Relativistic Potentials Research Articles

Relativistic Bohmian mechanics revisited: A covariant reformulation for spin-1/2 particles

We present a novel covariant relativistic guidance formula à la de Broglie-Bohm derived from conserved quantities associated with the Lagrangian of the Dirac equation in a 1+1-dimensional spacetime. In line with the standard guidance formula of Bohmian mechanics, this generalized guidance formula incorporates space-time derivatives of the Dirac spinor phases and consistently reproduces relativistic features such as mass-dependent trajectories and zitterbewegung. We formally show that this formulation explicitly reveals how the relativistic quantum potential affects the trajectories. Using numerical simulations, we compare these trajectories with those presented in the usual approaches. Finally, we show how the guidance formula naturally transitions to the standard de Broglie-Bohm theory in the non-relativistic limit and gives additional contributions in the expansions giving new insight into the zitterbewegung in pilot-wave theories.

Ionization energies of Cu- and Ni-like ions with Z ≤ 92

A two-stage technique is developed to interpolate and extrapolate the ionization energies of Cu- and Ni-like ions along Z with accuracy to the fifth significant digit. I) The first stage consists of scaling the known ionization energies (IE) along Z, which brings the IE(Z)-function to a quasi-straight line. Function straightening detects points where the function’s smoothness breaks down. They are fitted to the IE(Z) curve in the same way as it is usually done in some experiments. Scaling on successive overlapping segments allows a confident extrapolation to the region Z=92. II) The verification of the obtained results in stage I is performed using the parameter of the relativistic model potential of a Dirac equation. The results of techniques I and II agree well up to Z∼92.

Ground state spectra, decay properties of B and D mesons in a relativistic square root potential

We look at the mass spectra of the [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] mesons using a relativistic square root potential. Before looking at the mass spectra, we have to figure out the model parameters, which are [Formula: see text][Formula: see text]GeV and [Formula: see text][Formula: see text]GeV. The calculated result of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], findings of this study exhibit a notable concurrence with the experimental observations and pertinent theoretical projections. We estimate the decay constant, leptonic decay width, semileptonic decay width, and branching fractions of pseudoscalar and vector mesons, specifically B and D mesons, while keeping the model parameters unchanged. The pseudoscalar decay constants and partial decay widths of “B and D-mesons” reasonably agree with the theoretical predictions, lattice quantum chromodynamics (LQCD) calculations, and experimental data. Moreover, we have efficiently found the values for these mesons’ leptonic decay width and branching fraction, matching the experimental findings and theoretical forecasts. The calculated values of semileptonic decays are [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text], the proximity of the observed results to experimental and certain theoretical models is evident.

A new generation of effective core potentials: Selected lanthanides and heavy elements.

We construct correlation-consistent effective core potentials (ccECPs) for a selected set of heavy atoms and f elements that are currently of significant interest in materials and chemical applications, including Y, Zr, Nb, Rh, Ta, Re, Pt, Gd, and Tb. As is customary, ccECPs consist of spin-orbit (SO) averaged relativistic effective potential (AREP) and effective SO terms. For the AREP part, our constructions are carried out within a relativistic coupled-cluster framework while also taking into account objective function one-particle characteristics for improved convergence in optimizations. The transferability is adjusted using binding curves of hydride and oxide molecules. We address the difficulties encountered with f elements, such as the presence of large cores and multiple near-degeneracies of excited levels. For these elements, we construct ccECPs with core-valence partitioning that includes 4f subshell in the valence space. The developed ccECPs achieve an excellent balance between accuracy, size of the valence space, and transferability and are also suitable to be used in plane wave codes with reasonable energy cutoffs.

