Relativistic Wave Functions Research Articles

New phenomena in laser-assisted leptonic decays of the negatively charged boson W −

The majority of studies and experiments performed at electron-positron colliders over the last two decades have focused on studying W and Z weak force-carrying bosons and accurately measuring all their properties, not only because they play an important role in establishing Standard Model theory and providing an accurate test of its predictions of particle interactions, but also because they are a unique tool for probing manifestations of the new physics beyond the standard model. Therefore, it would be particularly important to discuss some of the new phenomena and changes that can arise in these bosons when their decay occurs under an external electromagnetic field. In a recent paper, we investigated the laser effect on the final products of Z boson decay and found that laser had an unprecedented effect on branching ratios. In this work and within the standard Glashow-Weinberg-Salam model of electroweak interactions, we study theoretically the leptonic decay of the W −-boson in the presence of a circularly polarized electromagnetic field and we examine the laser effect, in terms of its field strength and frequency, on the leptonic decay rate and the phenomenon of multiphoton processes. The calculations are carried out using the exact relativistic wave functions of charged particles in an electromagnetic field. It was found that the laser significantly contributed to reducing the probability of W −-boson decay. We show that the laser-assisted decay rate is equal to the laser-free one only when the famous Kroll-Watson sum rule is fulfilled. The notable effect of the laser on the leptonic decay rate was reasonably interpreted by the well-known quantum Zeno effect or by the opening of channels other than leptonic ones to decay. This work will pave the way for an upcoming one to study the hadronic decay of the W −-boson and then explore the laser effect on its lifetime and branching ratios.

Harmonically confined N -electron systems coupled to light in a cavity

The energy and wave function of a harmonically confined $N$-electron system coupled to light is calculated by separating the wave functions of the relative and center-of-mass (CM) motions. The light only couples to the CM variable, and the coupled equation can be solved analytically. The relative motion wave function has to be numerically approximated, but the relative Hamiltonian is independent of the coupling strength and it only gives a shift in the energy. The approach works for any coupling strength and the effective coupling strength can be increased by increasing the number of electrons. This gives an extra degree of freedom to fine tune the resonances and other properties of the light-matter coupled systems. Examples of wave functions of light-matter hybrid states are presented.

The newly observed state D_{s0}(2590)^{+}

We choose the Reduction Formula, PCAC and Low Energy Theory to reduce the S matrix of a OZI allowed two-body strong decay involving a light pseudoscalar, the covariant transition amplitude formula with relativistic wave functions as input is derived. After confirm this method by the decay D^*(2010)rightarrow Dpi , we study the newly observed D_{s0}(2590)^{+} with supposing it to be the state D_s(2^1S_0)^+, we find its decay width Gamma is highly sensitive to the D_{s0}(2590)^{+} mass, which result in the meaningless comparison of widths by different models with various input masses. Instead of width, we studied the overlap integral over the wave functions of initial and final states, here we parameterized it as X which is model-independent, and the ratio Gamma /{|{mathbf {P}_f}|^3}, both are almost mass independent, to give us useful information. The results show that, all the existing theoretical predictions X_{D_s(2S) rightarrow D^*K}=0.25sim 0.41 and Gamma /{|{mathbf {P}_f}|^3}=0.81sim 1.77hbox {MeV}^{-2} are smaller than experimental data 0.585^{+0.015}_{-0.035} and 4.54^{+0.25}_{-0.52}hbox {MeV}^{-2}. Further compared with X^{ex}_{D^*(2010) rightarrow Dpi }=0.540pm 0.009, the current data X^{ex}_{D_s(2S) rightarrow D^*K}=0.585^{+0.015}_{-0.035} is too big to be an reasonable value, so it is early to say D_{s0}(2590)^{+} is the conventional D_s(2^1S_0)^+ meson.

X-ray absorption spectra of f-element complexes: insight from relativistic multiconfigurational wavefunction theory.

