On theZminus;1andNminus;1/3expansions of Hartreendash;Fock atomic energies

摘要

Numerical Hartreendash;Fock (HF) calculations for all atoms and ions in the range2les;Nles;86andNles;Zles;N+20were performed and analyzed in terms of theZminus;1perturbation series. Using the theoretical values of the leading expansion coefficientegr;0(N),we obtainegr;1(N),egr;2(N),andegr;k(N),kges;3,by a least squares fitting of the HF results. It is found that the differenceEminus;(egr;0Z2+ egr;1Z+egr;2)is, in general, not governed byegr;3Zminus;1but by a higher order term involvingegr;k(N)above. The value ofkincrease fromk=3forN=2tok=8for60les;Nles;86.Next, we study theNhyphen;dependence of the expansion coefficientsegr;n(N),0les;nles;2,and of the total energiesE(Z,N)by means of anNminus;1/3power series expansion. It is noted that the extension of these functions over the set of nonintegral values ofNis not unique, and consequently theirNminus;1/3expansions are, in part, modelhyphen;dependent. We use our numerical data to extract the modelhyphen;independent part ofyequiv;E/Z7/3q1/3,qequiv;N/Z,which may be expressed in terms of the universal expansiony = F00(q)+ F10(q)Nminus;1/3+F20(q)Nminus;2/3+sdot;sdot;sdot;.The functionsF0n(q)are computed and displayed fornles;2.