Related papers: Refining spectroscopic calculations for trivalent …
In this letter, we derive an expression for magnetic dipole transitions that is analogous to the Lyddane-Sachs-Teller relation for dielectric polar lattice vibrations. We thereby define transverse and longitudinal optical frequencies at…
We show that similarity (or equivalent) transformations enable one to construct non-Hermitian operators with real spectrum. In this way we can also prove and generalize the results obtained by other authors by means of a gauge-like…
M\"ossbauer spectroscopy, which provides knowledge related to electronic states in materials, has been applied to various fields such as condensed matter physics and material sciences. In conventional spectral analyses based on least-square…
We show constructively that, under certain regularity assumptions, any system of coupled linear differential equations with variable coefficients can be tridiagonalized by a time-dependent Lanczos-like method. The proof we present formally…
The paper is devoted to the development of the octonion Fourier transform (OFT) theory initiated in 2011 in articles by Hahn and Snopek. It is also a continuation and generalization of earlier work by Blaszczyk and Snopek, where they proved…
In this paper we present an iterative method, inspired by the inverse iteration with shift technique of finite linear algebra, designed to find the eigenvalues and eigenfunctions of the Laplacian with homogeneous Dirichlet boundary…
The hyperfine structure of $^{229}$Th$^{3+}$ ions in the nuclear ground state is investigated via laser spectroscopy of trapped Th$^{3+}$ ions that are sympathetically cooled by laser-cooled $^{88}$Sr$^+$ ions in a linear Paul trap. The…
A complete effective Hamiltonian for relativistic corrections at orders $m\alpha^6$ and $m\alpha^6(m/M)$ in a one-electron molecular system is derived from the NRQED Lagrangian. It includes spin-independent corrections to the energy levels…
Translationnally invariant bidimensional magnetic Laplacians are considered. Using an improved version of the harmonic approximation, we establish the absence of point spectrum under various assumptions on the behavior of the magnetic…
We find transformation matrices allowing to express non-commutative three dimensional harmonic oscillator in terms of an isotropic commutative oscillator, following ``philosophy of simplicity'' approach. Non-commutative parameters have…
Quasi-forbidden electronic transitions in atoms and quasi-degenerate vibronic transitions in molecules serve as powerful probes of hypothetical temporal variations of fundamental constants. Computation of the sensitivity of a transition to…
The covariant Faddeev approach which describes baryons as relativistic three-quark bound states and is based on the Dyson-Schwinger and Bethe-Salpeter equations of QCD is briefly reviewed. All elements, including especially the baryons'…
We present a novel approach to electron-lattice interaction beyond the linear-coupling regime. Based on the solution of a Holstein-Peierls-type model, we derive explicit analytical expressions for the eigenvalue spectrum of the Hamiltonian,…
Energy levels, wavelengths, magnetic-dipole and electric-quadrupole transition rates between the low-lying states are evaluated for W$^{51+}$ to W$^{54+}$ ions with $3d^n$ (n = 2 to 5) electronic configurations using an approach combining…
The standard method for determining matrix elements in lattice QCD requires the computation of three-point correlation functions. This has the disadvantage of requiring two large time separations: one between the hadron source and operator…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
Numerous few-electron atomic systems are considered which can be used effectively for observing a potential variation of the fine-structure constant $\alpha$ and the electron-proton mass ratio $m_e/m_p$. We examine optical magnetic dipole…
We apply relativistic many-body methods to compute static differential polarizabilities for transitions inside the ground-state hyperfine manifolds of monovalent atoms and ions. Knowing this transition polarizability is required in a number…
We study the lattice dynamics of antiferromagnetic transition-metal oxides by using self-consistent Hubbard functionals. We calculate the ground states of the oxides with the on-site and intersite Hubbard interactions determined…
Numerical projection methods are elaborated for the calculation of eigenstates of the non-relativistic many-particle Coulomb Hamiltonian with selected rotational and parity quantum numbers employing shifted explicitly correlated Gaussian…