X-ray absorption near edge structure (XANES) spectroscopy, coupled with ab initio calculations, has emerged as the state-of-the-art tool for elucidating the metal-ligand bonding in f-element complexes. This highlight presents recent efforts in calculating XANES spectra of lanthanide and actinide compounds with relativistic multiconfiguration wavefunction approaches that account for differences in donation bonding in the ground state (GS) versus a core-excited state (ES), multiplet effects, and spin-orbit-coupling. With the GS and ES wavefunctions available, including spin-orbit effects, an arsenal of chemical bonding tools that are popular among chemists can be applied to rationalize the observed intensities in terms of covalent bonding.

Covalency in actinide(iv) hexachlorides in relation to the chlorine K-edge X-ray absorption structure.

Chlorine K-edge X-ray absorption near edge structure (XANES) in actinideIV hexachlorides, [AnCl6]2− (An = Th–Pu), is calculated with relativistic multiconfiguration wavefunction theory (WFT). Of particular focus is a 3-peak feature emerging from U toward Pu, and its assignment in terms of donation bonding to the An 5f vs. 6d shells. With or without spin–orbit coupling, the calculated and previously measured XANES spectra are in excellent agreement with respect to relative peak positions, relative peak intensities, and peak assignments. Metal–ligand bonding analyses from WFT and Kohn–Sham theory (KST) predict comparable An 5f and 6d covalency from U to Np and Pu. Although some frontier molecular orbitals in the KST calculations display increasing An 5f–Cl 3p mixing from Th to Pu, because of energetic stabilization of 5f relative to the Cl 3p combinations of the matching symmetry, increasing hybridization is neither seen in the WFT natural orbitals, nor is it reflected in the calculated bond orders. The appearance of the pre-edge peaks from U to Pu and their relative intensities are rationalized simply by the energetic separation of transitions to 6d t2gversus transitions to weakly-bonded and strongly stabilized a2u, t2u and t1u orbitals with 5f character. The study highlights potential pitfalls when interpreting XANES spectra based on ground state Kohn–Sham molecular orbitals.

Relativistic nonorthogonal configuration interaction: application to L2,3-edge X-ray spectroscopy.

In this article, we develop a relativistic exact-two-component nonorthogonal configuration interaction (X2C-NOCI) for computing L-edge X-ray spectra. This article to our knowledge is the first time NOCI has been used for relativistic wave functions. A set of molecular complexes, including SF6, SiCl4 and [FeCl6]3-, are used to demonstrate the accuracy and computational scaling of the X2C-NOCI method. Our results suggest that X2C-NOCI is able to satisfactorily capture the main features of the L2,3-edge X-ray absorption spectra. Excitations from the core require a large amount of orbital relaxation to yield reasonable energies and X2C-NOCI allows us to treat orbital optimization explicitly. However, the cost of computing the nonorthogonal coupling is higher than in conventional CI. Here, we propose an improved integral screening using overlap-scaled density combined with a continuous measure of the generalized Slater-Condon rules that allows us to estimate if an element is zero before attempting a two-electron integral contraction.

RELATIVISTIC CALCULATION OF THE RADIATIVE TRANSITION PROBABILITIES AND LIFETIMES OF EXCITED STATES FOR THE RUBIDIUM ATOM IN A BLACK-BODY RADIATION FIELD

We present the results of relativistic calculation of the radiative transition probabilities and excited states lifetimes for a heavy Rydberg atomic systems in a black-body (thermal) radiation field on example of the rubidium. As theoretical approach we apply the combined generalized relativistic energy approach and relativistic many-body perturbation theory with ab initio Dirac zeroth approximation. There are obtained the calculational data for the radiative transition probabilities and excited states lifetimes, in particular, the rubidium atom in the Rydberg states with principal quantum number n=10-100. It is carried out the comparison of obtained theoretical data on the effective lifetime for the group of Rydberg nS states of the rubidium atom at a temperature of T = 300K with experimental data as well as data of alternative theoretical calculation based on the improved quasiclassical model. It is shown that the accuracy of the theoretical data on the radiative transition probabilities and excited states lifetimes is provided by a correctness of the corresponding relativistic wave functions and accounting for the exchange-correlation effects.

