Coulomb Part Research Articles

Long-range dynamic polarization potentials forBe11projectiles onZn64

We investigate the effects of the long-range dynamic polarization (LRDP) potential, which consists of the Coulomb dipole excitation (CDE) potential and the long-range nuclear (LRN) potential, for the $^{11}\mathrm{Be}$ projectile on $^{64}\mathrm{Zn}$. To study these effects, we perform a ${\ensuremath{\chi}}^{2}$ analysis of an optical model including the LRDP potential as well as a conventional short-range nuclear (SRN) potential. To take these effects into account, we argue that both the CDE and LRN potentials are essential to explaining the experimental values of ${P}_{E}$, which is the ratio of the elastic scattering cross section to the Rutherford cross section. The Coulomb and nuclear parts of the LRDP potential are found to contribute to a strong absorption effect. Strong absorption occurs because the real part of the CDE and LRN potentials lowers the barrier, and the imaginary part of the CDE and LRN potentials removes the flux from the elastic channel in the $^{11}\mathrm{Be}+^{64}\mathrm{Zn}$ system. Finally, we extract the total reaction cross section ${\ensuremath{\sigma}}_{R}$ including the inelastic, breakup, and fusion cross sections. The contribution of the inelastic scattering by the first excited state at ${\ensuremath{\varepsilon}}_{\mathrm{x}}^{1\mathrm{st}}=0.32\phantom{\rule{4pt}{0ex}}\mathrm{MeV}\phantom{\rule{4pt}{0ex}}(1/{2}^{\ensuremath{-}})$ is found to be relatively large and cannot be ignored. In addition, our results are shown to agree quite well with the experimental breakup reaction cross section by using a fairly large radius parameter.

Bistable solutions for the electron energy distribution function in electron swarms in xenon: a comparison between the results of first-principles particle simulations and conventional Boltzmann equation analysis

At low reduced electric fields the electron energy distribution function in heavy noble gases can take two distinct shapes. This ‘bistability effect’—in which electron–electron (Coulomb) collisions play an essential role—is analyzed here for Xe with a Boltzmann equation approach and with a first principles particle simulation method. The solution of the Boltzmann equation adopts the usual approximations of (i) searching for the distribution function in the form of two terms (‘two-term approximation’), (ii) neglecting the Coulomb part of the collision integral for the anisotropic part of the distribution function, (iii) treating Coulomb collisions as binary events, and (iv) truncating the range of the electron–electron interaction beyond a characteristic distance. The particle-based simulation method avoids these approximations: the many-body interactions within the electron gas with a true (un-truncated) Coulomb potential are described by a molecular dynamics algorithm, while the collisions between electrons and the background gas atoms are treated with Monte Carlo simulation. We find a good general agreement between the results of the two techniques, which confirms, to a certain extent, the approximations used in the solution of the Boltzmann equation. The differences observed between the results are believed to originate from these approximations and from the presence of statistical noise in the particle simulations.

Hyperbolic statics in space-time

Based on the concept of a material event as an elementary material source that is concentrated on a metric sphere of zero radius—a light cone of Minkowski space-time, we deduce an analog of Coulomb’s law for a hyperbolic space-time field universally acting between space-time events. The collective field that provides interaction of world lines of a pair of particles at rest contains a standard 3-dimensional Coulomb part and a logarithmic addition. We find that the Coulomb part depends on a fine balance between the causal and geometric space-time characteristics (a concordance of two regularizations).

Form factors and charge radii in a quantum chromodynamics-inspired potential model using variationally improved perturbation theory

We use variationally improved perturbation theory (VIPT) for calculating the elastic form factors and charge radii of D,D s,B,B s and B c mesons in a quantum chromodynamics (QCD)-inspired potential model. For that, we use linear-cum-Coulombic potential and opt the Coulombic part first as parent and then the linear part as parent. The results show that charge radii and form factors are quite small for the Coulombic parent compared to the linear parent. Also, the analysis leads to a lower as well as upper bounds on the four-momentum transfer Q 2, hinting at a workable range of Q 2 within this approach, which may be useful in future experimental analyses. Comparison of both the options shows that the linear parent is the better option.