Chaos and integrability of relativistic homogeneous potentials in curved space

Relativistic Hamiltonian systems of n degrees of freedom in static curved spaces are considered. The source of space-time curvature is a scalar potential V(q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(\\varvec{q})$$\\end{document}. In the limit of weak potential 2V(q)/mc2≪1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2V(\\varvec{q})/mc^2\\ll 1$$\\end{document}, and small momentum |p|/mc≪1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\varvec{p} |/ mc\\ll 1$$\\end{document}, these systems transform into the corresponding non-relativistic flat Hamiltonian’s with the standard sum of kinetic energy plus potential V(q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(\\varvec{q})$$\\end{document}. We compare the dynamics of the classical and the corresponding relativistic curved counterparts on examples of important physical models: the Hénon–Heiles system, the Armbruster–Guckenheimer–Kim galactic system and swinging Atwood’s machine. Our main results are formulated for relativistic Hamiltonian systems with homogeneous potentials of non-zero integer degree k of homogeneity. First, we show that the integrability of a non-relativistic flat Hamiltonian with a homogeneous potential is a necessary condition for the integrability of its relativistic counterpart in curved space-time with the same homogeneous potential or with a non-homogeneous potential that the lowest homogenous part coincides with this homogeneous potential. Moreover, we formulate necessary integrability conditions for relativistic Hamiltonian systems with homogeneous potentials in curved space-time. These conditions were obtained from analysis of the differential Galois group of variational equations along a particular straight-line solution defined by a non-zero vector d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{d}$$\\end{document} satisfying V′(d)=γd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V'(\\varvec{d})=\\gamma \\varvec{d}$$\\end{document} for a certain γ≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma \ e 0$$\\end{document}. They are very strong: if the relativistic system is integrable in the Liouville sense, then either k=±2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=\\pm 2$$\\end{document}, or all non-trivial eigenvalues of the re-scaled Hessian γ-1V′′(d)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma ^{-1}V''(\\varvec{d})$$\\end{document} are either 0, or 1. Certain integrable relativistic systems are presented.

A possibility of Klein paradox in quaternionic (3 + 1) frame

In light of the significance of non-commutative quaternionic algebra in modern physics, this study proposes the existence of the Klein paradox in the quaternionic (3+1)-dimensional space-time structure. By introducing quaternionic wave function, we rewrite the Klein–Gordon equation in extended quaternionic form that includes scalar and the vector fields. Because quaternionic fields are non-commutative, the quaternionic Klein–Gordon equation provides three separate sets of the probability density and probability current density of relativistic particles. We explore the significance of these probability densities by determining the reflection and transmission coefficients for the quaternionic relativistic step potential. Furthermore, we also discuss the quaternionic version of the oscillatory, tunnelling, and Klein zones for the quaternionic step potential. The Klein paradox occurs only in the Klein zone when the impacted particle’s kinetic energy is less than [Formula: see text]. Therefore, it is emphasized that for the quaternionic Klein paradox, the quaternionic reflection coefficient becomes exclusively higher than value one while the quaternionic transmission coefficient becomes lower than zero.

Renormalization of Very Special Relativity gauge theories

Mandelstam-Leibbrandt (ML) regularization of Very Special Relativity (VSR) amplitudes in momentum space depends on two fixed null vectors nμ, {overline{n}}_{mu } besides external momenta. ML is known to preserve gauge invariance and naive power counting. The second null vector {overline{n}}_{mu } destroys the Sim(2) symmetry of the VSR model. We devise a systematic procedure to take the {overline{n}}_{mu } → 0 limit to recover the lost Sim(2) symmetry. The procedure produces Sim(2) and gauge invariant loop amplitudes. We show how to use this method to remove unphysical terms from the Non Relativistic Potential of Very Special Relativity Quantum Electrodynamics (VSR QED) with a massive photon. Then we compute the one loop renormalization of VSR QED. Finally we derive the anomalous magnetic moment of the electron, modified by neutrino and photon mass; and comments on the phenomenological implications.

Cross Sections for Electron Scattering from Cadmium: Theory and Experiment

Results from the application of optical potential, relativistic optical potential, relativistic convergent close-coupling, and binary encounter Bethe models to electron scattering from gas-phase cadmium are presented. In particular, integral cross sections for elastic scattering, summed discrete electronic-state excitation, and ionization scattering processes are reported over an extended incident electron-energy range. Total cross sections are constructed by taking their sum. Measurements are presented for elastic scattering and for excitation to the 51P1 state. The theoretical and experimental results are compared to previous calculations and measurements. Recommended electron cross-section datasets are constructed over an incident electron energy range of 0.01–10 000 eV.