Three-boson stability for boosted interactions towards the zero-range limit

We study the three-boson bound-state mass and wave functions for ground and excited states within the three-body relativistic framework with Kamada and Glöcke boosted potentials in the limit of a zero-range interaction. We adopt a nonrelativistic short-range separable potential, with Yamaguchi and Gaussian form factors, and drive them towards the zero-range limit by letting the form factors' momentum scales go to large values while keeping the two-body binding fixed. We show that the three-boson relativistic masses and wave functions are model-independent towards the zero-range limit, and the Thomas collapse is avoided, while the nonrelativistic limit kept the Efimov effect. Furthermore, the stability in the zero-range limit is a result of the reduction of boosted potential with the increase of the virtual pair center of mass momentum within the three-boson system. Finally, we compare the present results with Light-Front and Euclidean calculations.

Two electrons in harmonic confinement coupled to light in a cavity

The energy and wave function of a harmonically confined two-electron system coupled to light is calculated by separating the wave functions of the relative and center of mass (CM) motions. The relative motion wave function has a known quasi-analytical solution. The light only couples to the CM variable and the coupled equation can be solved with diagonalization without approximations. The approach works for any coupling strength. Examples of wave functions of light-matter hybrid states are presented.

Lewis Acid Behavior of MoF5 and MoOF4: Syntheses and Characterization of MoF5(NCCH3), MoF5(NC5H5)n, and MoOF4(NC5H5)n (n = 1, 2).

The Lewis acid-base adducts MoF5(NC5H5)n and MoOF4(NC5H5)n (n = 1, 2) were synthesized from the reactions of MoF5 and MoOF4 with C5H5N and structurally characterized by X-ray crystallography. Whereas the crystal structures of MoF5(NC5H5)2 and MoOF4(NC5H5)2 are isomorphous containing pentagonal-bipyramidal molecules, the fluorido-bridged, heptacoordinate [MoF5(NC5H5)]2 dimer differs starkly from monomeric, hexacoordinate MoOF4(NC5H5). For the weaker Lewis base CH3CN, only the 1:1 adduct, MoF5(NCCH3), could be isolated. All adducts were characterized by Raman spectroscopy in conjunction with vibrational frequency calculations. Multinuclear NMR spectroscopy revealed an unprecedented isomerism of MoOF4(NC5H5)2 in solution, with the pyridyl ligands occupying adjacent or nonadjacent positions in the equatorial plane of the pentagonal bipyramid. Paramagnetic MoF5(NC5H5)2 was characterized by electron paramagnetic resonance (EPR) spectroscopy as a dispersion in solid adamantane as well as in a diamagnetic host lattice of MoOF4(NC5H5)2; EPR parameters were computed using ZORA with the BPW91 functional using relativistic all-electron wave functions for Mo and simulated using EasySpin. Density functional theory calculations (B3LYP) and natural bond orbital analyses were conducted to elucidate the distinctive bonding and structural properties of all adducts reported herein and explore fundamental differences observed in the Lewis acid behavior of MoF5 and MoOF4.

