Relativistic Wave Functions Research Articles

The generalized K-G oscillator in the cosmic string space-time

In this contribution, the generalized K-G oscillator is introduced in the cosmic string space-time. The radial equations and angular equations have been obtained and solved for two different kinds of non-central potential functions separately and the corresponding relativistic energy and wave function have been found.

Study of relativistic excitation energies and transition data for EUV and SXR spectral lines in Ge XXIX and Kr XXXIII of fusion interest

Based on relativistic wavefunctions from multi-configurational Dirac–Fock method, a comprehensive theoretical study of atomic characteristics of energy levels, wavelengths, lifetimes, electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole radiative rates is performed for the lowest 98 levels of the 2s2, 2p2, 2s3s, 2s3d, 2p3p, 2s4s, 2s4d, 2p4p, 2p4f, 2s2p, 2s3p, 2p3s, 2p3d, 2s4p, 2s4f, 2p4s, and 2p4d configurations of Ge XXIX and Kr XXXIII. The correlations within the n=9 complex, n being the principal quantum number of the outermost electron are accounted for in a systematic way and the Breit interactions and quantum electrodynamics effects are estimated. Similar data are also determined using the many-body perturbation theory. The accuracy of our results is determined through extensive comparisons with the available data from the Atomic Spectra Database of the National Institute of Standards and Technology and with published theoretical values. Our computed wavelengths are almost of spectroscopic accuracy, aiding line identification in extreme ultraviolet (EUV) and soft X-ray (SXR) spectra. The present complete set of data are very useful for modeling and diagnosing fusion plasmas.

Single- and double-resonant enhancement of second-harmonic generation in asymmetric AlGaN/GaN/AlGaN quantum well heterostructures

The second-harmonic generation susceptibility is theoretically investigated based on the compact density-matrix formalism in two- and three-level AlGaN/GaN systems. The electronic states and their related wave functions were calculated by solving self-consistently the Schrödinger–Poisson equations within the effective mass and Hartree approximations. The presence of spontaneous and piezoelectric polarizations is taken into account in the modeling part. It was revealed from the relevant results that (i) the second-order susceptibility shows a multiple peak structure due to intersubband and their corresponding virtual transitions, (ii) the use of a back doping as well as the optimization of the layer widths in delta-doped AlGaN/GaN asymmetric quantum wells improved considerably the second-harmonic susceptibility, and (iii) the three-level AlGaN/GaN system is the most efficient structure, which generates the second-harmonic with a significant intensity up to 4.36 × 10−5 mV−1. Numerical results of the present work could lay the basis for research in AlGaN-related optoelectronic device applications.

Fluorescence yields for doubly excited 2s3s configuration in He-like ions

The wavelengths and rates of single- and double-electron transitions leading to the emission of a single photon between 2s3s and nsn′p (n = 1, 2 and n′ = 2–4) groups in He-like ions with empty K shell have been studied for 15 ions in the range 13 ≤ Z ≤ 54 using fully relativistic multi-configuration Dirac–Fock wavefunctions in the active space approximation. The complete relaxation of atomic orbitals and most important configuration interaction effects have been taken into account. The variations in the admixture of the correlation functions coupled with Breit interaction responsible for the sudden changes in the line intensities of certain transitions from 2s3s have been discussed in detail. The radiative rates of the electric dipole transitions have been evaluated as accurately as possible by taking into account all the non-negligible contributions to the X-ray rates. The Auger rates have been calculated using a scaling procedure on the already existing relativistic radial matrix elements for an initial K hole atom. The present results are compared with other available theoretical data. The computed data can be conveniently used in the analysis of experimental spectra and in the measurements of X-ray fluorescence yields for the doubly excited states under study.

