøm, K. J. Mork, and K. Razi Naqvi, Phys. Rev. A 28, 1659 (1983)] indicate that the transient modes have only a small influence in the determination of the coagulation coefficient.