Coulomb Terms Research Articles

A most misunderstood conditionally-solvable quantum-mechanical model

In this paper we show that several authors have derived wrong physical conclusions from a gross misunderstanding of the exact eigenvalues and eigenfunctions of a conditionally-solvable quantum-mechanical model. It consists of an eigenvalue equation with seemingly Coulomb, linear and harmonic terms. Here we compare the results derived by those authors with the actual eigenvalues of the models calculated by means of the Ritz variational method.

Decay properties of beauty and charm mesons within Isgur–Wise function formalism

We investigate the decay properties of some beauty and charm mesons with a phenomenological potential model. First, we consider the nonrelativistic Hamiltonian of the mesonic system with Coulomb plus exponential terms and study the wave function and the energy of the system using the variational approach. Thereby, we compute the masses, the decay constants, the leptonic branching fractions of heavy–light mesons and the mixing mass parameter $$\Delta {m_{{B_q}}}$$ . We study the radiative leptonic decay widths of $${D_s} \rightarrow \gamma \ell {{\bar{\nu }}} $$ , $${D^ - } \rightarrow \gamma \ell {{\bar{\nu }}} $$ and the semileptonic decay widths of $${{{\bar{B}}}_{(s)}} \rightarrow {D_{(s)}}\ell {{\bar{\nu }}} $$ and $${{{\bar{B}}}_{(s)}} \rightarrow D_{(s)}^*\ell {{\bar{\nu }}} $$ . Using Isgur–Wise function, we calculate the branching ratios of $$B \rightarrow {D^{(*)}}\pi $$ and two-body nonleptonic decay of $$D \rightarrow K\pi $$ . Our results are consistent with other theoretical models and the experimental results.

Semiclassical propagator approach for emission processes from deformed nuclei

We describe a more rigorous formulation of the 3D semiclassical approach, corresponding to deformed potentials, which leads to the exact results and we also compare them with the much simpler expressions given by the angular Wentzel–Krames–Brillouin (WKB) and linearized WKB with its approximation, known as Fröman WKB method. We define the semiclassical fundamental matrix of solutions, describing the effect of the deformed field. Its inverse, proportional to the so-called propagator matrix, connects the solution in two points. A comparison between the coupled channels fundamental matrix of solutions to various semiclassical counterparts evidences close results in the barrier region. We express the scattering amplitudes in terms of the propagator matrix multiplied by the ratio between internal wave function components and irregular Coulomb waves. The relative influence of nuclear and Coulomb action terms together with nuclear and Coulomb centrifugal barriers upon the penetration process reveals the dominance of the Coulombian parts. An analysis of alpha-emission processes between ground states and to excited states of even–even nuclei in terms of the propagator matrix evidenced the important role played by deformation of the Coulomb field and the shape of the nuclear interaction.

Robust marginal Fermi liquid in birefringent semimetals

We investigate the interplay of Coulomb interactions and correlated disorder in pseudospin-3/2 semimetals, which exhibit birefringent spectra in the absence of interactions. Coulomb interactions drive the system to a marginal Fermi liquid, both for the two-dimensional (2d) and three-dimensional (3d) cases. Short-ranged correlated disorder in 2d, or a power-law correlated disorder 3d, has the same engineering dimension as the Coulomb term, in a renormalization group (RG) sense. In order to analyze the combined effects of these two kinds of interactions, we apply a dimensional regularization scheme and derive the RG flow equations. The results show that the marginal Fermi liquid phase is robust against disorder.

Angular momentum redistribution in laser-induced demagnetization

The ultimate fate of the spin moment in ultrafast demagnetization is to appear as a gain in momentum of the lattice. However, the route by which it occurs remains to be conclusively demonstrated. Employing state-of-the-art time-dependent density functional theory we show that spin-orbit coupling at femtosecond timescales drives a transfer of spin angular momentum into orbital angular momentum, which via the Coulomb term transfers from this orbital angular momentum instantaneously to the lattice. The rate of change of angular and spin momenta have, respectively, predominantly extrinsic (the pulse duration) and intrinsic (spin-orbit coupling) timescales. This facilitates the design of pulses to clearly disentangle the physics of angular momentum redistribution. While experiments predominantly use bulk elemental Ni, we propose Co in thin film geometry with an experimentally realizable time resolution for ultrashort pulses will allow clear observation of the ultrafast transfer of momentum via orbital degrees of freedom to the lattice.