Analytical solution of the proca equation for the modified posch teller potential

We study the solution of the Proca equation for the modified Posch Teller potential. Proca equation is a relativistic wave equation for a massive spin-1 particle. Proca equation also describes the imaginary mass of photons. Vector fields are used to describe spin-1 mesons. The hypergeometric method was used to solve the Proca equation to obtain the relativistic energy and wave function of the particle. This work is limited to radial part of the spherical coordinate system. Using the improved approximation scheme to deal with the centrifugal term, we solve approximately the Proca equation for the modified Posch Teller potential. The relativistic energy eigenvalue and radial wave function equations are obtained.

L-Shell Ionization during the Alpha Decay of Superheavy Nuclei from 117 294 Ts Tennessine Decay Chain and the Alpha Decay of the Polonium Isotope 84 210 Po

The probabilities for L-shell ionization following the alpha decay of 117 294 Ts, 113 286 Nh, 109 278 Mt, and 105 270 Db superheavy nuclei from the decay chain of tennessine, which was synthesized at the Joint Institute for Nuclear Research (JINR Dubna), and the alpha decay of the isotope 84 210 Po are calculated and analyzed. The respective calculations rely on a quantum-mechanical model that takes into account alpha-particle tunneling through the Coulomb barrier of an atom. The relativistic electron wave functions obtained by the Dirac-Fock method were employed. The probabilities for L-shell ionization that were calculated here for the isotope 84 210 Po are in better agreement with experimental data than the results of earlier calculations. In contrast to what we have for K-shell ionization, where monopole transitions make a dominant contribution to the ionization probability, a significant contribution to the probability for L-shell ionization also comes from dipole and quadrupole transitions. The results of the present study will be of use in interpreting superheavy-element spectra obtained by methods of combined alpha, gamma, and electron-conversion spectroscopy.

Bound-state double- β decay

We consider new modes of two-neutrino and neutrinoless double-$\beta$ decays in which one $\beta$ electron goes over to a continuous spectrum and the other occupies a vacant bound level of the daughter ion. We calculate the corresponding phase-space factors of the final states, estimate the partial decay rates, and derive the one- and two-electron energy spectra using relativistic many-electron wave functions of atoms provided by the multiconfiguration Dirac-Hartree-Fock package GRASP2K. While the bound-state neutrinoless double-$\beta$ decays are strongly suppressed, their two-neutrino counterparts can be observed in the next-generation double-$\beta$-decay experiments, most notably SuperNEMO.

An Ontology of Nature with Local Causality, Parallel Lives, and Many Relative Worlds

Parallel Lives (PL) is an ontological model of nature in which quantum mechanics and special relativity are unified in a single universe with a single space-time. Point-like objects called lives are the only fundamental objects in this space-time, and they propagate at or below c, and interact with one another only locally at point-like events in space-time, very much like classical point particles. The only causes and effects in the universe occur when lives meet locally, and thus the causal structure of interaction events in space-time is Lorentz invariant. Each life traces a continuous world-line through space-time, and experiences its own relative world, fully defined by the outcomes of past events along its world-line (never superpositions), which are encoded in its external memory. A quantum field comprises a continuum of lives throughout space-time, and familiar physical systems like particles each comprise a sub-continuum of the lives of the field. Each life carries an internal memory containing a local relative wavefunction, which is a local piece of a pure universal wavefunction, but only the relative wavefunctions are physically real in PL, and not the universal wavefunction in configuration space. Furthermore, while the universal wavefunction tracks the average behavior of the lives of a system, it fails to track their individual dynamics and trajectories. There is always a preferred separable basis, and for an irreducible physical system, each orthogonal term in this basis is a different relative world - each containing some fraction of the lives of the system. The relative wavefunctions in the lives' internal memories govern which lives of different systems can meet during future local interactions, and thereby enforce entanglement correlations - including Bell inequality violations.

Investeigated on the essence of discrete solutions of relativistic Fourier series expression wave function

Investeigated on the essence of discrete solutions of relativistic Fourier series expression wave function

Excited-State Reactivity of [Mn(im)(CO)3 (phen)]+ : A Structural Exploration.

