Relativistic semiempirical-core-potential calculations in Ca+,Sr+ , and Ba+ i

Abstract

Relativistic atomic structure calculations are carried out in alkaline-earth-metal ions using a semiempirical-core-potential approach. The systems are partitioned into frozen-core electrons and an active valence electron. The core orbitals are defined by a Dirac-Hartree-Fock calculation using the grasp2k package. The valence electron is described by a Dirac-like Hamiltonian involving a core-polarization potential to simulate the core-valence electron correlation. The associated equation is solved with the Lagrange-mesh method, which is an approximate variational approach having the form of a mesh calculation because of the use of a Gauss quadrature to calculate matrix elements. Properties involving the low-lying metastable 2 D 3/2,5/2 states of Ca + , Sr + , and Ba + are studied, such as polarizabilities, one-and two-photon decay rates, and lifetimes. Good agreement is found with other theory and observation, which is promising for further applications in alkali-like systems.

POLALMM: A program to compute polarizabilities for nominal one-electron systems using the Lagrange-mesh method

“…where φ v (r) is the usual 4-component relativistic Dirac spinor [3,10] and v represents the ensemble of quantum numbers associated with the valence state, i.e.,…”

“…accounts for the polarization of the core [3,16,17] and therefore depends on the core polarizability of multiplicity λ. The symbol ∑ ∫…”

“…We combine a semiempirical approach with the Lagrange-mesh method (LMM) as it was proposed in Ref. [3] for alkali-like ions. The computations of polarizabilities involve sum-over-all-state integrals, including bound states and both continua, which are described with difficulty by usual computational atomic methods.…”

“…[1] with its application to solve the Dirac equation and estimate energies [6], polarizabilities [7] and multiphoton transition amplitudes [8]. The theory of semiempirical-core-potential approaches is presented in detail in a paper by Filippin et al [3] and shall therefore only be summarized in Section 2.…”

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We present a program to compute polarizabilities of nominal one-electron systems using the Lagrangemesh method (LMM) (Baye, 2015), that was used by Filippin et al, (2018). A semiempirical-corepotential approach is implemented, ultimately solving a Dirac-like equation by diagonalizing the corresponding Hamiltonian matrix.

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