Coulomb Part Research Articles

Reanalysis of the top-quark pair production via the e+e− annihilation near the threshold region up to N3LO QCD corrections

In this paper, we present an improved analysis of the top-quark pair production via the process e+e−→γ⁎→tt¯ near the threshold region up to next-to-next-to-next-to-leading order (N3LO) QCD corrections. Near the threshold region, the top-quark velocity v tends to zero, leading to Coulomb singularity. To achieve a reasonable prediction in the threshold region, we reconstruct the analytical expression for the Coulomb-terms up to N3LO accuracy by using the PSLQ algorithm, whose numerical values agree well with the previous N3LO-level calculations. It is found that the N3LO series still has sizable renormalization scale dependence, and to improve the precision of the series, we apply the Principle of Maximum Conformality to eliminate such scale dependence. After that, the Coulomb part is resummed into a Sommerfeld-Gamow-Sakharov factor, which finally leads to a much more reasonable behavior near the threshold region.

Hydrogen-iodine scattering. I. Development of an accurate spin-orbit coupled diabatic potential energy model.

The scattering of H by I is a prototypical model system for light-heavy scattering in which relativistic coupling effects must be taken into account. Scattering calculations depend strongly on the accuracy of the potential energy surface (PES) model. The methodology to obtain such an accurate PES model suitable for scattering calculations is presented, which includes spin-orbit (SO) coupling within the Effective Relativistic Coupling by Asymptotic Representation (ERCAR) approach. In this approach, the SO coupling is determined only for the atomic states of the heavy atom, and the geometry dependence of the SO effect is accounted for by a diabatization with respect to asymptotic states. The accuracy of the full model, composed of a Coulomb part and the SO model, is achieved in the following ways. For the SO model, the extended ERCAR approach is applied, which accounts for both intra-state and inter-state SO coupling, and an extended number of diabatic states are included. The corresponding coupling constants for the SO operator are obtained from experiments, which are more accurate than computed values. In the Coulomb Hamiltonian model, special attention is paid to the long range behavior and accurate c6 dispersion coefficients. The flexibility and accuracy of this Coulomb model are achieved by combining partial models for three different regions. These are merged via artificial neural networks, which also refine the model further. In this way, an extremely accurate PES model for hydrogen iodide is obtained, suitable for accurate scattering calculations.

The role of the Callan–Witten anomaly density as a Chern–Simons term in Skyrme model *

We consider axially symmetric solutions of the U(1) gauged Skyrme model supplemented with a Callan–Witten (CW) anomaly density term. The main properties of the solutions are studied, several specific features introduced by the presence of the CW term being identified. We find that the solitons possess a nonzero angular momentum proportional to the electric charge, which in addition to the usual Coulomb part, acquires an extra (topological) contribution from the CW term. Specifically, it is shown that the slope of mass/energy M electric charge Qe and angular momentum J can be both positive and negative. Furthermore, it is shown that the gauged Skyrmion persists even when the quartic (Skyrme) kinetic term disappears.

Benchmarking Aspects of Ab Initio Fragment Models for Accurate Excimer Potential Energy Surfaces.

While Coupled-Cluster methods have been proven to provide an accurate description of excited electronic states, the scaling of the computational costs with the system size limits the degree for which these methods can be applied. In this work different aspects of fragment-based approaches are studied on noncovalently bound molecular complexes with interacting chromophores of the fragments, such as π-stacked nucleobases. The interaction of the fragments is considered at two distinct steps. First, the states localized on the fragments are described in the presence of the other fragment(s); for this we test two approaches. One method is founded on QM/MM principles, only including the electrostatic interaction between the fragments in the electronic structure calculation with Pauli repulsion and dispersion effects added separately. The other model, a Projection-based Embedding (PbE) using the Huzinaga equation, includes both electrostatic and Pauli repulsion and only needs to be augmented by dispersion interactions. In both schemes the extended Effective Fragment Potential (EFP2) method of Gordon et al. was found to provide an adequate correction for the missing terms. In the second step, the interaction of the localized chromophores is modeled for a proper description of the excitonic coupling. Here the inclusion of purely electrostatic contributions appears to be sufficient: it is found that the Coulomb part of the coupling provides accurate splitting of the energies of interacting chromophores that are separated by more than 4 Å.