A new Δh method and its application to the asymptotic normalization constants of the 16O bound states

A new Δh method for finding the asymptotic normalization coefficient (ANC) was recently proposed by the author (2021). It was shown that the denominator of the re-normalized scattering amplitude f˜l includes the factor dl(E)=Δl(E)+hr(E)−h(η), where Δl(E) is the nuclear interaction part of the effective-range function (ERF) and Δh(E)=hr(E)−h(η) is the difference of the related Coulomb terms. Here hr(E)=Reh(η) for E>0, η=1/aBk is the Sommerfeld parameter, aB is the Bohr radius. The equation dl(E)=0 determines the f˜l poles at E=−ε (ε is a binding energy). In the present paper to calculate Δh(−ε) the function hr(E) is analytically continued to E<0. For this the series of hr(E) in powers of (aBk)2 which converges if (aBk)2<1 should be used. It is found that the first dominant term (aBk)2/12 of the asymptotic series has(E) is the same for hr(E) and h(η) (at E<0 for h(η)) when E→0. The subtraction of this dominant term from both hr(E) and h(η) simplifies the Δh(−ε) calculation. Here the Δh method applies to the ground and first excited S-wave bound states of 16O (16O↔4He+12C) which meet the condition |aBk|2<1. For 16O the standard ERF method does not work due to the large product Z1Z2 of the 4He and 12C charges. For the P− and D- wave 16O states the binding energies ε are so small that the approximate Δ method, when dl(E)≈Δl(E), is valid. ANCs for the ground and first excited P-wave bound states of 7Be (7Be↔3He+4He) are also calculated by polynomial fitting the sum Δl(E)+hr(E) up to E2 in an analogy with the ERF method. The results for Δh and EFR methods are close to each other. For this system aBκ>1 and the Δh method has no advantages over the standard ERF method. The Δh method opens up a new direction for systems with large Z1Z2 values when the ERF method no longer works.

Implementation of Coulomb Counting Method for Estimating the State of Charge of Lithium-Ion Battery

An accurate estimate of the state of charge, which describes the remaining percentage of a battery’s capacity, has been an important and ever existing problem since the invention of the electrochemical cell. State of charge estimation is one of the important function of a battery management system which ensures the safe, efficient and reliable operation of a battery. In this paper, the coulomb counting method is implemented for the estimation of the state of charge of lithium-ion battery. The hardware comprises an Arduino based platform for control and data processing, and a 16-bit analog to digital converter for current and voltage measurement. The embedded algorithm initializes with a self-calibration phase, during which the battery capacity, coulombic efficiency and initial state of charge are evaluated. The initial state of charge is determined at the fully charged state (100% state of charge) or the fully discharged state (0% state of charge). The cumulative error of this method was addressed by routine recalibration of the capacity, coulombic efficiency and state of charge at the fully-charged and fully-discharged states. The algorithm was validated by charging/discharging a lithium-ion battery through fifty complete cycles and evaluating the error in the estimated state of charge. The result shows a mean absolute error of 0.35% in the estimated state of charge during the test. Further analysis, considering prolonged battery operation without parameters recalibration, suggests that error in the coulombic efficiency term contributes the most to the increasing error in the estimated state of charge with each cycle.

Ab initio based interionic interactions in calcium aluminotitanate oxide melts: structure and diffusion

Calcium aluminotitanate (CaO–Al2O3–TiO2) ternary oxides are of fundamental interest in Materials as well as Earth and environmental science, and a key system for several industrial applications. As their properties at the atomic scale are scarcely known, interionic interactions for the melts are built from a bottom up strategy consisting in fitting first only Al2O3, CaO and TiO2 single oxide compounds separately with a unified description of the oxygen charge and O–O interaction term. For this purpose, a mean-square difference minimization of the partial pair-correlation functions with respect to the ab initio reference was performed. The potentials for the ternary oxide are finally built straightforwardly by adding purely Coulomb terms for dissimilar cation–cation interactions without further fit. This general and unified approach is transferable and successfully describes the structural and diffusion properties of the three single oxides as well as the ternary melts simultaneously. A possible underlying structural mechanism at the origin of the diffusion evolution with TiO2 content is proposed based on the formation of Ti induced triply bonded oxygen.