The electronic excited state reactivity of [Mn(im)(CO)3 (phen)]+ (phen = 1,10-phenanthroline; im = imidazole) ranging between 420 and 330 nm have been analyzed by means of relativistic spin-orbit time-dependent density functional theory and wavefunction approaches (state-average-complete-active-space self-consistent-field/multistate CAS second-order perturbation theory). Minimum energy conical intersection (MECI) structures and connecting pathways were explored using the artificial force induced reaction (AFIR) method. MECIs between the first and second singlet excited states (S1 /S2 -MECIs) were searched by the single-component AFIR (SC-AFIR) algorithm combined with the gradient projection type optimizer. The structural, electronic, and excited states properties of [Mn(im)(CO)3 (phen)]+ are compared to those of the Re(I) analogue [Re(im)(CO)3 (phen)]+ . The high density of excited states and the presence of low-lying metal-centered states that characterize the Mn complex add complexity to the photophysics and open various dissociative channels for both the CO and imidazole ligands. © 2018 Wiley Periodicals, Inc.

Ab Initio Study of Covalency in the Ground versus Core-Excited States and X-ray Absorption Spectra of Actinide Complexes.

Relativistic multireference ab initio wave function calculations within the restricted active space (RAS) framework were performed to calculate metal and ligand X-ray absorption (XAS) near-edge spectroscopy (XANES) intensities for the metal M4,5 edges of [PuO2(H2O)5]2+, [AnVIO2]2+ (An = U, Np, Pu), and [AmCl6]3- and the Cl K edge of the Am complex. The extent of An(5f)-ligand bonding was determined via natural localized molecular orbital analyses of the relevant spin-orbit coupled multireference states. The calculated spectra are in good agreement with experiments and allow a detailed assignment of the observed spectral features. The XANES M4,5-edge spectra are representative of the actinide orbital covalency in the probed core-excited states, which may be different from the ground-state covalency. An assignment of ground-state An orbital covalency based on XAS spectra should therefore be made with caution.

Pressure-driven collapse of the relativistic electronic ground state in a honeycomb iridate

Honeycomb-lattice quantum magnets with strong spin-orbit coupling are promising candidates for realizing a Kitaev quantum spin liquid. Although iridate materials such as Li2IrO3 and Na2IrO3 have been extensively investigated in this context, there is still considerable debate as to whether a localized relativistic wavefunction (Jeff = 1/2) provides a suitable description for the electronic ground state of these materials. To address this question, we have studied the evolution of the structural and electronic properties of α-Li2IrO3 as a function of applied hydrostatic pressure using a combination of x-ray diffraction and x-ray spectroscopy techniques. We observe striking changes even under the application of only small hydrostatic pressure (P ≤ 0.1 GPa): a distortion of the Ir honeycomb lattice (via X-ray diffraction), a dramatic decrease in the strength of spin-orbit coupling effects (via X-ray absorption spectroscopy), and a significant increase in non-cubic crystal electric field splitting (via resonant inelastic X-ray scattering). Our data indicate that α-Li2IrO3 is best described by a Jeff = 1/2 state at ambient pressure, but demonstrate that this state is extremely fragile and collapses under the influence of applied pressure.

Electron-impact excitation of Xe+ and polarization of its subsequent emissions

Fully relativistic distorted wave calculations have been performed to study the electron impact excitation of singly ionized xenon from its ground 5p5 (J = 3/2) state to different fine structure excited states of the 5p46s, 5p46p, 5p47s, 5p47p, 5p45d and 5p46d configurations. The ground and excited bound states of Xe+ion have been represented through the relativistic multi-configuration Dirac-Fock wave functions while projectile electron distorted continuum wave functions are obtained by solving the Dirac equations. Results are reported for the excitation cross sections and the corresponding rate-coefficients of the considered different transitions. For each transition, analytic fitting to the calculated cross sections are also provided for plasma modeling purposes. In addition, using the density matrix theory and the calculated different magnetic sub-level excitation cross sections the linear polarization of the radiation emitted by the different optically allowed transitions are obtained and presented.