The study of angular momentum on the fusion of [formula omitted]Si+[formula omitted]Si, using SEDF in semiclassical extended Thomas-Fermi approach

The total fusion cross-sections are calculated for energies both above and below the potential barrier by using the properties of the interaction potential in Hill-Wheeler approximation for a positive Q-value system 1428Si+1428Si. The Coulomb and centrifugal parts of the potentials are added directly to the nuclear proximity potential to calculate the total interaction potential, where nuclear proximity potential is obtained in semiclassical extended Thomas-Fermi approach of Skyrme energy density formalism for Skyrme SIV parametrization. The angular momentum spectrum of total cross sections is obtained and calculated by using angular momentum dependent properties of the total interaction potential. The properties of total interaction potential, which are usually treated as independent of angular momentum, i.e. barrier height, barrier position and its width are calculated and found to depend sharply on the angular momentum value at a fixed center of mass energy. It effect the fusion cross-section sufficiently above the barrier energy. However at energies below the barrier energy the addition of large angular momentum values have negligible effects on fusion cross-section. Further, the maximum in fusion cross-section is observed at a particular value of angular momentum, which is not equal to the maximum value of angular momentum.

Incorporating the Coulomb potential into a finite, unitary perturbation theory

We have constructed a perturbation theory to treat interactions that can include the Coulomb interaction, describing a physical problem that is often encountered in nuclear physics. The Coulomb part is not treated perturbatively; the exact solutions are employed. The method is an extension of the results presented in the work of Hoffmann [J. Math. Phys. 62, 032105 (2021)]. It is designed to calculate phase shifts directly rather than the full form of the wavefunctions in position space. We present formulas that allow for the calculation of the phase shifts to second order in the perturbation. The phase shift results to second order, for a short-range potential, were compared with the exact solution, where we found an error of third order in the coupling strength. A different model, meant as a simple approximation of nuclear scattering of a proton on helium-4 and including a Coulomb potential and a spherical well, was constructed to test the theory. The wavepacket scattering formalism of Hoffmann [J. Phys. B: At., Mol. Opt. Phys. 50, 215302 (2017)], known to give everywhere finite results, was employed. We found physically acceptable results and a cross section of the correct order of magnitude.

Observation of two zeros of the real amplitude in pp scattering at LHC energies

Elastic scattering of charged hadrons is described by the combination of nuclear and Coulomb amplitudes. It is well know that at the very forward range the nuclear real and Coulomb parts interplay a crucial role in the determination of the magnitude of the real part at |t|=0. However, beyond |t|=0 the real and imaginary nuclear amplitudes have different t dependencies and we show that at LHC energies the zeros formed by the combination T_C(t)+T_R^N(s,t)=0 in pp process can be potentially observed when the background due to the imaginary part is removed. This observation constrains the real part at this forward range.

Effects of surface rigidity and metallicity on dielectric properties and ion interactions at aqueous hydrophobic interfaces.

Using classical molecular dynamics simulations, we investigate the dielectric properties at interfaces of water with graphene, graphite, hexane, and water vapor. For graphite, we compare metallic and nonmetallic versions. At the vapor-liquid water and hexane-water interfaces, the laterally averaged dielectric profiles are significantly broadened due to interfacial roughness and only slightly anisotropic. In contrast, at the rigid graphene surface, the dielectric profiles are strongly anisotropic and the perpendicular dielectric profile exhibits pronounced oscillations and signchanges. The interfacial dielectric excess, characterized by the shift of the dielectric dividing surface with respect to the Gibbs dividing surface, is positive for all surfaces, showing that water has an enhanced dielectric response at hydrophobic surfaces. The dielectric dividing surface positions vary significantly among the different surfaces, which points to pronounced surface-specific dielectric behavior. The interfacial repulsion of a chloride ion is shown to be dominated by electrostatic interactions for the soft fluid-fluid interfaces and by non-electrostatic Lennard-Jones interactions for the rigid graphene-water interface. A linear tensorial dielectric model for the ion-interface interaction with sharp dielectric interfaces located on the dielectric dividing surface positions works well for graphene but fails for vapor and hexane, because these interfaces are smeared out. The repulsion of chloride from the metallic and nonmetallic graphite versions differs very little, which reflects the almost identical interfacial water structure and can be understood based on linear continuum dielectric theory. Interface flexibility shows up mostly in the nonlinear Coulomb part of the ion-interface interaction, which changes significantly close to the interfaces and signals the breakdown of linear dielectric continuum theory.

