0030-400X/01/9006- $21.00 © 2001 MAIK “Nauka/Interperiodica” 0817 Optics and Spectroscopy, Vol. 90, No. 6, 2001, pp. 817–821. Translated from Optika i Spektroskopiya, Vol. 90, No. 6, 2001, pp. 909–913. Original Russian Text Copyright © 2001 by Rakhlina, Kozlov, Porsev. INTRODUCTION Atoms and ions with several valence electrons and an unfilled d shell are of great interest for atomic phys- ics as well as other fields of physics (astrophysics and reactor physics) [1–3]. In this paper, the energy of electron affinity is calcu- lated for a zirconium atom. To do this, energies of the ground states of a neutral atom and its negative ion should be calculated. The ground configuration of Zr and Zr – are 1s 2 …4p 6 4d 2 5s 2 and 1s 2 …4p 6 4d 3 5s 2 , respectively [2]. The method of superposition of configurations (SC) is one of the most popular methods for calculating com- plicated polyvalent atoms. This method, which was repeatedly used by our group for the calculation of energy levels and various observables in heavy atoms [4–6], is applicable to Zr atoms as well. All electrons are separated into two parts. [1s 2 …4p 6 ] electrons are related to the core, and 4d and 5s electrons are left in the valence domain. Because the number of valence electrons is large (four for a neutral atom and five for a negative ion), the dimensions of the configuration space turn out to be so great that diagonalization of the Hamilton matrix becomes impossible. For this reason, Schrödinger’s matrix equation is solved in a certain subspace with the calculation of the second-order cor- rection by the method of the determinant perturbation theory (PT). The first part of this paper is devoted to the general formalism of the method proposed (the SC method in combination with the determinant PT). In the second part of the work, results of the calculation of ground state energies for Zr and Zr – are discussed and g-factors are calculated for these states. GENERAL FORMALISM As mentioned above, the calculation of the energy of electron affinity for a Zr atom by the SC method requires the knowledge of the ground state energies of a neutral atom and its negative ion. As usual, this requires the solution of a many-particle Schrödinger’s equation (1) where E n is the energy of the nth level and Ψ n is the cor- responding wave function, which is sought in the form of a linear combination of Slater determinants (2) Here, N is the dimensionality of the configuration space and det i are determinants constructed from basis orbit- als. The latter were found in the following way. Har- tree–Fock–Dirac (HFD) equations were solved for the [1s 2 …4p 6 ]4d 2 5s 2 configuration of neutral zirconium and for the [1s 2 …4p 6 ]4d 3 5s 2 configuration of a negative zirconium ion. Further, in the calculation of Zr, the [1s 2 …4p 6 ] orbitals were frozen and the orbital 5p was obtained from the solution of the HFD equation for the 5s 2 5p 2 configuration. The remaining orbitals were constructed virtually. The method for constructing virtual orbitals is described in detail in [5]. As a result, the complete basis set includes the orbitals 1–15s, 2-15p, 3–15d, 4–15f, 5-15g, where the numbers indicate the principal quan- tum numbers. For Zr – , we have the following Hartree–Fock orbit- als: 4d and 5s for the 4d 3 5s 2 configuration and 5p for the 4d5s 2 5p configuration. The remaining orbitals are virtual. The complete basis set includes the orbitals 1-15s, 2–15p, 3–15d, 4–16f, and 5–16g. Now substitut- ing (2) into (1) and varying over the coefficients , we obtain H ˆ Ψ n E n Ψ n , = Ψ n C i n () det i . i 1 = N ∑ = C i n () H ik C k n () k ∑ E n C i n () = The Energy of Electron Affinity to a Zirconium Atom Yu. G. Rakhlina, M. G. Kozlov, and S. G. Porsev St. Petersburg Institute of Nuclear Physics, Gatchina, 188300 Russia e-mail: rakhlina@thd.pnpi.spb.ru Received August 31, 2000 Abstract—Energies and g-factors of the ground states of a zirconium atom and its negative ion and energy of electron affinity to a neutral atom are calculated. The method used represents a combination of the superposition of configurations and the determinant perturbation theory. A satisfactory agreement is obtained between the cal- culated energy of electron affinity and the experimental value. This shows that the theory can provide an ade- quate description of complicated multielectron systems. © 2001 MAIK “Nauka/Interperiodica”. ATOMIC SPECTROSCOPY