Forbidden transition properties of fine-structure 2p3 4S3/2−2p3 2D3/2,5/2 for nitrogen-like ions**Project supported by the National Natural Science Foundation of China (Grant Nos. 11604385 and 91436103).

Based on relativistic wave functions from multiconfiguration Dirac–Hartree–Fock and configuration interaction calculations, E2 and M1 transition probabilities of 2p3 4S3/2–2p3 2D3/2,5/2 are investigated in the nitrogen-like sequence with 7 ≤ Z ≤ 16. The contributions of the electron correlations, Breit interaction, and the quantum electrodynamic (QED) effects on the transition properties are analyzed. The present results can be used for diagnosing plasma. In addition, several N-like ions can also be recommended as a promising candidate for a highly charged ion (HCI) clock with a quality factor (Q) of transition as high as 1020.

The Application of Minimal Length in Klein-Gordon Equation with Hulthen Potential Using Asymptotic Iteration Method

The application of minimal length formalism in Klein-Gordon equation with Hulthen potential was studied in the case of scalar potential that was equal to vector potential. The approximate solution was used to solve the Klein-Gordon equation within the minimal length formalism. The relativistic energy and wave functions of Klein-Gordon equation were obtained by using the Asymptotic Iteration Method. By using the Matlab software, the relativistic energies were calculated numerically. The unnormalized wave functions were expressed in hypergeometric terms. The results showed the relativistic energy increased by the increase of the minimal length parameter. The unnormalized wave function amplitude increased for the larger minimal length parameter.

Bound-state double-beta decay

We study a new mode of the neutrinoless and two-neutrino double-beta decays in which a single electron is emitted from the atom. The other electron is assumed to occupy one of the vacant s1/2 or p1/2 subshells of the daughter ion. Such process could manifest itself through an additional background signal in the single-electron spectra, which will be accessible in the next-generation experiment SuperNEMO. We calculate the phase-space factors in terms of relativistic electron wave functions obtained as the solutions to the Dirac equation and evaluated at the nuclear radius, while taking into account the shielding effect of nuclear charge via the multiconfiguration Dirac–Hartree–Fock package Grasp2K. Half-lives are estimated for the most relevant double-beta-decay isotopes and experimental significance is discussed.

Low-Spin Fe(III) Macrocyclic Complexes of Imidazole-Appended 1,4,7-Triazacyclononane as Paramagnetic Probes.

Two macrocyclic complexes of 1,4,7-triazacyclononane (TACN), one with N-methyl imidazole pendants, [Fe(Mim)]3+, and one with unsubstituted NH imidazole pendants, [Fe(Tim)]3+, were prepared with a view toward biomedical imaging applications. These low-spin Fe3+ complexes produce moderately paramagnetically shifted and relatively sharp 1H NMR resonances for paraSHIFT and paraCEST applications. The [Fe(Tim)]3+ complex undergoes pH-dependent changes in NMR spectra in solution that are consistent with the consecutive deprotonation of all three imidazole pendant groups at high pH values. N-Methylation of the imidazole pendants in [Fe(Mim)]3+ produces a complex that dissociates more readily at high pH in comparison to [Fe(Tim)]3+, which contains ionizable donor groups. Cyclic voltammetry studies show that the redox potential of [Fe(Mim)]3+ is invariant with pH ( E1/2 = 328 ± 3 mV vs NHE) between pH 3.2 and 8.4, unlike the Fe(III) complex of Tim which shows a 590 mV change in redox potential over the pH range of 3.3-12.8. Magnetic susceptibility studies in solution give magnetic moments of 0.91-1.3 cm3 K mol-1 (μeff value = 2.7-3.2) for both complexes. Solid-state measurements show that the susceptibility is consistent with a S = 1/2 state over the temperature range of 0 to 300 K, with no crossover to a high-spin state under these conditions. The crystal structure of [Fe(Mim)](OTf)3 shows a six-coordinate all-nitrogen bound Fe(III) in a distorted octahedral environment. Relativistic ab initio wave function and density functional theory (DFT) calculations on [Fe(Mim)]3+, some with spin orbit coupling, were used to predict the ground spin state. Relative energies of the doublet, quartet, and sextet spin states were consistent with the doublet S = 1/2 state being the lowest in energy and suggested that excited states with higher spin multiplicities are not thermally accessible. Calculations were consistent with the magnetic susceptibility determined in the solid state.