Effective Fragment Potential-Based Molecular Dynamics Studies of Diffusion in Acetone and Hexane.

To facilitate more reliable descriptions of transport properties in liquids, molecular dynamics (MD) simulations are performed based on the effective fragment potential (EFP) method derived from first-principles quantum mechanics (in contrast to MD based upon empirically fitted potentials). The EFP method describes molecular interactions in terms of Coulomb, polarization/induction, dispersion, exchange-repulsion, and charge-transfer interactions. The EFP MD simulations described in this paper, performed on hexane and acetone, are able to track the mean-square displacement of molecules for sufficient time to reliably extract translational diffusion coefficients. The results reported here are in reasonable agreement with experiment.

Exploring the effect of temperature on microscopic heat transfer of liquid organics by molecular dynamics simulations

Temperature is one of the important factors affecting the heat transfer of liquid organic, but the mechanism of the effect of temperature on the thermal conductivity of liquids is not deeply studied. In this paper, the microscopic thermal conduction of heptane, hexanal, 2-hexanone and hexanol at different temperatures were simulated by nonequilibrium molecular dynamics. Based on the simulation results, the relationship between the heat transfer of liquid organics and temperature was analyzed mainly from the molecular structure and the simulated system, and the thermal conductivity at the corresponding temperature was predicted. The results indicate that the Coulomb interaction term, the van der Waals interaction term and the torsion term, which contribute significantly to the total heat flux, all decrease with increasing temperature, which makes the thermal conductivity of the four organics decrease with increasing temperature. This paper speculates that the rise of temperature increases the atomic vibration of the simulated molecules, accelerates the molecular motion, and decreases the mass density of the simulated system, and make the four organic thermal conductivity of the changes described above. In addition, the mean relative deviation of the calculated thermal conductivity from the experimental values is 8.54% and the maximum deviation is 9.23%, the simulation results are basically consistent with the experimental values. The present work provides a preliminary understanding for studying the effect of temperature on the thermal conduction of liquid organics.

A new Δ method for bound state asymptotic normalization coefficients with a finite limit of the nuclear part of the effective-range function at zero energy

A new bound state Δ method for finding an asymptotic normalization coefficient (ANC) is proposed. This is valid, while the standard effective-range function (ERF) Kl(k2) method does not work when the product of colliding particles charges increases. The denominator of the strict expression of the re-normalized scattering amplitude f˜l includes the factor dl(E)=Δl(E)+hr(E)−h(η), where η=1/aBk, aB is the Bohr radius. In the physical region, the Coulomb term hr=Reh(η). So an analytical continuation of hr(E) from the physical region to E≤0 can be found by fitting hr(E) for E≥0. The related analytical continuation of h(η) consists in a simple sign change, E→−E, using an explicit dependence of h(η) on E. This is important that for E≤0, abs(Δh)=abs(h−hr)=0 at E=0, and it increases when abs(E) does. Thus, a new real equation, dl(−ε)=0, is obtained for a binding energy ε. It is applied to find a residue W of f˜l at the bound state pole E=−ε, the nuclear vertex constant (NVC) and (ANC). The Coulomb-nuclear phase shift δlcs, cotδlcs and a finite limit of the nuclear part Δl(k2) of Kl(k2) are also derived for an arbitrary orbital momentum l when E→0. It is shown that cotδlcs has an essential singularity at zero energy, but Δl(k2) does not. The explicit finite limit of Δl(k2) when E→0 is found using the expression for Kl(k2). These results are in agreement with those for the S-wave scattering, which are widely accepted. The ANCs for the ground and first excited bound states for the vertex Be7↔3He4He are calculated using the proposed new method, and are compared with those for the approximate method when dl(E)=Δl(E) proposed by Ramírez Suárez and Sparenberg (2017). The fit of Δl(E) is found from the experimental phase-shift input data and the additional equation dl(−ε)=0.

