Calculating the many-potential vacuum polarization density of the Dirac
equation in the finite-basis approximation
- URL: http://arxiv.org/abs/2304.09008v1
- Date: Tue, 18 Apr 2023 14:23:06 GMT
- Title: Calculating the many-potential vacuum polarization density of the Dirac
equation in the finite-basis approximation
- Authors: Maen Salman and Trond Saue
- Abstract summary: We propose an efficient and accurate computational method to evaluate the many-potential vacuum polarization density of hydrogen-like atoms.
To prove the performance of our computational method, we choose to work with the one-electron $_,,,92238textU$ atom.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this work, we propose an efficient and accurate computational method to
evaluate the many-potential $\alpha\left(Z\alpha\right)^{n\ge3}$ vacuum
polarization density of hydrogen-like atoms within the finite-basis
approximation of the Dirac equation. To prove the performance of our
computational method, we choose to work with the one-electron
$_{\,\,\,92}^{238}\text{U}$ atom. In summary, we find that compliance with
charge conjugation symmetry is a priori required to obtain physical results
that are in line with our knowledge of the analytical problem. We also note
that the final numerical results are found to be in excellent agreement with
previous formal analytical (and numerical) evaluations that are limited to a
few simple nuclear distribution models. Our technique can be efficiently
implemented and evaluated in codes that solve the radial Dirac equation in the
finite basis set framework and allows the use of arbitrary (radial) nuclear
charge distribution. The obtained numerical results of the non-perturbative
vacuum polarization density automatically account for the extended nuclear size
effect. This method is hence of special importance for atomic Dirac problems
whose analytical Green's functions expressions are not at hand or have
relatively complicated analytical forms. Furthermore, we propose a vacuum
polarization density formula that forces compliance with charge conjugation
symmetry and can be used in cases where the relativistic basis violates this
symmetry, as is the case in most relativistic basis set programs. In addition,
we have shown that vector components of the vacuum polarization four-current
vanish in the case where the Dirac Hamiltonian is symmetric under time-reversal
symmetry.
Related papers
- Vacuum polarization and Wichmann-Kroll correction in the finite basis set approximation [0.0]
We study the convergence of the finite basis set method with different types and sizes of basis sets.
We consider several heavy hydrogen-like ions and evaluate the vacuum polarization correction for $S$ and $P$ electron orbitals.
arXiv Detail & Related papers (2024-06-10T19:36:11Z) - Calculation of Relativistic Single-Particle States [0.0]
Method is an extension of a non-relativistic one, where the potential is represented in a Coulomb-Sturmian basis.
In the extension to relativistic problems, we cast the Klein-Gordon and Dirac equations into an effective Schr"odinger form.
arXiv Detail & Related papers (2023-12-05T05:07:09Z) - Sampling with Mollified Interaction Energy Descent [57.00583139477843]
We present a new optimization-based method for sampling called mollified interaction energy descent (MIED)
MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs)
We show experimentally that for unconstrained sampling problems our algorithm performs on par with existing particle-based algorithms like SVGD.
arXiv Detail & Related papers (2022-10-24T16:54:18Z) - Statistical Efficiency of Score Matching: The View from Isoperimetry [96.65637602827942]
We show a tight connection between statistical efficiency of score matching and the isoperimetric properties of the distribution being estimated.
We formalize these results both in the sample regime and in the finite regime.
arXiv Detail & Related papers (2022-10-03T06:09:01Z) - Hadronic vacuum polarization correction to atomic energy levels [0.0]
Shift of atomic energy levels due to hadronic vacuum polarization is evaluated in a semiempirical way for hydrogenlike ions and for muonic hydrogen.
A parametric hadronic polarization function obtained from experimental cross sections of $e-e+$ annihilation into hadrons is applied to derive an effective relativistic Uehling potential.
arXiv Detail & Related papers (2022-09-07T15:41:46Z) - Relativistic quantum theory and algorithms: a toolbox for modeling
many-fermion systems in different scenarios [0.0]
We discuss the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements.
We show the application of our relativistic quantum mechanical framework to the assessment of the elastic differential scattering cross section of electrons impinging on molecular targets.
arXiv Detail & Related papers (2021-10-02T10:20:50Z) - B-Spline basis Hartree-Fock method for arbitrary central potentials:
atoms, clusters and electron gas [0.0]
An implementation of the Hartree-Fock method capable of robust convergence for well-behaved arbitrary central potentials is presented.
For the Coulomb central potential, convergence patterns and energies are presented for a selection of atoms and negative ions.
For the harmonically confined electron-gas problem, comparisons are made with the Thomas-Fermi method and its accurate analytical solution.
arXiv Detail & Related papers (2021-08-12T16:57:21Z) - Optimal radial basis for density-based atomic representations [58.720142291102135]
We discuss how to build an adaptive, optimal numerical basis that is chosen to represent most efficiently the structural diversity of the dataset at hand.
For each training dataset, this optimal basis is unique, and can be computed at no additional cost with respect to the primitive basis.
We demonstrate that this construction yields representations that are accurate and computationally efficient.
arXiv Detail & Related papers (2021-05-18T17:57:08Z) - $\mathcal{P}$,$\mathcal{T}$-odd effects for RaOH molecule in the excited
vibrational state [77.34726150561087]
Triatomic molecule RaOH combines the advantages of laser-coolability and the spectrum with close opposite-parity doublets.
We obtain the rovibrational wave functions of RaOH in the ground electronic state and excited vibrational state using the close-coupled equations derived from the adiabatic Hamiltonian.
arXiv Detail & Related papers (2020-12-15T17:08:33Z) - Local optimization on pure Gaussian state manifolds [63.76263875368856]
We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm.
The method is based on notions of descent gradient attuned to the local geometry.
We use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.
arXiv Detail & Related papers (2020-09-24T18:00:36Z) - A multiconfigurational study of the negatively charged nitrogen-vacancy
center in diamond [55.58269472099399]
Deep defects in wide band gap semiconductors have emerged as leading qubit candidates for realizing quantum sensing and information applications.
Here we show that unlike single-particle treatments, the multiconfigurational quantum chemistry methods, traditionally reserved for atoms/molecules, accurately describe the many-body characteristics of the electronic states of these defect centers.
arXiv Detail & Related papers (2020-08-24T01:49:54Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.