The α-particle clustering and half-lives of the newly discovered 207,208Th decay chains within relativistic-Hartree-Bogoliubov approach

The structural and decay properties of the ground state of recently discovered neutron-deficient 207Th and remeasured 208Th isotopes Yang et al. (2022) [26] is examined using the Relativistic-Hartree-Bogoliubov (RHB) formalism using the DD-ME2 parameter set within the preformed cluster-decay model (PCM). The relativistic medium-dependant R3Y so-called DD-R3Y NN potentials are for the first time used to obtain the nucleus-nucleus potential as input into the PCM. The penetration probability is calculated using the WKB approximation, and the preformation probability (Pα) is estimated using our newly derived formula, which is based on parameters well known to influence the α -particle radioactivity. A close correlation is observed between the α-preformation factor and the crucial role of the pairing correlation in the α-decay process. Furthermore, the Pα values for the even-even nuclei are generally found to be of higher magnitude than those for the odd-A nuclei. Our results further affirm that the odd-even staggering effect on the Qα values and its accompanying effects on other observables such as the charge radii and the decay half-lives, which can be largely attributed to the pairing correlation and Pauli blocking of the unpaired valence nucleons.

The Space-Time Properties of Three Static Black Holes

In the curved space-time, the neutral test particle is not affected by any other force except for the influence of the curved space-time. Similar to the free sub in the flat space, the Lagrangian of the test particle only contains the kinetic energy term—the kinetic energy term of the four-dimensional curved space-time. In the case of small space-time curvature, linear approximation can be made. That is, under the weak field approximation, the Lagrangian quantity degenerates into the Lagrangian quantity in the axisymmetric gravitational field in Newtonian mechanics. In this paper, the curved space-time composed of axisymmetric equidistant black holes is taken as a model. We study the geodesic motion of the test particles around three black holes with equal mass and static axisymmetric distribution, including time-like particles and photons. The three extreme Reissner–Nordstrom black holes are balanced by electrostatic and gravitational forces. We first give the geodesic motion equation of particles in Three black holes space-time, give the relativistic effective potential, discuss the possible motion state of particles, and classify their motion trajectories. Then, the particle motion of the special plane (equatorial plane) is studied. The circular orbits of the two types of particles in the symmetric plane are studied, respectively. The circular orbits outside the symmetric plane are also studied, and their stability is also discussed. We will show the influence of the separation distance of the three black holes on the geodesic motion and explore the change of the relativistic effective potential. Then, the relationship between the inherent quantity and the coordinate quantity in space-time is analyzed. Finally, the chaos of the test particle orbit is explored.

Энергии ионизации Cu-подобных ионов с Z≤92

The overview of the experimental and theoretical data on the ionization energies (IE) of the Cu -like ions is presented. In various works data are obtained by interpolation and extrapolation the parameters of model potentials for Dirac equations. In other approaches, the function of the dependence of the ionization energy on Z (Z is nuclear charge) is approximated by a polynomial with power-law dependence on Z in order to achieve a minimum difference between theoretical and experimental data. The compilation of ionization energies is in database of the National Institute of Standards and Technology (USA), where the typical uncertainty is several units in the fourth significant digit. This means that for heavy ions the error can reach several tens of thousands cm–1. In this work, the ionization energies of Cu-like ions are refined to achieve accuracy to the fifth significant digit. Two methods have been developed for the interpolation and extrapolation. Scaling ionization energies along Z: scaling results in the function of the dependence of ionization energies on Z to the form of a quasi-line, i.e., weakly varying function on interval of 10−15 Z values. This allows the function to be interpolated up to the fifth significant numbers. The scaled refined function of the dependence of the ionization energy on Z is approximated by analytical functions that allow extrapolation with good accuracy to the Z~92 region. The relativistic model potential is used to interpolate and extrapolate ionization energies. The parameter of the relativistic model potential for the 4s1/2 orbital turned out to be almost linear function of Z for Z > 70, which made it possible to extrapolate with high accuracy to the Z region of 92. The results of both methods are in good agreement up to Z~ 92.

A consistent description of the relativistic effects and three-body interactions in atomic nuclei

A microscopic relativistic Hamiltonian containing consistent relativistic and 3N potentials is, for the first time, constructed based on the leading-order covariant pionless effective field theory, and this Hamiltonian is solved by developing a new accurate relativistic ab initio method with a novel symmetry-based artificial neural network for A≤4 nuclei. It is found that the relativistic effects overcome the energy collapse problem for 3H and 4He without promoting a repulsive three-nucleon interaction to leading order as in nonrelativistic calculations. To exactly reproduce the experimental ground-state energies, a three-nucleon interaction is needed and its interplay with the relativistic effects plays a crucial role. The presented results open the new avenue for a unified and consistent study on relativistic effects and many-body interactions in atomic nuclei, and would also help to achieve more accurate ab initio calculations for nuclei.