An energy partition method based on localized molecular orbitals

A new energy partition scheme based on the use of the molecular orbitals (MO) derived from an isopycnic localization of the natural MOs of the system is presented. The method is inspired in the Interacting Quantum Atoms (IQA) methodology and leads to an exact decomposition of the total energy of the molecule into intra-atomic self-energies and inter-atomic interaction energies. The latter, in turn, can be partitioned into a Coulombic or classical electrostatic part and an exchange–correlation contribution that measures the covalency of the interaction. In principle, the scheme presented can be used with both single- and multi-determinant wavefunctions. However, in the first case, and contrary to what happens in the IQA method, as long as the numerical overlap integrals between the isopycnic MOs over the atomic domains in which the physical space is divided are accurate enough, all the energy components are computed analytically. We have performed calculations in the H2 and LiH molecules, and in several Hydrogen bonded systems, and compared the results with those previously reported using the IQA methodology.

Comments on the perturbation of Cornell potential in a QCD potential model

We find in the analysis that the linear part of the Cornell potential can be treated as perturbation for a set of larger values of σs in the range 0.4 ≤ σs ≤ 0.75 with a constant shift within the range of −0.4GeV ≤ c ≤ −1 GeV. Moreover with the same range of constant shift in the Potential, we expect better results with Coulombic part as perturbation for σs ≤ 0.4.

Study of Electromagnetic Multipole Transition Half-Lives of One-Hole 15O–15N and One-Particle 17O–17F Mirror Nuclei

Energy spectrum and wave functions are obtained numerically with a potential consisting of Woods-Saxon, Coulomb, and spin-orbit coupling parts for the nuclei 15O, 15N, 17O, and 17F. The radial parts of the wave functions are used to calculate some matrix elements of electromagnetic transitions. These results are applied to calculate half-lives of low-lying exited states in the one-particle 17O and 17F as well as in the one-hole 15O and 15N isotopes. The calculated half-lives are compared with available experimental and theoretical results based on harmonic oscillator wave functions and Weisskopf units. In comparison with the results calculated from the other methods, our results based on the Woods-Saxon potential indicate a satisfactory agreement with accessible experimental data.

MCMC2 (version 1.1): A Monte Carlo code for multiply-charged clusters

MCMC2 (version 1.1): A Monte Carlo code for multiply-charged clusters

Space group symmetry applied to SCF calculations with periodic boundary conditions and Gaussian orbitals

Space group symmetry is exploited and implemented in density functional calculations of extended systems with periodic boundary conditions. Our scheme for reducing the number of two-electron integrals employs the entire set of operations of the space group, including glide plains and screw axes. Speedups observed for the Fock matrix formation in simple 3D systems range from 2X to 9X for the near field Coulomb part and from 3X to 8X for the Hartree-Fock-type exchange, the slowest steps of the procedure, thus leading to a substantial reduction of the computational time. The relatively small speedup factors in special cases are attributed to the highly symmetric positions atoms occupy in crystals, including the ones tested here, as well as to the choice of the smallest possible unit cells. For quasi-1D systems with most atoms staying invariant only under identity, the speedup factors often exceed one order of magnitude reaching almost 70X (near-field Coulomb) and 57X (HFx) for the largest tested (16,7) single-walled nanotube with 278 symmetry operations.

