Nonrelativistic Approach Research Articles

What are the quantum commutation relations for the total angular momentum of light? tutorial

The total angular momentum of light has received attention for its application in a variety of phenomena such as optical communication, optical forces, and sensing. However, the quantum behavior including the commutation relations has been relatively less explored. Here, we derive the correct commutation relation for the total angular momentum of light using both relativistic and non-relativistic approaches. An important outcome of our work is the proof that the widely assumed quantum commutation relation for the total observable angular momentum of light is fundamentally incorrect. Our work will motivate experiments and lead to new insights on the quantum behavior of the angular momentum of light.

Interference effects in Compton scattering of keV photons at H 2+ : a nonrelativistic analytical approach

In this paper we study interference effects in Compton scattering at molecule by keV photons. As a test case we investigate the molecular system H 2+ at the equilibrium internuclear distance and in the dissociative channel. The initial molecular wavefunction is described as a linear combination of atomic orbitals centered on each nucleus. The final continuum state is a two-centre continuum Coulomb wavefunction. Using these approximations, we obtain an analytical form for the Compton scattering fully differential cross section. We investigate the molecular effects at various internuclear distance for an incident photon energy close to 2.1 keV. The relative contribution of the A⋅P and A 2 coupling terms in the Compton scattering magnitude is discussed (where P is the electron momentum operator and A the vector potential of the field). We focus on Cohen-Fano type interference effects, as the ones observed in the photoionization of molecules.

Light one-electron molecular ions within the finite-basis-set method for the two-center Dirac equation

During the last decades outstanding results on the precision description of light diatomic molecular compounds have been achieved. The most advanced calculations of electron binding energies have been realized mainly in the framework of the nonrelativistic approach with a consistent account of relativistic and radiative QED corrections. Recently, it has been shown that methods based on the Dirac equation are also suitable for obtaining highly accurate results in simple light molecules. In this paper, we present a completely relativistic method and discuss its application to the description of diatomic systems. In particular, the electronic spectra of the light one-electron quasi-molecular compounds H-H+, He+-He2+ and He+-H+ are analyzed. For this purpose, the two-center Dirac equation is solved by a dual-kinetic balanced finite-basis-set method for axially symmetric systems, called A-DKB. This method allows for a complete relativistic consideration of the electron at fixed inter-nuclear distances. A comparison of the obtained results with the nonrelativistic and relativistic calculations presented in the literature is performed. Without pursuing the goal of high accuracy calculations, the advantages and disadvantages of the approach, as well as possible applications of the method, are discussed in detail.

Towards a measurement theory in QFT: "Impossible" quantum measurements are possible but not ideal

Naive attempts to put together relativity and quantum measurements lead to signaling between space-like separated regions. In QFT, these are known as impossible measurements. We show that the same problem arises in non-relativistic quantum physics, where joint nonlocal measurements (i.e., between systems kept spatially separated) in general lead to signaling, while one would expect no-signaling (based for instance on the principle of no-nonphysical communication). This raises the question: Which nonlocal quantum measurements are physically possible? We review and develop further a non-relativistic quantum information approach developed independently of the impossible measurements in QFT, and show that these two have been addressing virtually the same problem. The non-relativistic solution shows that all nonlocal measurements are localizable (i.e., they can be carried out at a distance without violating no-signaling) but they (i) may require arbitrarily large entangled resources and (ii) cannot in general be ideal, i.e., are not immediately reproducible. These considerations could help guide the development of a complete theory of measurement in QFT.

New bound-state energy of double magic number plus one nucleon nuclei with a relativistic and non-relativistic mean-field approach in 3D-RNCQS and 3D-NRNCQS symmetries

New bound-state energy of double magic number plus one nucleon nuclei with a relativistic and non-relativistic mean-field approach in 3D-RNCQS and 3D-NRNCQS symmetries

Compton desintegration of positronium

We study the Compton disintegration of positronium in comparison with the same of hydrogen. The initial photon energy of a few keV allows one to apply the non-relativistic approach and use A2 approximation. Interesting features in the behavior of various differential cross sections are observed. In particular, the conditions were found, under which the electron and positron move parallel to each other with equal velocities. This leads to a number of specific Coulomb resonances

