Slater sum for central field problems characterized by its s-wave component alone

For the hydrogenlike atom, with central potential -Z/r, partial differentia l equations exist for the Slater sum Z(r,beta) [beta = (k(B)T)(-1)] and for its s-wave (l = 0) component Z(0)(r,beta). It is shown that Z can be elimi nated, to lead to a result in which Z(r,beta) is solely characterized by Z( 0)(r,beta). A similar situation is exhibited for the three-dimensional isot ropic harmonic oscillator, for which closed forms of both Z(r,beta,omega) a nd Z(0)(r,beta,omega) can be obtained explicitly. Finally, a third central field problem is considered in which independent electrons are confined wit hin a sphere of radius R, but are otherwise free. We are able to derive exp licitly for this model the s-wave component Z(0)(r,beta,R). The full Slater sum Z(r,beta,R) then is also analyzed in some detail. (C) 1999 American In stitute of Physics. [S0022-2488(99)01706-5].