Static multipole polarizabilities of S atoms or ions using the Frozen-Core approximation

2014 Static multipole polarizabilities of S atoms or ions have been calculated by two equivalent variational methods. Our results are in harmony with an earlier work which used the uncoupled Hartree-Fock approximation. LE JOURNAL DE PHYSIQUE TOME 40, FÉVRIER 1979, Classification Physics Abstracts 31.10 Recently we reported [1] a variational treatment for static multipole polarizabilities of atomic systems ; this treatment was the generalization of Rivail and Rinaldi’s method [2] of a one-parameter variational calculation to an arbitrary number of variational parameters until convergent values for static multipole polarizabilities, a2L(o), were achieved. Subsequently it was applied to obtain OE2L(o) for the hydrogen-atom and helium sequences. It was noted that the values of a2L(o) obtained from this method [1, 2] were identical with those obtained from the hydrodynamic model to quantum mechanics [3]. We have already reported our calculation of a2L(o) for atomic Li [4] and its sequences [5] from the hydrodynamic analogy to quantum mechanics using the frozen-core approximation whereby the effective Hamiltonian of Lisequences becomes identical with a hydrogen-like atom with a different nuclear charge and outermost orbital. In the frozen-core approximation Be, Mg and Ca atoms become identical with the He atom with a different nuclear charge and outermost orbital. This enables us to work out OE2L(o) for such systems and their sequences with our model for He atom as reported earlier [1]. Also, oC2L(o) for K atom has been performed in the frozen-core approximation. By using either of our methods [1, 3], OE2L(o) is given by the following expression : where and we have chosen 5 variational constants [1, 3]. Note that expression (1) is applicable to the Ca atom, Mgand Be-sequences with Y’o(R ) being the radial part of 4 S2, 3 S2 and 2 S2 Clementi wave function [6] respectively. On the other hand, for the K atom, Liand Na-sequences ’P o(R) is taken to be the radial part of the 4 SI, 2 S1 and 3 S1 Clementi wave function [6] respectively and formula (2) is applicable to such systems. Moreover, the equations governing the variational constants C are with matrix elements The present calculations for a2L(o) of S atoms or ions are listed in table I. Langhoff and Hurst [7] replaced the unperturbed Hamiltonian for S atoms or ions by the Hartree-Fock Hamiltonian. Then the time dependent variational perturbation scheme developed by Karplus and Kolker [8] was utilized to work out the static multipole polarizability of the atomic system under consideration. They also considered contributions of all closed sub-shells. On the other hand our Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01979004002013700