Hadronic vacuum polarization correction to atomic energy levels

The 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. The energy corrections originating from hadronic vacuum polarization are calculated for low-lying levels using analytical Dirac-Coulomb wave functions, as well as bound wave functions accounting for the finite nuclear size. Closed formulas for the hadronic Uehling potential of an extended nucleus as well as for the relativistic energy shift in case of a point-like nucleus are derived. These results are compared to existing analytic formulas from non-relativistic theory.

Medium-dependent relativistic NN potential: Application to fusion dynamics

In-medium effects are introduced in the microscopic description of the effective nucleon-nucleon (NN) interaction potential entitled DDR3Y in terms of the density-dependent nucleon-meson couplings within the Relativistic-Hartree-Bogoliubov (RHB) approach. The nuclear densities of the interacting target and projectile nuclei and NN potentials are obtained for non-linear NL3$^*$ and TM1 parameter sets within the relativistic mean-field approach and density-dependent DDME1 and DDME2 parameter sets within the Relativistic-Hartree-Bogoliubov (RHB) formalism. The DDR3Y NN potential and the densities are used to obtain the nuclear potential by adopting the double folding approach. This nuclear potential is further used to probe the fusion dynamics within the $\ell-$summed Wong model for a few {\it even-even} systems leading to the formation of light, heavy and superheavy nuclei. The calculations are also performed for the relativistic R3Y, density-dependent and independent M3Y interaction potentials for the comparison. We observed that the DDR3Y NN potential gives a better overlap with the experimental data as compared to non-relativistic M3Y and DDM3Y NN potentials. From the comparison of R3Y and DDR3Y interactions, it is manifested that the inclusion of in-medium effects in terms of density-dependent nucleon-meson couplings raises the fusion barrier and consequently decreases the fusion and/or capture cross-section. Moreover, the nuclear densities, as well as the relativistic R3Y NN potential obtained for the NL3$^*$ parameter set, are observed to give a comparatively better fit to the experimental data.

A new generation of effective core potentials from correlated and spin-orbit calculations: Selected heavy elements.

We introduce new correlation consistent effective core potentials (ccECPs) for the elements I, Te, Bi, Ag, Au, Pd, Ir, Mo, and W with 4d, 5d, 6s, and 6p valence spaces. These ccECPs are given as a sum of spin-orbit averaged relativistic effective potential (AREP) and effective spin-orbit (SO) terms. The construction involves several steps with increasing refinements from more simple to fully correlated methods. The optimizations are carried out with objective functions that include weighted many-body atomic spectra, norm-conservation criteria, and SO splittings. Transferability tests involve molecular binding curves of corresponding hydride and oxide dimers. The constructed ccECPs are systematically better and in a few cases on par with previous effective core potential (ECP) tables on all tested criteria and provide a significant increase in accuracy for valence-only calculations with these elements. Our study confirms the importance of the AREP part in determining the overall quality of the ECP even in the presence of sizable spin-orbit effects. The subsequent quantum Monte Carlo calculations point out the importance of accurate trial wave functions that, in some cases (mid-series transition elements), require treatment well beyond a single-reference.

Bi-local fields interacting with a constant electric field and related problems including the Schwinger effect

The bi-local fields are the quantum fields of two-particle systems, the bi-local systems, bounded by relativistic potentials. Since those form constrained dynamical systems, it is limited to introduce the interactions of the bi-local fields with other fields. In this paper, the interaction between the bi-local fields and a constant electric field E is studied with consideration for the consistency of constraints. Then, we evaluate the Schwinger effect for the bi-local systems, which gives the pair production probability of the bound states as a function of the charges of respective particles and the coupling constant in the binding potential. Through this analysis, we also discuss the possibility for the dissociation of bi-local systems due to the electric field.

Theoretical Investigation of α-decay Chains of Fm-isotopes

Background: The theoretical and experimental investigations of decay properties of heavy and superheavy nuclei are crucial to explore the nuclear structure and reaction dynamics.
 Purpose: The aim of this study is to probe the α-decay properties of 243Fm and 245Fm isotopic chains using relativistic mean-field (RMF) approach within the framework of preformed cluster-decay model (PCM).
 Methods: The RMF densities are folded with the relativistic R3Y NN potential to deduce the nuclear interaction potential between the α particle and daughter nucleus. The penetration probability is calculated within the WKB approximation.
 Results: The α-decay half-lives of even-odd 243Fm and 245Fm isotopes and their daughter nuclei are obtained from the preformed cluster-decay model. These theoretically calculated half-lives are found to be in good agreement with the recent experimental measurements.
 Conclusions: The novel result here is the applicability of the scaling factor within the PCM as a signature for shell/sub-shell closures in α-decay studies. As such, we have also demonstrated that N=137, 139 and Z=94 corresponding to 231,233Pu could be shell/sub-shell closures. The least T1/2 is found at 243,245Fm which indicate their individual stability and α-decay as their most probable decay mode.