Determination of $$\alpha $$-optical potential for reactions with p-nuclei from the study of ($$\alpha $$,n) reactions in the astrophysically relevant energy region

Optical potential parameters in nuclear model calculations are determined by fitting elastic scattering angular distribution data. Due to the dominance of Coulomb part, elastic scattering is performed at much higher energies. As a result, a change in potential is required for low-energy astrophysical reactions. A different approach is suggested using (\(\alpha \),n) reaction to determine the modified alpha optical potentials suitable for astrophysically relevant low energy regions. Reactions on p-nuclei in the mass region A \(\approx \) 92–168 have been chosen and a modified McFadden–Satchler \(\alpha \)-optical potential is obtained from fitting the (\(\alpha \),n) reaction data. The effect of level density and \(\gamma \)-ray strength function is also studied using this new potential by analyzing (\(\alpha ,\gamma \)) cross-sections.

Gauge invariant propagators and states in quantum electrodynamics

We study combined matter/gauge field gauge invariant states in terms of data living on the boundary of gauge invariant path-integrals. To get concrete results, this is done for scalar and spinor QED, for both ‘time-slice’, and ‘causal diamond’ boundaries. We discuss both the standard case where the gauge field falls off to zero at the spatial boundaries, and the case of ‘large gauge transformations’, where it remains finite at these boundaries. The path-integral naturally generates a specific dressing factor for states living on time-slices, without fixing any gauge, and we identify a universal contribution which depends only on the nature of the boundaries. We also derive the analogous dressing for states defined on null infinity, showing both its Coulombic parts as well as soft-photon parts.

Thermodynamic or density scaling of the electrical conductivity of molten salts.

Thermodynamic or density scaling of high-pressure conductivities and molar conductivities of the high-temperature molten salts NaOH, and the alkali chlorides, bromides, and nitrates, from Na to Cs, taken from the literature, is found to be consistent with the simulations of Knudsen, Niss, and Bailey (KNB). They used a simple model fluid of point particles interacting through an interionic potential with a repulsive inverse power law part varying as r-9 and an attractive Coulombic part. This yields values between the limits 0.33-3 for the scaling parameter, γ. The Coulombic potential reduces the scaling parameter to values much lower than are normally found for molecular liquids, and KNB used this to explain the low values typically found for ionic liquids. Here, it is shown that the high-temperature molten salts examined behave similarly.

Electroosmotic Flow in Polarizable Charged Cylindrical Nanopores.

We present a simulation method to study electroosmotic flow in charged nanopores with dielectric contrast between their interior and the surrounding medium. To perform simulations, we separate the electrostatic energy into the direct Coulomb and the polarization contributions. The polarization part is obtained using periodic Green functions and can be expressed as a sum of fast converging modified Bessel functions. On the other hand, the direct Coulomb part of the electrostatic energy is calculated using fast converging three-dimensional (3D) Ewald summation method, corrected for a pseudo one-dimensional (1D) geometry. The effects of polarization are found to be particularly important for systems with multivalent counterions and narrow nanopores. Depending on the surface charge density, polarization can increase the volumetric flow rate by 200%. For systems with 3:1 electrolyte, we observe that there is a saturation of the volumetric flow rate. In this case, for polarizable pores, the flow rate is 100% higher than for nonpolarizable pores.

