New analytical independent-particle model potential for atoms

Abstract

A new analytical, independent-particle model potential with four shell-independent parameters is proposed, which is suitable for high, medium, and low Z atoms. The four parameters are determined for 101 atoms from Li to Lr by fitting the results of the Xa method found in the literature. The average fitting error 0. 675% of the new potential for the 101 atoms is far better than 3. 92% of the widely used Green's potential. The radial Schrödinger equation with the new potential is solved by using Numerov's numerical method for 7 typical atoms: Ne, Ca, Zn, Zr, Sn, Yb, and Th. The energy eigenvalues, radial wave functions, and atomic ground-state energy are in good agreement with the results of the Xa method. The new potential here shows greater flexibility and better accuracy compared with the Green's potential. © 2009 Versita Warsaw and Springer-Verlag Berlin Heidelberg.