Computational investigation of static multipole polarizabilities and sum rules for ground-state hydrogenlike ions

Abstract

High-precision multipole polarizabilities, α for 4 of the 1s ground state of the hydrogen isoelectronic series, are obtained from the Dirac equation using the B-spline method with Notre Dame boundary conditions. Compact analytic expressions for the polarizabilities as a function of Z with a relative accuracy of 10 −6 up to Z = 100 are determined by fitting to the calculated polarizabilities. The oscillator strengths satisfy the sum rules i f ( ) gi = 0 for all multipoles from = 1 to = 4. The dispersion coefficients for the long-range H-H and H-He + interactions are given.

Static electric multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

“…Calculations have been done for two values of the inverse of the fine-structure constant: α −1 = 137.035 999 139 (from CODATA 2014) and α −1 = 137.035 999 074 (from CODATA 2010), in the latter case to enable making comparison with data available in Refs. [21,22]. Table I confirms almost perfect numerical accuracy of results obtained computationally by Tang et al [21] using the B-spline Galerkin method, and also high quality of numbers generated by Filippin et al [22] with the use of the Langrange-mesh method.…”

“…The calculations reported in Refs. [20][21][22] used the same value of the fine structure constant (taken from the CODATA 2010 recommendation). Numerical data for the four multipole polarizabilities presented by both groups, although obtained with different methods, appeared to be in a very good agreement.The multipole polarizabilities α L are closely related to the far-field electric multipole moments induced in an atom by external weak, static, electric multipole fields.…”

“…The latter study was pushed further in Ref. [21], where numerical data for α L with 1 L 4 were provided. Finally, very recently Filippin et al…”

Dynamic polarizabilities for the low-lying states of Ca+

“…The functions chosen are Bsplines with Notre-Dame boundary conditions [39]. The large and small components are expanded in terms of a B-spline basis of k order defined on the finite cavity [0, R max ], The finite cavity is set as a knots sequence, {t i }, satisfying an exponential distribution [40,41]. The specifics of the grid were that R max = 60 a 0 and 50 B-splines of order k = 7 were used to represent the single particle states.…”

Theoretical investigation of boundary contours of ground-state atoms in uniform electric fields

“…Local density approximation method is employed in the calculation of Y [56], Nb [56], Ru [56], Rh [56], Pd [56] and Te [56] atoms. H [57] atom is carried out with Dirac but with finite mass correction method. The result of Be [58] atom is produced by CI + MBPT method.…”