Application of the residual surface delta interaction in the /beta+ decay of (_^"40" )"Sc" nucleus

In this paper the beta decay of Sc40 has been investigated. Using the eigenfunctions of the spherical oscillator the eigenvalues and eigenfunctions of the Woods-Saxon potential with spin-orbit and Coulomb terms have been calculated. In order to obtain the more realistic nuclear wave functions, the surface delta interaction potential has been used as the residual interaction between the valence nucleons in the frame work of Tamm-Dancoff approximation (TDA) in the case of Ca40 and particle-hole Tamm-Dancoff approximation (pnTDA) in the case of Sc40 . The potential constants have been obtained by fitting the results with the experimental data. The half-life and transition probability of positive beta decay of Sc40 have been calculated. Good greement with the experimental data was observed.

Solving the Bethe-Salpeter equation on a subspace: Approximations and consequences for low-dimensional materials

It is well known that the ambient environment can dramatically renormalize the quasiparticle gap and exciton binding energies in low-dimensional materials, but the effect of the environment on the energy splitting of the spin-singlet and spin-triplet exciton states is less understood. A prominent effect is the renormalization of the exciton binding energy and optical strength (and hence the optical spectrum) through additional screening of the direct Coulomb term describing the attractive electron-hole interaction in the kernel of the Bethe-Salpeter equation (BSE). The repulsive exchange interaction responsible for the singlet-triplet slitting, on the other hand, is unscreened within formal many-body perturbation theory. However, Loren Benedict argued that in practical calculations restricted to a subspace of the full Hilbert space, the exchange interaction should be appropriately screened by states outside of the subspace, the so-called $S$ approximation \cite{Benedict2002}. Here, we systematically explore the accuracy of the $S$ approximation for different confined systems, including a molecule and heterostructures of semiconducting and metallic layered materials. We show that the $S$ approximation is actually exact in the limit of small exciton binding energies (i.e., small direct term) and can be used to significantly accelerate convergence of the exciton energies with respect to the number of empty states, provided that a particular effective screening consistent with the conventional Tamm-Dancoff approximation is employed. We further find that the singlet-triplet splitting in the energy of the excitons is largely unaffected by the external dielectric environment for most quasi-two-dimensional materials.

Analysis of nonrelativistic particles in noncommutative phase-space under new scalar and vector interaction terms

The Schrödinger equation in noncommutative phase space is considered with a combination of linear, quadratic, Coulomb and inverse square terms. Using the quasi exact ansatz approach, we obtain the energy eigenvalues and the corresponding wave functions. In addition, we discuss the results for various values of in noncommutative phase space and discuss the results via various figures.

Diffusion Monte Carlo calculations of fully-heavy multiquark bound states

We use a diffusion Monte Carlo method to solve the many-body Schr\"odinger equation describing fully-heavy tetraquark systems. This approach allows to reduce the uncertainty of the numerical calculation at the percent level, accounts for multi-particle correlations in the physical observables, and avoids the usual quark-clustering assumed in other theoretical techniques applied to the same problem. The interaction between particles was modeled by the most general and accepted potential, i.e. a pairwise interaction including Coulomb, linear-confining and hyperfine spin-spin terms. This means that, in principle, our analysis should provide some rigorous statements about the mass location of the all-heavy tetraquark ground states, which is particularly timely due to the very recent observation made by the LHCb collaboration of some enhancements in the invariant mass spectra of $J/\psi$-pairs. Our main results are: (i) the $cc\bar c\bar c$, $cc\bar b\bar b$ ($bb\bar c\bar c$) and $bb\bar b \bar b$ lowest-lying states are located well above their corresponding meson-meson thresholds; (ii) the $J^{PC}=0^{++}$ $cc\bar c\bar c$ ground state with preferred quark-antiquark pair configurations is compatible with the enhancement(s) observed by the LHCb collaboration; (iii) our results for the $cc\bar c\bar b$ and $bb\bar c\bar b$ sectors seem to indicate that the $0^+$ and $1^+$ ground states are almost degenerate with the $2^+$ located around $100\,\text{MeV}$ above them; (iv) smaller mass splittings for the $cb\bar c\bar b$ system are predicted, with absolute mass values in reasonable agreement with other theoretical works; (v) the $1^{++}$ $cb\bar c\bar b$ tetraquark ground state lies at its lowest $S$-wave meson-meson threshold and it is compatible with a molecular configuration.