J/ψ polarization in large- PT semi-inclusive deep-inelastic scattering at the EIC

We present a detailed phenomenological study of $J/\psi$ polarization in semi-inclusive deep inelastic scattering processes, focusing on the kinematics accessible at the future Electron-Ion Collider. We show theoretical estimates for the standard polarization parameters for different frames usually adopted in the literature, in the large $P_T$ region, namely $P_T\gg \Lambda_\text{QCD}$, where collinear factorization is expected to hold. We adopt both the Color Singlet Model and the Nonrelativistic QCD approach, paying special attention to the role of different sets of Long Distance Matrix Elements. Finally we present a preliminary analysis of some frame independent polarization invariants.

Higgs boson decays to Bc meson in the fragmentation-function approach

In the paper, we present a calculation of the decay widths for the Higgs boson decays to the $B_c$, $B_c^*$, $B_c(2^1S_0)$ and $B_c^*(2^3S_1)$ mesons using the fragmentation-function approach. In the calculation, the fragmentation functions up to order $\alpha_s^3$ based on the nonrelativistic QCD factorization theory are used, and the decay widths for $H\to Q+X$ and $H \to g+X$ at the partonic level are calculated up to order $\alpha_s$. The large logarithms of $m_H^2/m_{Bc}^2$ are resummed up to next-to-leading logarithmic accuracy by solving the evolution equations for the running quark masses and the fragmentation functions. Compared to the leading-order decay widths based on the nonrelativistic QCD approach, the decay widths based on the fragmentation-function approach that include the higher-order QCD corrections are reduced significantly. Our numerical results show that there are about $1.2\times 10^5$ $B_c$ events via the Higgs decays to be produced at the HL-LHC with $3ab^{-1}$, and about $1.6\times 10^6$ $B_c$ events via the Higgs decays to be produced at the HE-LHC with $15ab^{-1}$.

Magnetic quadrupole transitions in the relativistic energy density functional theory

Magnetic quadrupole (M2) excitation represents a fundamental feature in atomic nucleus associated to nuclear magnetism induced by spin and orbital transition operator. Since it has only been investigated within the non-relativistic theoretical approaches, and available experimental data are rather limited, it is interesting to study the properties of M2 transitions using the framework of relativistic nuclear energy density functional. In this work the nuclear ground state is calculated with relativistic Hartree-Bogoliubov model, while the M2 excitations are described using the relativistic quasiparticle random phase approximation with the residual interaction extended with the isovector-pseudovector term. The M2 transition strength distributions are described and analyzed for closed shell nuclei $$^{16}$$ O, $$^{48}$$ Ca, $$^{208}$$ Pb, open-shell $$^{18} \mathrm O$$ , $$^{42}$$ Ca, $$^{56}$$ Fe, and semi-magic $$^{90}$$ Zr. The evolution of M2 transition properties has been investigated within the $$^{36-64} \mathrm Ca$$ isotope chain. The main M2 transitions have rather rich underlying structure and detailed analysis shows that collectivity increases with the mass number due to larger number of contributing particle-hole configurations. Pairing correlations in open shell nuclei have strong effect, causing the reduction of M2 strength and shifts of the centroid energies to higher values. The analysis of M2 transition strengths indicate that considerable amount of experimental strength may be missing, mainly due to limitations to rather restricted energy ranges. The calculated M2 strengths for Ca isotopes, together with the future experimental data will allow constraining the quenching of the g factors in nuclear medium.

Effect of generalized uncertainty principle on anharmonic oscillator

The minimal length Generalized Uncertainty Principle (GUP) is a proposed theory based on the basic phenomenology of Quantum Gravity (QG) to study the effect of gravity in the quantum realm in a nonrelativistic way. In this paper, we study the GUP effect on anharmonic oscillator by the ladder operator and perturbation theory. Taking different orders of perturbation from the potential of anharmonic oscillator, the first and second order energy corrections and the first order correction of wavefunction have been derived. We have also studied the variation of energy spectrum in general harmonic and anharmonic oscillator in an undergraduate nonrelativistic approach.

