Relativistic polarizabilities with the Lagrange-mesh method

Filippin, Livio; Godefroid, Michel; Baye, Daniel Jean

doi:10.1103/physreva.90.052520

Cited by 17 publications

(34 citation statements)

References 41 publications

(97 reference statements)

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“…For relativistic multipolar polarizabilities, a simple calculation involving different meshes for the initial and final wave functions and for the calculation of matrix elements was devised in Ref. [23]. This calculation provides very accurate values for all charges Z, for the ground state and excited states of hydrogenic atoms with Coulomb or Yukawa potentials.…”

Section: Discussionmentioning

confidence: 99%

“…Some remarks on their numerical calculation can be found in Appendix B in Ref. [23]. The integral over ω 1 appearing in Eq.…”

Section: B Two-photon Decay Rates In Lagrange Meshesmentioning

confidence: 99%

“…The approximate wave functions provide mean values of powers of the coordinate that are also extremely precise. Reference [23] shows that accurate static dipole polarizabilities can be obtained for Yukawa potentials with the Lagrange-mesh method, for the ground state as well as for excited states. Potential (44) has the singular behavior…”

Section: B Yukawa Potentialmentioning

confidence: 99%

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Relativistic two-photon decay rates with the Lagrange-mesh method

2016

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Relativistic two-photon decay rates of the 2s 1/2 and 2p 1/2 states towards the 1s 1/2 ground state 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. Highly accurate values are obtained by a simple calculation involving different meshes for the initial, final, and intermediate wave functions and for the calculation of matrix elements. The accuracy of the results with a Coulomb potential is improved by several orders of magnitude in comparison with benchmark values from the literature. The general requirement of gauge invariance is also successfully tested, down to rounding errors. The method provides high accuracies for two-photon decay rates of a particle in other potentials and is applied to a hydrogen atom embedded in a Debye plasma simulated by a Yukawa potential.

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Section: Discussionmentioning

confidence: 99%

“…Some remarks on their numerical calculation can be found in Appendix B in Ref. [23]. The integral over ω 1 appearing in Eq.…”

Section: B Two-photon Decay Rates In Lagrange Meshesmentioning

confidence: 99%

Section: B Yukawa Potentialmentioning

confidence: 99%

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Relativistic two-photon decay rates with the Lagrange-mesh method

2016

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“…The prefactors are chosen in (39) such that the unit operator O = 1 is diagonal in the (α, α) representation with (1)…”

Section: Lagrange-mesh Methodsmentioning

confidence: 99%

“…This variational approach has been developed mainly to study non-relativistic problems and found many applications [33][34][35][36][37]. There are only few applications of the Lagrange-mesh method to relativistic systems, mainly for simple cases like hydrogenic atoms [38,39].…”

Section: Introductionmentioning

confidence: 99%

Lagrange-Mesh Method for Deformed Nuclei With Relativistic Energy Density Functionals

Typel

2018

Front. Phys.

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The application of relativistic energy density functionals to the description of nuclei leads to the problem of solving self-consistently a coupled set of equations of motion to determine the nucleon wave functions and meson fields. In this work, the Lagrange-mesh method in spherical coordinates is proposed for numerical calculations. The essential field equations are derived from the relativistic energy density functional and the basic principles of the Lagrange-mesh method are delineated for this particular application. The numerical accuracy is studied for the case of a deformed relativistic harmonic oscillator potential with axial symmetry. Then the method is applied to determine the point matter distributions and deformation parameters of self-conjugate even-even nuclei from 4 He to 40 Ca.

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Confinement of hydrogen atom with Dirac equation

Baye

2019

Int J of Quantum Chemistry

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The problem of a particle confined in a spherical cavity is studied with the Dirac equation. A hard confinement is obtained by forcing the large component to vanish at the cavity radius. It is shown that the small component cannot vanish simultaneously at this radius. In the case of a confined hydrogen atom, the energies are given by an implicit equation. For some values of the radius, explicit analytical expressions of the energy exist like in the nonrelativistic case. Very accurate energies and wave functions are obtained with the Lagrange‐mesh method with few mesh points. To this end, two differently regularized Lagrange‐Jacobi bases associated with the same mesh are used for the large and small components. The importance of relativistic effects is discussed for hydrogen‐like ions. The validity of this definition of hard confinement is discussed with a soft‐confinement model studied with the R‐matrix method.

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Relativistic polarizabilities with the Lagrange-mesh method

Cited by 17 publications

References 41 publications

Relativistic two-photon decay rates with the Lagrange-mesh method

Relativistic two-photon decay rates with the Lagrange-mesh method

Lagrange-Mesh Method for Deformed Nuclei With Relativistic Energy Density Functionals

Confinement of hydrogen atom with Dirac equation

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