On Simple Gas Reactions

[Following the publication of Arrhenius's paper (Paper 2) on the significance of the temperature dependence of the rates of chemical reactions, a number of workers interested themselves in the problem of the significance of the activation energy. With the advent, in the nineteen-twenties, of the new quantum mechanics it was natural to see to what extent activation energies could be calculated by the same methods that were beginning to be used for the calculation of the energies of stable molecules. The most successful of the early attempts of this kind was that described in the paper reproduced in part below. In it Eyring and Polanyi show that a reasonable estimate of the activation energy of a reaction involving three atoms can be obtained by applying quantum-mechanical procedures with some assistance from empirical methods. A particularly important feature of the Eyring–Polanyi work is their use of potential-energy surfaces, which provide a very valuable pictorial representation of the course of a chemical reaction. Henry Eyring was born in 1901, and at the time this paper was written was a (U.S.) National Research Fellow in Berlin. Later he became Professor of Chemistry at Princeton University and is now Dean of the Graduate School at the University of Utah. He has made many distinguished contributions, particularly in the application of theoretical methods, to the understanding of the rates of chemical and physical processes. Perhaps his most pioneering work is represented by the present paper and by Paper 5, which deals with the application of statistical methods to the rates of chemical reactions. Michael Polanyi was born in 1891 in Budapest, and at the time this paper was written was a member of the Kaiser Wilhelm Institut fur Physikalische Chemie in Berlin. He was later Professor of Physical Chemistry at Manchester University, and in 1948 became Professor of Social Studies at that University. He has made important contributions in kinetics and in related branches of physical chemistry, and is the author of a number of books on sociology.] Abstract A further development of London's theory of adiabatic chemical processes, especially atom reactions. The total binding energy of single pairs of atoms is determined from optical data as a function of the interatomic distance and is corrected for the coulombic parts by means of the Heitler–London relation. As examples are taken the linear conversions in the systems The course of a conversion is represented as a motion of a representative point over a surface which represents the binding energy of the atomic system, plotted in space as a function of the interatomic distances.

STRONGLY INTERACTING QGP AND QUARKONIUM SUPPRESSION AT RHIC AND LHC ENERGIES

We have developed an equation of state for strongly interacting quark–gluon plasma (QGP) in the framework of strongly coupled plasma with appropriate modifications to take account of color and flavor degrees of freedom and the interactions among themselves. For this purpose we used the effective potential to improve the plasma parameter (Γ) by correcting the full Cornell potential with a dielectric function embodying the effects of the deconfined medium and not its Coulomb part alone and obtain the equation of state in terms of Γ. Our results on thermodynamic observables viz. pressure, energy density, speed of sound etc. nicely fit to the results of lattice equation of state for gluon, massless as well massive flavored plasma. We have then employed our equation of state to estimate the quarkonium suppression in an expanding QGP produced in the relativistic heavy-ion collisions. We have found that our predictions matches with the recent PHENIX data on the centrality dependence of J/ψ suppression in Au+Au collisions at BNL RHIC within the limit of other uncertainties. We have also predicted for the ϒ suppression in Pb+Pb collisions at LHC energy which could be tested in the ALICE experiments at CERN LHC.

Semileptonic Decay of <i>B<sub>c</sub></i> Meson into <i>S</i> Wave Charmonium in a QCD Potential Model with Coulombic Part as Perturbation

We present the semileptonic decay of Bc meson in a QCD potential model with the coulombic part of the Cornell potential -4αs/3r+br+c as perturbation. Computing the slope and curvature of Isgur Wise function in this approach, we study the pseudoscalar and vector form factors for the transition of Bc meson to its S wave charmonium states. Numerical estimates of widths for the transitions of Bc→J|ψ(ηc)lv1 are presented.

Range effects of the Coulombic forces on structures, thermodynamic properties and potential energy landscapes: (KCl)32 and related systems

By introducing two shielding parameters into the Coulombic part of the Coulomb plus Born–Mayer potential originally developed for (KCl)n systems, we study the effects of the range of the Coulombic interactions on the structures, thermodynamic properties and the potential energy landscapes of binary ionically bonded systems as illustrated by the case of n=32. Our calculations show that shortening of the Coulomb interaction range leads to a decrease in the energy of the most stable structure, and the structure itself changes from the rocksalt cubic to a hollow cage type. The energy range, in which the heat capacity exhibits a negative value, gradually narrows and eventually disappears. The number of stationary points on the potential energy surface increases, and their energies get spread over a larger interval. The extent of the Coulombic interaction also affects the energy difference (gap) between the most stable structure and the structure that follows it. All these changes translate into changes in the melting behavior of the system. An analysis of the melting behavior as a function of the range of the Coulombic interaction is presented and correlated with the range-dependent changes in the topography of the underlying potential energy surface.