Accurate calculations for the Dirac electron in the field of two-center Coulomb field: Application to heavy ions

The relativistic Dirac equation for a bound electron in the field of two fixed positive charges is revisited. In contrast to the one center case this three dimensional equation is separable only partially around the azimuthal angle φ, because of the commutation of the Dirac Hamiltonian only with the z component of the total angular momentum Jz. In this work we determine the variational exact solution of this two center problem using a basis constructed by linear combinations of relativistic Slater type spinor wave functions with non integer powers of the radii r1 and r2 on the two centers. We present in some detail the determination of the two center integrations involved. The solutions are obtained by a minimax procedure, that we have developed with a new iterative scheme. We use independent large and small components of the Dirac spinor. This permits us to take control of the spurious solutions, and gives us the possibility to avoid them by the appropriate choice of the wave function parameters. We investigate the behavior of the electron in its 1sσg level of the diatomic homo-nuclear systems A2(2Z-1)+, where A represents the heavy element and Z its atomic number. In the case of heavy ions we study the dependance of the electron energy on the internuclear distance, this gives us an indication for the conditions of atomic collapse, which can induce electron-positron pair production. Our approach has the advantage of needing small basis sets for a relative error of the of 10-7-10-8. It can also be extended easily to the excited level such as the 1sσu level.

Development of the kinetically and atomically balanced generalized pseudospectral method

The kinetically and atomically balanced conditions have been extensively used in various basis-set expansion methods to remove the nonphysical spurious states appearing in the numerical calculation of the Dirac equation; however, they are generally not applicable for methods in discrete variable representation. In this paper we show that these conditions can be conveniently introduced into the generalized pseudospectral (GPS) method. Four types of balanced condition, the mono kinetic balance (MKB), dual kinetic balance, mono atomic balance (MAB), and dual atomic balance, are incorporated into the GPS method to eliminate the spurious states. Numerical calculations for a variety of bound states of H-like ions in point-charge models are compared with the analytical solutions to demonstrate the accuracy and efficiency of the developed methods. The application to highly charged ions with extended nuclear models is performed to show the flexibility of the balanced GPS methods in practical atomic structure calculations. It is concluded that the MAB-GPS and MKB-GPS methods, which are both free of any spurious states, show better performance and simpler implementation than the others in solving the Dirac equation with the potential in point-charge and extended nuclear models, respectively. The balanced GPS methods developed in this paper provide a useful tool for accurately solving the one-electron Dirac equation and efficiently constructing the multielectron relativistic wave functions.

Mass spectra and wave functions of TQQQ¯Q¯ tetraquarks

The compact tetraquark states with fully heavy quark contents $QQ\overline{Q}\overline{Q}$ are studied as the bound states of the diquark-antidiquark within the Bethe-Salpeter framework. The (anti)diquark masses and form factors used are the same as we calculated the doubly heavy baryons in a previous work. Under the instantaneous approximation, the three-dimensional (Bethe-)Salpeter equation of the tetraquarks is derived and solved numerically to obtain the corresponding mass spectra and wave functions of the tetraquarks with ${J}^{PC}={0}^{++}$, ${1}^{+\ensuremath{-}}$, and ${2}^{++}$. Our results show that the three ground states of $cc\overline{c}\overline{c}$ locate in the mass range of 6.4--6.5 GeV, and the $bb\overline{b}\overline{b}$ states in mass range of 19.2--19.3 GeV. The obtained relativistic wave functions naturally include the mixing effects from the possible $D$ (or $G$) partial waves, and then can be further used to do precise calculations of the tetraquark decays. Based on the obtained results, the LHCb's observation $X(6900)$ is less likely to be the ground states of compact $cc\overline{c}\overline{c}$ tetraquarks but might be the first or second excited states. In addition, a widely used propagatorlike form factor is also investigated and discussed.

Calculation of optical properties with spin-orbit coupling for warm dense matter

Optical properties of warm dense matter are computed within linear response theory using the Kubo-Greenwood formula in the framework of Density Functional Theory and the Projector Augmented–Wave (PAW) method. For transition metals, the effect of spin-orbit coupling (SOC) has to be taken into account. We present the theoretical framework to introduce SOC in the PAW formalism and then to compute optical properties including SOC using the Kubo-Greenwood formula. This formulation has been implemented in the abinit software. Moreover, for high energy absorption spectra, we use Dirac relativistic core wave functions from the atompaw code to obtain the correct SOC energy splitting. This implementation enables a description of optical properties for warm dense metals including SOC for both core and valence orbitals. Example calculations are presented for warm dense gold and copper.