Analyzing supersymmetric transformed α-nucleus potentials with electric-multipole transitions

Alpha(4He or α)-cluster models have often been used to describe light nuclei. Towards the application to multi-cluster systems involving heavy clusters, we study the relative wave functions of the α+16O and α+40Ca systems generated from phase-shift-equivalent potentials. In general, a potential between clusters is deep accommodating several redundant bound states which should be removed in an appropriate way. To avoid such a complicated computation, we generate a shallow-singular potential by using supersymmetric transformations from the original deep potential. Changes in the relative wave functions by the transformations are quantified with electric-multipole transitions which give a different radial sensitivity to the wave function depending on their multipolarity. Despite the fact that the original and transformed potentials give exactly the same phase shift, some observables are unfavorably modified. A possible way to obtain a desired supersymmetric potential is proposed.

Jj-Coupling-based atomic self-consistent-field calculations with relativistic effective core potentials and two-component spinors

A self-consistent-field (SCF) program for the calculation of atomic energies and wave functions defined in jj-coupling using two-component atomic spinors and relativistic effective core potentials (RECPs) is described. The code is based on the linear combination of atomic orbitals SCF algorithm for atomic states defined in LS-coupling developed by Roothaan and Bagus. Hamiltonian matrix elements with respect to one- and two-electron operators, including RECPs, are calculated for two-component atomic spinor basis functions of either Gaussian-type orbitals (GTOs) or Slater-type orbitals (STOs). Electronic states are defined as eigenfunctions of the total angular momentum squared operator and tables of the required vector coupling coefficients that define such pure states are provided. In addition, one or more GTO expansions of large- and small-core RECPs and their corresponding GTO basis sets are supplied for all elements Z=3 through Z=118. Optimized two-component basis sets of STOs or GTOs can be calculated for use in molecular structure codes based on RECPs and relativistic electronic structure theory. Atomic asymptotic state energies at the SCF level of theory for analysis of molecular dissociation limits can be studied. Program summaryProgram title: jjatomProgram Files doi:http://dx.doi.org/10.17632/zs4twp8r67.1Licensing provisions: GPLv3Programming language: Fortran 90Nature of problem: Relativistic atomic energies and wave functions; optimization of two component spinor basis sets.Solution method: Atomic spinors defined in jj-coupling and expansions in two-component spinor basis functions of Gaussian- or Slater-type functions. Self-consistent field optimization of the total energy. Used for optimization of two-component atomic spinor basis sets and calculations of valence spectra of heavy elements.

Analysis of Eigenvalue and Eigenfunction of Klein Gordon Equation Using Asymptotic Iteration Method for Separable Non-central Cylindrical Potential

Analysis of relativistic energy and wave function for zero spin particles using Klein Gordon equation was influenced by separable noncentral cylindrical potential was solved by asymptotic iteration method (AIM). By using cylindrical coordinates, the Klein Gordon equation for the case of symmetry spin was reduced to three one-dimensional Schrodinger like equations that were solvable using variable separation method. The relativistic energy was calculated numerically with Matlab software, and the general unnormalized wave function was expressed in hypergeometric terms.