Charmonium suppression in the presence of dissipative forces in a strongly-coupled quark–gluon plasma

We study the survival of charmonium states in a strongly-coupled quark–gluon plasma in the presence of dissipative forces. We consider first-order dissipative corrections to the plasma equation of motion in the Bjorken boost-invariant expansion with a strongly-coupled equation of state for QGP and study the survival of these states with the dissociation temperatures obtained by correcting the full Cornell potential not its Coulomb part alone with a dielectric function encoding the effects of deconfined medium. We further explore the sensitivity of prompt and sequential suppression of these states to the shear viscosity-to-entropy density ratio, η/s from perturbative QCD and AdS/CFT predictions. Our results show nice agreement with the recent experimental results at RHIC.

Deciphering the Influence of Short-Range Electronic Couplings on Optical Properties of Molecular Dimers: Application to “Special Pairs” in Photosynthesis

The excited states of chromophore dimers are, in general, delocalized, and the transition energies and transition dipoles are different from those of the monomers. The intermolecular interaction that is responsible for these effects has two contributions: Forster-type Coulomb coupling and a short-range coupling, which depends on the intermolecular overlap of electronic wave functions. The latter contains the Dexter-type exchange coupling and the coupling of excited states to intermolecular charge-transfer (CT) states. Recently, we developed a method (TrEsp) for an accurate and numerically efficient calculation of the Forster-type Coulomb part (Madjet et al. J. Phys. Chem. B 2006, 110, 17268). Here, we combine the latter with quantum chemical calculations to evaluate the short-range contribution, extending a method developed earlier by Scholes et al. (J. Phys. Chem. B 1999, 103, 2543). An effective two-state model is used, which relates the transition energies and transition dipole moments obtained by quantum chemical calculations of the monomers to those calculated for the dimer. From this relation, the short-range excitonic coupling and effective shifts of the local transition energies due to the coupling to intermolecular CT states can be inferred including a consistency check to evaluate quantum chemical methods that differ in the treatment of electron correlation. The method is applied to the special pairs of the reaction centers of purple bacteria (bRC) and photosystem I (PSI). We find that the short-range coupling represents the dominant contribution to the total excitonic coupling in both special pairs (80% in PSI and 70% in the bRC) and exhibits a monoexponential dependence on the distance between the pi-planes of the pigments with an attenuation factor of 2.8 A(-1). We obtain significant red-shifts of the local transition energies, which show a biexponential distance dependence with one attenuation factor being 2.8 A(-1) and another factor being in the range 0.3-0.7 A(-1) for PSI and 0.8-0.9 A(-1) for bRC. Both effects of the short-range coupling determine the excitation energy sink in the reaction centers at the special pairs.

Effect of octupole and higher deformations on Coulomb barrier

The effect of octupole deformation, β 3 , and the higher multipole deformations, β 6 and β 8 , on the distribution of barriers in orientation degrees of freedom, is studied. Coulomb barriers are derived in the frame work of the double folding model with the realistic M3Y nucleon–nucleon interaction and its density dependent version. 48Ca + 244Pu spherical-deformed nuclear interacting pair is considered, as an example, to study the effect of deformation parameters on the height and position of the Coulomb barrier. Although the dependence of the Coulomb barrier parameters on the higher deformations is complicated, numerically, if it is treated in microscopic way, we found a simple linear variation of barrier parameters with the different orders of deformation. We found that the variation of the barrier parameters with deformation exactly follows the change of the half density radius of the deformed nucleus in the direction of the separation vector between the centers of mass of the interacting nuclei. This suggests a simple and straightforward way to predict the behavior of the barrier parameters with different orders of deformations. We compared the results of present work with a similar recent study of the same quantities based on simple expression derived by Wong for the Coulomb part and proximity approach for the nuclear part of heavy ion potential, respectively.