High-Performance, Graphics Processing Unit-Accelerated Fock Build Algorithm.

We present a high-performance, GPU (graphics processing unit)-accelerated algorithm for building the Fock matrix. The algorithm is designed for efficient calculations on large molecular systems and uses a novel dynamic load balancing scheme that maximizes the GPU throughput and avoids thread divergence that could occur due to integral screening. Additionally, the code adopts a novel ERI digestion algorithm that exploits all forms of permutational symmetry, combines efficiently the evaluation of both Coulomb and exchange terms together, and eliminates explicit thread synchronization requirements. Performance results obtained using a number of large molecules reveal remarkable speedups up to 24.4× with respect to the QUICK GPU code and up to 237× with respect to the GAMESS CPU parallel code.

Pseudo-spin rotation symmetry breaking by Coulomb interaction terms in spin–orbit coupled systems

By transforming from the pure-spin-orbital (t 2g) basis to the spin-orbital entangled pseudo-spin-orbital basis, the pseudo-spin rotation symmetry of the different Coulomb interaction terms is investigated under SU(2) transformation in pseudo-spin space. While the Hubbard and density interaction terms are invariant, the Hund’s coupling and pair-hopping interaction terms explicitly break pseudo-spin rotation symmetry systematically. The form of the symmetry-breaking terms obtained from the transformation of the Coulomb interaction terms accounts for the easy x–y plane anisotropy and magnon gap for the out-of-plane mode, highlighting the importance of mixing with the nominally non-magnetic J = 3/2 sector, and providing a physically transparent approach for investigating magnetic ordering and anisotropy effects in perovskite (Sr2IrO4) and other d 5 pseudo-spin compounds.

Dirac Fermions in Half‐Metallic Ferromagnetic Mixed Cr1−xMxPSe3 Monolayers

AbstractThe electronic and magnetic properties of pristine CrPSe3 and mixed CrMxPSe3 (M = Zn, Cd, Hg) monolayers are studied using density functional theory including an on‐site Coulomb term (density functional theory (DFT) ) and tight‐binding approach. While pristine CrPSe3 monolayer has an antiferromagnetic ground state, its alloying with MPSe3 may give rise to half‐metallic ferromagnet with high Curie temperature. The resulting monolayers demonstrate single‐spin Dirac cones of mainly Cr‐d character located in the first Brillouin zone directly at the Fermi energy. The calculated Fermi velocities of Dirac fermions indicate very high mobility in mixed CrMxPSe3 monolayers, that makes this material appealing for low‐dimensional spintronics applications.

Quantization of the charge in Coulomb plus harmonic potential

Abstract We consider two models where the wave equation can be reduced to the effective Schrödinger equation whose potential contains both harmonic and the Coulomb terms, $\omega^{2}r^{2}-a/r$. The equation reduces to the biconfluent Heun’s equation, and we find that the charge as well as the energy must be quantized and state-dependent. We also find that two quantum numbers are necessary to count radial degrees of freedom and suggest that this is a general feature of differential equation with higher singularity like the Heun’s equation.

Interaction between Trinuclear Regium Complexes of Pyrazolate and Anions, a Computational Study.

The geometry, energy and electron density properties of the 1:1, 1:2 and 1:3 complexes between cyclic (Py-M)3 (M = Au, Ag and Cu) and halide ions (F−, Cl− and Br−) were studied using Møller Plesset (MP2) computational methods. Three different configurations were explored. In two of them, the anions interact with the metal atoms in planar and apical dispositions, while in the last configuration, the anions interact with the CH(4) group of the pyrazole. The energetic results for the 1:2 and 1:3 complexes are a combination of the specific strength of the interaction plus a repulsive component due to the charge:charge coulombic term. However, stable minima structures with dissociation barriers for the anions indicate that those complexes are stable and (Py-M)3 can hold up to three anions simultaneously. A search in the CSD confirmed the presence of (Pyrazole-Cu)3 systems with two anions interacting in apical disposition.