Mathematical questions about the computation of eigenvalues of Dirac operators with critical potentials in atomic and molecular physics

Esteban, Maria J.

doi:10.5802/crphys.16

Cited by 3 publications

(1 citation statement)

References 45 publications

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“…This allows us to select the Sobolev space W 1,2 (R + ) 2 [29,46] as the natural domain for the (unbound) Dirac operator (or similarly for a four-component wave function in the three-dimensional case W 1,2 (R 3 ) 2 ) lying dense in L 2 (R + ) 2 , such that dom(H D ) ⊆ W 1,2 (R 3 ) 2 ⊆ L 2 (R 3 ) 2 . The domain problem of the Dirac-Coulomb operator has been very recently discussed and critically analyzed by Estaban [564]. In the subcritical nuclear charge region ( √ 3/2 ≤ Zα ≤ 1), φ is an eigenfunction to a non-self-adjoint Dirac-Coulomb Hamiltonian with real eigenvalues and norm ||φ || 2 < ∞, but does not belong to dom(H D ) (H D self-adjoint)!…”

Section: Systemmentioning

confidence: 99%

Pushing the Limits of the Periodic Table -- A Review on Atomic Relativistic Electronic Structure Theory and Calculations for the Superheavy Elements

Smits,

Indelicato,

Nazarewicz

et al. 2023

Preprint

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We review the progress in atomic structure theory with a focus on superheavy elements and the aim to predict their ground state configuration and element's placement in the periodic table. To understand the electronic structure and correlations in the regime of large atomic numbers, it is important to correctly solve the Dirac equation in strong Coulomb fields, and also to take into account quantum electrodynamic effects. We specifically focus on the fundamental difficulties encountered when dealing with the many-particle Dirac equation. We further discuss the possibility for future many-electron atomic structure calculations going beyond the critical nuclear charge Z crit ≈ 170, where levels such as the 1s shell dive into the negative energy continuum (E nκ < −m e c 2 ). The nature of the resulting Gamow states within a rigged Hilbert space formalism is highlighted.* Here we define the starting point of the superheavy element region at the transactinides, Z ≥ 103

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Section: Systemmentioning

confidence: 99%

Pushing the Limits of the Periodic Table -- A Review on Atomic Relativistic Electronic Structure Theory and Calculations for the Superheavy Elements

Smits,

Indelicato,

Nazarewicz

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Pushing the limits of the periodic table — A review on atomic relativistic electronic structure theory and calculations for the superheavy elements

Smits,

Indelicato,

Nazarewicz

et al. 2023

Physics Reports

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Effective quantum electrodynamics: One-dimensional model of the relativistic hydrogen-like atom

Audinet

Toulouse

2023

The Journal of Chemical Physics

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We consider a one-dimensional effective quantum electrodynamics (QED) model of the relativistic hydrogen-like atom using delta-potential interactions. We discuss the general exact theory and the Hartree–Fock approximation. The present one-dimensional effective QED model shares the essential physical feature of the three-dimensional theory: the nuclear charge polarizes the vacuum state (creation of electron–positron pairs), which results in a QED Lamb-type shift of the bound-state energy. Yet, this 1D effective QED model eliminates some of the most serious technical difficulties of the three-dimensional theory coming from renormalization. We show how to calculate the vacuum-polarization density at zeroth order in the two-particle interaction and the QED Lamb-type shift of the bound-state energy at first order in the two-particle interaction. The present work may be considered a step toward the development of a quantum-chemistry effective QED theory of atoms and molecules.

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Mathematical questions about the computation of eigenvalues of Dirac operators with critical potentials in atomic and molecular physics

Cited by 3 publications

References 45 publications

Pushing the Limits of the Periodic Table -- A Review on Atomic Relativistic Electronic Structure Theory and Calculations for the Superheavy Elements

Pushing the Limits of the Periodic Table -- A Review on Atomic Relativistic Electronic Structure Theory and Calculations for the Superheavy Elements

Pushing the limits of the periodic table — A review on atomic relativistic electronic structure theory and calculations for the superheavy elements

Effective quantum electrodynamics: One-dimensional model of the relativistic hydrogen-like atom

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