Projectile-target core interaction in single ionization of helium by 100-MeV/uC6+and 1-GeV/uU92+ions

We consider single ionization of helium by very fast highly charged ions. The ionization is treated as a three-body problem which involves the ``active'' target electron, the target core (consisting of the target nucleus and the ``passive'' target electron) and the projectile ion. In contrast to the previous studies of this process, in which the interaction between the projectile and the target core was treated as a purely Coulomb one, we describe this interaction using the same core potential which acts on the active electron and which has both Coulomb and short-range parts. According to our results the deviation of the interaction between the projectile and the target core from the purely Coulomb law has on overall a weak effect on the ionization dynamics. In particular, we show that the account of this deviation does not enable one to get any better agreement with experimental data on the fully differential cross section for the electron emission into the so-called perpendicular plane.

The role of the atomic potential in the regime of strong-field tunnelling ionization: imprints on longitudinal and 2D momentum distributions

We present a theoretical study of strong-field ionization of selected rare-gas atoms and hydrogen in the tunnelling regime, using two- and ten-cycle laser pulses. For two-cycle pulses, ionization occurs via the tunnelling process, and the Coulombic long-range part of the atomic potentials leads to bimodal longitudinal momentum distributions. The momentum distributions are not sensitive to the electronic structure of the probed atom. For ten-cycle pulses, a multiphoton picture emerges even in the tunnelling regime, and the momentum distributions are influenced by the internal structure of the probed atom. The effect of the internal structure is clearly demonstrated in the case of Ar, where the longitudinal momentum distribution obtained using a ten-cycle pulse peaks at zero momentum.

Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange

In this paper, the possibility is explored to speed up Hartree–Fock and hybrid density functional calculations by forming the Coulomb and exchange parts of the Fock matrix by different approximations. For the Coulomb part the previously introduced Split-RI-J variant (F. Neese, J. Comput. Chem. 24 (2003) 1740) of the well-known ‘density fitting’ approximation is used. The exchange part is formed by semi-numerical integration techniques that are closely related to Friesner’s pioneering pseudo-spectral approach. Our potentially linear scaling realization of this algorithm is called the ‘chain-of-spheres exchange’ (COSX). A combination of semi-numerical integration and density fitting is also proposed. Both Split-RI-J and COSX scale very well with the highest angular momentum in the basis sets. It is shown that for extended basis sets speed-ups of up to two orders of magnitude compared to traditional implementations can be obtained in this way. Total energies are reproduced with an average error of <0.3kcal/mol as determined from extended test calculations with various basis sets on a set of 26 molecules with 20–200 atoms and up to 2000 basis functions. Reaction energies agree to within 0.2kcal/mol (Hartree–Fock) or 0.05kcal/mol (hybrid DFT) with the canonical values. The COSX algorithm parallelizes with a speedup of 8.6 observed for 10 processes. Minimum energy geometries differ by less than 0.3pm in the bond distances and 0.5° in the bond angels from their canonical values. These developments enable highly efficient and accurate self-consistent field calculations including nonlocal Hartree–Fock exchange for large molecules. In combination with the RI-MP2 method and large basis sets, second-order many body perturbation energies can be obtained for medium sized molecules with unprecedented efficiency. The algorithms are implemented into the ORCA electronic structure system.

GRB 060218: The Nature of the Optical‐UV Component

The optical-UV component in GRB 060218 is assumed to be due to optically thick cyclotron emission. The key aspect of this model is the high temperature of the absorbing electrons. The heat input derives from nuclei accelerated in semirelativistic internal shocks, like in ordinary gamma-ray bursts. Coulomb collisions transfer part of that energy to electrons. Inverse Compton cooling on the X-ray photons leads to electron temperatures around ~100 keV. Such a high brightness temperature for the optical-UV emission implies an emitting area roughly equal to that of the thermal X-ray component. This suggests a model in which the radio, optical-UV, and thermal X-ray emission are closely related. Although the optical-UV and thermal X-ray emission are two separate spectral components, it is argued that they both come from the photosphere of a quasi-spherical, continuous outflow, whose interaction with the circumstellar medium gives rise to the radio emission. The properties of GRB 060218, as measured in the comoving frame, are similar to those of ordinary gamma-ray bursts; i.e., the main difference is the much lower value of the bulk Lorentz factor in GRB 060218. The cyclotron absorption implies a magnetic field in rough equipartition with the matter energy density in the outflow. Hence, the magnetic field could have a dynamically important role, possibly with a magnetar as the central engine.