Relativistic polarizabilities with the Lagrange-mesh method

Abstract

Relativistic dipolar to hexadecapolar polarizabilities of the ground state and some excited states of hydrogenic atoms are calculated by using numerically exact energies and wave functions obtained from the Dirac equation with the Lagrange-mesh method. This approach is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. The partial polarizabilities conserving the absolute value of the quantum number $\kappa$ are also numerically exact with small numbers of mesh points. The ones where $|\kappa |$ changes are very accurate when using three different meshes for the initial and final wave functions and for the calculation of matrix elements. The polarizabilities of the $n=2$ excited states of hydrogenic atoms are also studied with a separate treatment of the final states that are degenerate at the nonrelativistic approximation. The method provides high accuracies for polarizabilities of a particle in a Yukawa potential and is applied to a hydrogen atom embedded in a Debye plasma.

arXiv comment3 figures, published in Physical Review A. arXiv admin note: text overlap with arXiv:1512.02815

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• High-precision calculations of In I and Sn II atomic properties
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• Accurate solution of the Dirac equation on Lagrange meshes
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Cited by in corpus (4)

• Relativistic calculations of quasi-one-electron atoms and ions using Laguerre and Slater spinors
• Relativistic two-photon decay rates with the Lagrange-mesh method
• Static electric multipole susceptibilities of the relativistic hydrogen-like atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
• Relativistic semiempirical-core-potential calculations in Ca${}^{+}$, Sr${}^{+}$, and Ba${}^{+}$ ions on Lagrange meshes