Modeling photoelectron spin polarization of xenon atoms in intense circularly polarized pulses

We propose a model for studying the ionization, photoelectron spectra, and spin polarization of xenon atoms under intense circularly polarized (CP) pulses by solving the time-dependent Schrödinger equation (TDSE) with an effective potential for Xe. The ionization mechanism is mainly due to multiphoton absorption in these strong CP fields. The effective potential of a single active electron for Xe consists of asymptotic Coulomb and parametric screening parts and yields low-lying levels that are comparable to those by other models for the total angular momentum J = 3 / 2 of X e + and new for J = 1 / 2 . We show in detail the absorption pathways, above-threshold ionization (ATI) spectra, and spin polarization mechanisms of photoelectrons originated from the initial state 5 p m l of Xe with the magnetic quantum number m l being − 1 , 0, or 1. There exists a substructure with sub-peaks in each of multiple ATI peaks from 5 p − 1 due to pulse effects on the valence electron passing through the absorption pathways. ATI and spin polarization results agree qualitatively with experimental data at the focal volume average to include the spatial effect of CP pulses. We also present the spin polarization results of the widely used strong-field approximation model (SFA), which are inconsistent with those of TDSE and experiments. This shows that TDSE is more accurate with more details than SFA for studying spin polarization in strong CP fields.

Molecular basis for reduced cleavage activity and drug resistance in D30N HIV-1 protease

Nelfinavir is one of the FDA-approved HIV-1 protease inhibitors and a part of highly active anti-retroviral therapy (HAART) for the treatment of HIV-AIDS. Nelfinavir was the first HIV-1 protease inhibitor to be approved as a paediatric formulation. The application of HAART had resulted in significant improvement in the lives of AIDS patients. However, the emergence of drug resistance in HIV-1 protease has limited the use of many of these drugs including nelfinavir. A unique mutation observed frequently in patients treated with nelfinavir is D30N as it is selected exclusively by nelfinavir. The D30N mutation imparts very high resistance to nelfinavir but unlike other primary mutations does not give cross-resistance to the majority of other drugs. D30N mutation also significantly reduces cleavage activity of HIV-1 protease and affects viral fitness. Here, we have determined crystal structures of D30N HIV-1 protease in unliganded form and in complex with nelfinavir. These structures provide the rationale for reduced cleavage activity and the molecular basis of drug resistance induced by D30N mutation. The loss of coulombic interaction part of a crucial hydrogen bond between the drug and the protease is likely to play a major role in reduced affinity and resistance towards nelfinavir. The decreased catalytic activity of D30N HIV-1 protease due to altered interaction with the substrates and reduced stability of folding core may be the reason for the reduced replicative capacity of the virus harboring mutant HIV-1 protease. Communicated by Ramaswamy H. Sarma

An alternative to the Simon tensor

The Simon tensor gives rise to a local characterization of the Kerr-NUT family in the stationary class of vacuum spacetimes. We find that a symmetric and traceless tensor in the quotient space of the stationary Killing trajectory offers a useful alternative to the Simon tensor. Our tensor is distinct from the spatial dual of the Simon tensor and illustrates the geometric property of the three dimensional quotient space more manifest. The reconstruction procedure of the metric for which the generalized Simon tensor vanishes is spelled out in detail. We give a four dimensional description of this tensor in terms of the Coulomb part of the imaginary selfdual Weyl tensor, which corresponds to the generalization of the three-index tensor defined by Mars. This allows us to establish a new and simple criterion for the Kerr-NUT family: the gradient of the Ernst potential becomes the non-null eigenvector of the Coulomb part of the imaginary selfdual Weyl tensor. We also discuss the SU(1, 2) covariant extension of the obstruction tensor into the Einstein–Maxwell system as an intrinsic characterization of the Kerr–Newman-NUT family.

Мeson resonances in the relativistic quark model

In this paper, the relativistic quark model is developed for the study of mesons and resonances as quasi-bound quark states. A classic analogue of the spinless Salpeter equation is analyzed. It is shown that the potential for a conservative isolated two-particle system is the Lorentz-scalar function of the distance between quarks and can be included into the particle mass, which leads to the position-dependent quark mass. The funnel-type potential is modified with taking into account the dependence of the strong coupling αS on the distance. The concept of free motion of particles in a bound state is developed. The eigenvalue problem for the bound state is defined by the relativistic quasiclassical wave equation for the scalar potential. Two exact asymptotic solutions of the equation for the Coulomb and linear parts of the potential are obtained analytically; on this basis, the complex-mass formula for mesons and resonances is written. The efficiency of the model is demonstrated by comparison of the calculation results with the data for the masses of ρ and D mesons.