Probing Multiconfigurational States by Spectroscopy: The Cerium XAS L3 -edge Puzzle.

The Ce L3 edge XAS spectra of CeO2 and cerocene [Ce(C8 H8 )2 ] were calculated with relativistic ab-initio multireference wavefunction approaches capable of reproducing the observed spectra accurately. The study aims to resolve the decades-long puzzle regarding the relationship between the number and relative intensities of the XAS peaks and the 4f electron occupation in the ground state (GS) versus the core-excited states (ESs). CeO2 and cerocene exemplify the different roles of covalent bonding and wavefunction configurational composition in the observed intensity patterns. Good agreement is found between the calculated GS 4f-shell occupations and the value derived from XAS measurements using peak areas (nf ). The identity of the two-peaked Ce L3 edge is fully rationalized from the perspective of the relaxed wavefunctions for the GS and core ESs. The states underlying the different peaks differ from each other in a surprisingly simple way that can be associated with 4f1 vs. 4f0 sub-configurations. Furthermore, part of one of the cerocene spectral peaks is associated with 4f2 sub-configurations. The pattern therefore reveals excited states that can be interpreted in terms of Ce IV and III oxidation numbers, as long assumed, with Ce II states additionally appearing in the cerocene spectrum. While this work demonstrates the rough accuracy of the conventional approach to determining nf from Ce L3 -edge XAS, limitations are highlighted in terms of the ultimate accuracy of this approach and the potential of observing new types of excited states. The need to determine the sources of nf by calculations, is stressed.

Atomic form factors and inverse Primakoff scattering of axion

We reexamine the inverse Primakoff scattering of axions, whose scattering cross section depends on the distribution of electrons in target atoms. We evaluate it using a form factor computed with a relativistic Hartree-Fock wave function and compare it with the previous results obtained with those based on the screened Coulomb potential for the electrostatic field in the atom. We take xenon as an example for the target atom and show that the scattering cross section was overestimated by more than an order of magnitude for axions with ≲O(10) keV energies, like solar axions. It is also found that inelastic scattering processes, in which the final state contains an excited or ionized atom, can be comparable or even be dominant when the size of momentum transfer is ≲1 keV. For more energetic axions, on the other hand, the total scattering cross section is found to be well approximated by a simple expression and has little dependence on the atomic structure. As an application of this result, we consider supernova axions, whose energy is 10–100 MeV, and show that O(1) inverse Primakoff events are expected for axions from a nearby supernova in the future neutrino experiments, which may warrant a more detailed study on the search strategy of this process.

Noether symmetries and quantum cosmology in extended teleparallel gravity

We apply the Noether Symmetry Approach to point-like teleparallel Lagrangians in view to derive minisuperspaces suitable for Quantum Cosmology. Adopting the Arnowitt–Deser–Misner formalism, we find out related Wave Functions of the Universe. Specifically, by means of appropriate changes of variables suggested by the existence of Noether symmetries, it is possible to obtain the cosmological Hamiltonians whose solutions are classical trajectories interpretable as observable universes.