Relativistic Ritz approach to hydrogenlike atoms: Theoretical considerations

The Rydberg formula along with the Ritz quantum defect ansatz has been a standard theoretical tool used in atomic physics since before the advent of quantum mechanics, yet this approach has remained limited by its non-relativistic foundation. Here I present a long-distance relativistic effective theory describing hydrogen-like systems with arbitrary mass ratios, thereby extending the canonical Ritz-like approach. Fitting the relativistic theory to the hydrogen energy levels predicted by bound-state QED indicates that it is superior to the canonical, nonrelativistic approach. An analytic analysis reveals nonlinear consistency relations within the bound-state QED level predictions that relate higher-order corrections to those at lower order, providing guideposts for future perturbative calculations as well as insights into the asymptotic behavior of Bethe logarithms. Applications of the approach include fitting to atomic spectroscopic data, allowing for the determination the fine-structure constant from large spectral data sets and also to check for internal consistency of the data independently from bound-state QED.

Study of Differential Scattering Cross-Section Using Yukawa Term of Medium-Modified Cornell Potential

In the present work, we have studied the differential scattering cross-section for ground states of charmonium and bottomonium in the frame work of the medium-modified form of quark-antiquark potential and Born approximation using the nonrelativistic quantum chromodynamics approach. To reach this end, quasiparticle (QP) Debye mass depending upon baryonic chemical potential ( μ b ) and temperature has been employed, and hence the variation of differential scattering cross-section with baryonic chemical potential and temperature at fixed value of the scattering angle ( θ = 9 0 o ) has been studied. The variation of differential scattering cross-section with scattering angle θ (in degree) at fixed temperature and baryonic chemical potential has also been studied. We have also studied the effect of impact parameter and transverse momentum on differential scattering cross-section at θ = 90 o .

Vibrational Corrections to NMR Spin-Spin Coupling Constants from Relativistic Four-Component DFT Calculations.

Zero-point vibrational (ZPV) corrections to the nuclear spin–spin coupling constants have been calculated using four-component Dirac–Kohn–Sham DFT for H2X (where X = O, S, Se, Te, Po), XH3 (where X = N, P, As, Sb, Bi), and XH4 (where X = C, Si, Ge, Sn, and Pb) molecules and for HC≡CPbH3. The main goal was to study the influence of relativistic effects on the ZPV corrections and thus results calculated at relativistic and nonrelativistic approaches have been compared. The effects of relativity become notable for the ZPV corrections to the spin–spin coupling constants for compounds with lighter elements (selenium and germanium) than for the spin–spin coupling constants themselves. In the case of molecules containing heavier atoms, for instance BiH3 and PbH4, relativistic effects play a crucial role on the results and approximating ZPV corrections by the nonrelativistic results may lead to larger errors than omitting ZPV corrections altogether.

Charmonium spectrum and the color-octet heavy-quark potential from the instanton vacuum


 The properties of quarkonia are discussed in the framework of the nonrelativistic potential approach based on the instanton-induced interactions from the instanton vacuum. we have obtained the spectrum of charmonia and discuss the results. We also examine the instanton effects on the color-octet heavy-quark potential.

Many Body Current Density from Foldy–Wouthuysen Transformation of the Dirac–Coulomb Hamiltonian

This paper analyzes how special relativity changes the equation for the many-body-induced current density starting from the Foldy–Wouthuysen diagonalization of the Dirac–Coulomb Hamiltonian. This current density differs from that obtained with the Gordon decomposition due to the presence of a spin-orbit coupling contribution not considered before for many-body molecular systems. This contribution diverges on atomic nuclei due to the nature of the point charges considered in the nonrelativistic approach, demonstrating that conventionally used nonrelativistic methods are not suitable for dealing with spin effects such as spin-orbit coupling or effects smaller than α2, with α the fine structure constant, and that a fully relativistic approach with a finite charge should be used. Despite the singularity, the spin-orbit coupling current becomes an important contribution to the total current in open-shell systems with high-spin multiplicity and a high atomic number in the nuclear proximity. On long ranges, this contribution is overcome by the Coulomb potential and the derived electric field which decays very quickly for small distances from nuclear charges. An evaluation of this spin-orbit current has been performed in the linear response approach at the HF/DFT level of theory.