Static force potential of a non-Abelian gauge theory in a finite box in Coulomb gauge

Force potential exerting between two classical static sources of pure non-abelian gauge theory in the Coulomb gauge is reconsidered at a periodic/twisted box of size $L^3$. Its perturbative behavior is examined by the short-distance expansion as well as by the derivative expansion. The latter expansion to one-loop order confirms the well-known change in the effective coupling constant at the Coulomb part as well as the Uehling potential while the former is given by the convolution of two Coulomb Green functions being non-singular at $\bm{x}=\bm{y}$. The effect of the twist comes in through its Green function of the sector.

Construction of Explicit Symplectic Integrators in General Relativity. II. Reissner–Nordström Black Holes

Abstract In a previous paper, second- and fourth-order explicit symplectic integrators were designed for a Hamiltonian of the Schwarzschild black hole. Following this work, we continue to trace the possibility of construction of explicit symplectic integrators for a Hamiltonian of charged particles moving around a Reissner–Nordström black hole with an external magnetic field. Such explicit symplectic methods are still available when the Hamiltonian is separated into five independently integrable parts with analytical solutions as explicit functions of proper time. Numerical tests show that the proposed algorithms share desirable properties in their long-term stability, precision, and efficiency for appropriate choices of step size. For the applicability of one of the new algorithms, the effects of black hole’s charge, the Coulomb part of the electromagnetic potential and the magnetic parameter on the dynamical behavior are surveyed. Under some circumstances, the extent of chaos becomes strong with an increase of the magnetic parameter from a global phase-space structure. No variation of the black hole’s charge other than the Coulomb part affects the regular and chaotic dynamics of the particles’ orbits. A positive Coulomb part more easily induces chaos than a negative one.

Confining potential under the gauge field condensation in the SU(2) Yang–Mills theory

Abstract $Q\bar{Q}$ potential is studied in the SU(2) gauge theory. Based on the nonlinear gauge of the Curci–Ferrari type, the possibility of a gluon condensation $\langle A_{\mu}^+A_{\mu}^-\rangle$ in a low-energy region has been considered at the one-loop level. Instead of the magnetic monopole condensation, this condensation makes classical gluons massive, and can yield a linear potential. We show that this potential consists of the Coulomb plus linear part and an additional part. Comparing with the Cornell potential, we study this confining potential in detail, and find that the potential has two implicit scales: $r_c$ and $\tilde{R}_0$. The meanings of these scales are clarified. We also show that the Cornell potential that fits well to this confining potential is obtained by taking these scales into account.

An improved seminumerical Coulomb and exchange algorithm for properties and excited states in modern density functional theory.

A seminumerical algorithm capable of performing large-scale (time-dependent) density functional theory (TD-DFT) calculations to extract excitation energies and other ground-state and excited-state properties is outlined. The algorithm uses seminumerical integral techniques for evaluating Coulomb and exchange parts for a set of density matrices as occurring in standard TD-DFT or similar methods for the evaluation of vibrational frequencies. A suitable optimized de-aliasing procedure is introduced. The latter does not depend on further auxiliary quantities and retains the symmetry of a given density matrix. The algorithm is self-contained and applicable to any orbital basis set available without the need for further auxiliary basis sets or optimized de-aliasing grids. Relativistic two-component excited-state TD-DFT calculations are reported for the first time using the developed seminumerical algorithm for standard and local hybrid density functional approximations. Errors are compared with the widely used "resolution of the identity" (RI) approximations for Coulomb (RI-J) and exchange integrals (RI-K). The fully seminumerical algorithm does not exhibit an enlarged error for standard DFT functionals compared to the RI approximation. For the more involved local hybrid functionals and within strong external fields, accuracy is even considerably improved.