Simple relativistic quark models

A class of phenomenological relativistic models of hadronic systems motivated by QCD that have dual representations as models of mesons and nucleons or quarks and gluons is investigated. These models are designed to provided qualitative insight into the role of sea quarks in hadronic structure and reactions. The model assumption is that the Hamiltonian can be divided into two parts; one that involves degrees of freedom in the same connected local and global color singlet and the remaining interactions that allow the connected local and global color singlets to interact. The first class of interactions results in infinite towers of bare "particles" with hadronic quantum numbers. All but a finite number of these remain stable when the second class of interactions is included. The model interactions are expressed in terms of sub-hadronic degrees of freedom, which determine the bare hadronic spectrum and the interactions involving the bare hadrons in terms of a small number of sub-hadronic model parameters. As a first test, this paper considers the simplest case of mesons that interact via a string-breaking interaction. One virtue of this model is that all of the bare meson masses and eigenfunctions can be computed analytically. In addition, the string breaking interaction leads to production vertices that can also be computed analytically. The relativistic wave functions have a light-front kinematic symmetry. The goal is to find a simple relativistic quantum mechanical model based on sub-hadronic degrees of freedom that can provide an efficient, qualitatively consistent description of hadronic masses, lifetimes, cross sections, sea quark effects, and electromagnetic properties. The simplicity of the model makes it a potentially useful tool to study the impact of sea quarks on hadronic structure and reactions.

Theoretical Calculations of Electron Excitation of the Lowest Autoionization States of the Rb Atom

Purpose. The value of the autoionization cross section and its energy dependence are determined to a great extent by excitation and subsequent electron decay of the lowest energy states. Recently, experimental data on the excitation cross sections of the rubidium atom lowest doublet (4p55s2)2P3/2,1/2 and quartet (4p54d5s)4P1/2,3/2,5/2 autoionizing states were obtained which promoted their theoretical investigations. Methods. Theoretical calculations were performed using the Flexible Atomic Code universal program package which takes account of the relativistic nature of the complex atoms excitation by the use of the Dirac-Coulomb Hamiltonian. The radial orbitals for basic relativistic wavefunctions were obtained by solving the Dirac-Fock-Slater equation. Results. Comparison of the experimental excitation cross sections for the doublet (4p55s2)2P3/2,1/2 and quartet (4p54d5s)4P1/2,3/2,5/2 autoionizing states with available theoretical data and our relativistic calculations is presented. The results of the study of the parameter R0 for the intensity ratio for the 2P3/2 and 2P1/2 states of the 4p55s2 configuration are presented. Our calculations in the distorted waves approximation is shown to well describe the experimental data in the energy region above 70 eV. At low collision energies our calculations qualitatively predict the presence of the threshold resonant excitation; however in the energy region 20-50 eV only the R-matrix method qualitatively describes the complex nature of excitation and decay of the lowest quartet autoionizing states of the rubidium atom. Conclusions. Electron excitation of the doublet (4p55s2)2P3/2,1/2 and quartet (4p54d5s)4P1/2,3/2,5/2 autoionizing states of the rubidium atom in the collision energy range from the excitation thresholds up to 700 eV was studied in the terms of the distorted waves relativistic approximation. A comprehensive analysis of the obtained results using the available experimental and theoretical data showed that the relativistic distorted waves approximation taking into account the configurational mixing is a suitable tool for describing the autoionizing states of the rubidium atom in a wide range of collision energies and allowed one to obtain the absolute values of the experimental excitation cross sections of the (4p55s2)2P3/2,1/2 and (4p54d5s)4P1/2,3/2,5/2 states.

Role of external fields on the nonlinear optical properties of a n-type asymmetric $$\delta$$-doped double quantum well

The effects of in-growth applied electric fields and in-plane (x-oriented) magnetic fields on the nonlinear optical rectification (NOR), second harmonic generation (SHG) and third harmonic generation (THG) of n-type asymmetric double $$\delta$$ -doped GaAs quantum well are theoretically investigated. One-dimensional Schrodinger equation is solved by considering effective mass and parabolic band approximations to obtain subband energy levels and their related wave functions. The variations in the NOR, SHG and THG coefficients are determined by using the iterative solutions of the compact density matrix approach. Obtained results indicate that the applied electric field leads to optical red-shift on NOR, SHG and THG coefficients while the magnetic field causes optical blue-shift on that coefficients. Hence we can conclude that applied electromagnetic fields can be used to tune optical properties of devices working within the region of infrared electromagnetic spectrum.