Spectra and Decay Properties of $$\varLambda _b$$ and $$\varSigma _b$$ Baryons

In this article, we study the radial states as well as orbital states mass spectra of the nonstrange baryons from bottom family utilizing hypercentral Constituent Quark Model(hCQM), a non-relativistic approach by employing screened potential as confining potential with color Coulomb potential. The spin-spin, spin-orbital and tensor interaction are considered for hyperfine splitting calculation. The mass spectra calculated and compared with other theoretical approaches. The Regge trajectories has been plotted in $(J, M^2)$ plane using the calculated mass spectra. Further, the single-pion decay and radiative decay have been described and magnetic moments are determined for the ground state.

Production of the B_c meson at the CEPC

In this paper, we make a detailed study on the production of the B_c, B_c^*, B_c(2,^1S_0), and B^*_c(2,^3S_1) mesons via the three planned running modes (Z, W, and H) at the future Circular Electron–Positron Collider (CEPC). The fragmentation-function and full nonrelativistic QCD approaches are adopted to calculate the production cross sections. Considering the excited states shall decay to the ground B_c state (e.g. 1^1S_0-state) with almost 100% probability, our numerical results show that up to next-to-leading order QCD corrections, there are about 1.4times 10^8B_c events to be accumulated via the Z mode (sqrt{s}=m_{_Z}) of the CEPC, but only about 1.6times 10^4 and 1.1times 10^4B_c events to be accumulated via the W (sqrt{s}=160,mathrm{GeV}) and H (sqrt{s}=240,mathrm{GeV}) modes, respectively. Since the Z mode is the best mode among the three planned modes of the CEPC for studying the production of the B_c, B_c^*, B_c(2,^1S_0), and B^*_c(2,^3S_1) mesons and the differential distributions of these mesons may be measured precisely at this mode, we further present the differential cross sections dsigma /(dz,dmathrm{cos}theta ) and dsigma /dz via the Z mode of the CEPC.

Scattering of an intense laser beam by atomic systems

A nonrelativistic quantum approach is adopted to describe the scattering of an intense laser beam from a simple atomic system. Two forms of the corresponding transition amplitude (TA) are derived, one involving the kinetic momentum operator of the electron and the other involving the force operator. The spectral and angular distribution of the scattered radiation is expressed in terms of TA by a relation recalling the classical one. The formalism is applied to the scattering of radiation by an electron (free or bound) with the absorption of two photons from the incident laser beam. Analytic and numeric results are presented for the distributions of the emitted photons in the case of the nonlinear Compton scattering from a hydrogenic atom in the ground state.

A Non-relativistic Approach to Relativistic Quantum Mechanics: The Case of the Harmonic Oscillator

A recently proposed approach to relativistic quantum mechanics (Grave de Peralta, Poveda, Poirier in Eur J Phys 42:055404, 2021) is applied to the problem of a particle in a quadratic potential. The methods, both exact and approximate, allow one to obtain eigenstate energy levels and wavefunctions, using conventional numerical eigensolvers applied to Schrödinger-like equations. Results are obtained over a nine-order-of-magnitude variation of system parameters, ranging from the non-relativistic to the ultrarelativistic limits. Various trends are analyzed and discussed—some of which might have been easily predicted, others which may be a bit more surprising.

Comparative studies on nuclear elastic magnetic form factors between the relativistic and non-relativistic mean-field approaches * *Supported by the National Natural Science Foundation of China (11505292, 11605105, 11822503, 11975167, 12035011), the Shandong Provincial Natural Science Foundation, China (ZR2020MA096), the Fundamental Research Funds for the Central Universities (20CX05013A, 22120210138), and the Graduate Innovative Research Funds of China University of Petroleum (East

It is known that elastic magnetic electron scattering can be used to study the magnetic properties of nuclei and determine the outermost-shell single-particle orbitals. In this study, the magnetic form factors of odd-A nuclei calculated with relativistic and non-relativistic models are systematically compared. We use the relativistic mean-field (RMF) and Skyrme Hartree-Fock (SHF) models to generate single-particle wave functions and calculate the values of selected nuclei under relativistic and non-relativistic frameworks, respectively. Geometric factors are introduced through the spherical limit method to consider the influences of deformation, which improves the agreement between the theoretical results and experimental data. It is shown that both the models have the capability to describe the magnetic form factors in the spherical and deformed cases, and the discrepancies in reflect the differences in the descriptions of the single-particle orbital between the two models.