NORMAL APPROACH TO THE LINEARIZED FOKKER-PLANCK EQUATION FOR THE INVERSE-SQUARE FORCE

It is found that the customary approach to Fokker-Planck coefficients for the inverse-square force has three defects. First, a small scatter ing angle cannot guarantee a small Taylor expansion argument. Second, a cutoff on the scattering angle did not fulfill Debye cutoff theory b ecause it cannot exclude distant (weak) collisions with small relative velocity nor include close (effective) collisions with large relative velocity. Third, a singularity attributed to zero relative velocity h ad been overlooked. These defects had been vaguely covered up by the a rtificial treatment of replacing a variable relative velocity in a Cou lomb logarithm by the constant thermal velocity. Therefore, the custom ary approach is questionable because one cannot regard the replacement as some kind of ''average'' or ''approximation.'' In this paper, the difference between small-angle scattering and small-momentum-transfer collisions of the inverse-square force has been clarified. The probabi lity function P(v,Delta v) for Maxwellian scatters is derived by choos ing velocity transfer Delta v, which is the true measure of collision strength, as an independent variable. With the help of the probability function, Fokker-Planck coefficients can be obtained by the normal or iginal Fokker-Planck approach. The previous unproved treatment of the replacement of the relative velocity is naturally avoided, and the com pleted linearized Fokker-Planck coefficients are generated as a unifor m expression.