Systematic study of fusion barrier characteristics within the relativistic mean-field formalism

Background: The nuclear interaction potential and hence the fusion barrier formed between the interacting nuclei are the keys to understanding the complex fusion process dynamics. Purpose: This work intends to explore the fusion barrier characteristics of different target-projectile combinations within the relativistic mean-field (RMF) formalism. Methods: The density distributions of interacting nuclei and the microscopic R3Y NN interaction are obtained from relativistic mean-field (RMF) formalism for non-linear NL1, NL3, TM1, and relativistic-Hartree-Bogoliubov (RHB) approach for DDME2 parameter sets. The fusion and/or capture cross-section for the different reaction systems is calculated using the well-known $\ell$-summed Wong model. Results: The barrier height and position of 24 heavy-ion reaction systems are obtained for different nuclear density distributions and effective NN interaction potentials. The comparison of fusion and/or capture cross-section obtained from the $\ell$-summed Wong model is made with the available experimental data. Conclusions: The phenomenological M3Y NN potential is observed to give higher barrier heights than the relativistic R3Y NN potential for all the reaction systems. The comparison of results obtained from different relativistic parameter sets shows that the densities from NL1 and TM1 parameter sets give the lowest and highest barrier heights for all the systems under study. We observed higher barrier heights and lower cross-sections for DDR3Y NN potential as compared to density-independent R3Y NN potentials obtained for considered non-linear NL1, NL3 and TM1 parameter sets. According to the present analysis, it is concluded that the NL1 and NL3 parameter sets provide comparatively better overlap with the experimental fusion and/or capture cross-section than the TM1 and DDME2 parameter sets.

Benchmarking intranuclear cascade models for neutrino scattering with relativistic optical potentials

The description of final-state interactions (FSI) in the large phase space probed in neutrino experiments poses a great challenge. In neutrino experiments, which operate under semi-inclusive conditions, cascade models are commonly used for this task, while under exclusive conditions FSI can be treated with relativistic optical potentials (ROP). We formulate conditions under which the ROP approach and cascade model can be directly compared. We feed the NEUT cascade with events from a relativistic distorted-wave impulse approximation calculation that uses the real part of an optical potential. Cuts on the missing energy of the resulting events are applied to define a set of events that can be directly compared to RDWIA calculations with the full optical potential. The NEUT cascade and ROP agree for proton kinetic energies $T_p > 150$ MeV for carbon, oxygen and calcium nuclei when a realistic nuclear density is used to introduce events in the cascade. For $T_p < 100$ MeV the ROP and NEUT cross sections differ in shape and differences in magnitude are larger than 50 \%. Single transverse variables allow to distinguish different approaches to FSI, but due to a large non-QE contribution the comparison to T2K data does not give an unambiguous view of FSI. We discuss electron scattering and argue that with a cut in missing energy FSI can be studied with minimal confounding factors in e.g. $e4\nu$. The agreement of the ROP and NEUT for T2K conditions lends confidence to these models as a tool in oscillation analyses for sufficiently large nucleon kinetic energies. These results urge for caution when a cascade model is applied for small nucleon energies. The assessment of model assumptions relevant to this region are strongly encouraged. This paper provides novel constraints on cascade models from proton-nucleus scattering that can be easily applied to other neutrino event generators.

Accurate Relativistic Chiral Nucleon-Nucleon Interaction up to Next-to-Next-to-Leading Order.

We construct a relativistic chiral nucleon-nucleon interaction up to the next-to-next-to-leading order in covariant baryon chiral perturbation theory. We show that a good description of the np phase shifts up to T_{lab}=200 MeV and even higher can be achieved with a χ[over ˜]^{2}/d.o.f. less than 1. Both the next-to-leading-order results and the next-to-next-to-leading-order results describe the phase shifts equally well up to T_{lab}=200 MeV, but for higher energies, the latter behaves better, showing satisfactory convergence. The relativistic chiral potential provides the most essential inputs for relativistic abinitio studies of nuclear structure and reactions, which has been in need for almost two decades.