Born Contribution Research Articles

Competition between Born solvation, dielectric exclusion, and Coulomb attraction in spherical nanopores.

The recent measurement of a very low dielectric constant, ε, of water confined in nanometric slit pores leads us to reconsider the physical basis of ion partitioning into nanopores. For confined ions in chemical equilibrium with a bulk of dielectric constant ε_{b}>ε, three physical mechanisms, at the origin of ion exclusion in nanopores, are expected to be modified due to this dielectric mismatch: dielectric exclusion at the water-pore interface (with membrane dielectric constant, ε_{m}<ε), the solvation energy related to the difference in Debye-Hückel screening parameters in the pore, κ, and in the bulk κ_{b}, and the classical Born solvation self-energy proportional to ε^{-1}-ε_{b}^{-1}. Our goal is to clarify the interplay between these three mechanisms and investigate the role played by the Born contribution in ionic liquid-vapor (LV) phase separation in confined geometries. We first compute analytically the potential of mean force (PMF) of an ion of radius R_{i} located at the center of a nanometric spherical pore of radius R. Computing the variational grand potential for a solution of confined ions, we then deduce the partition coefficients of ions in the pore versus R and the bulk electrolyte concentration ρ_{b}. We show how the ionic LV transition, directly induced by the abrupt change of the dielectric contribution of the PMF with κ, is favored by the Born self-energy and explore the decrease of the concentration in the pore with ε both in the vapor and liquid states. Phase diagrams are established for various parameter values and we show that a signature of this phase transition can be detected by monitoring the total osmotic pressure as a function of R. For charged nanopores, these exclusion effects compete with the electrostatic attraction that imposes the entry of counterions into the pore to enforce electroneutrality. This study will therefore help in deciphering the respective roles of the Born self-energy and dielectric mismatch in experiments and simulations of ionic transport through nanopores.

EPC-SAFT advanced - Part I: Physical meaning of including a concentration-dependent dielectric constant in the born term and in the Debye-Hückel theory

The transition from aqueous electrolyte systems to non-aqueous electrolyte systems is highly demanded in industrial applications and especially challenging for physics-based thermodynamic models. Electrolyte thermodynamics is a complex matter, and still not all physico-chemical effects are accounted for in state-of-the-art equations of state. The dielectric constant of non-aqueous electrolyte systems changes drastically compared to aqueous systems. One main consequence is that ions are very differently solvated in non-aqueous medium compared to aqueous medium. The Born term represents a methodology to account for the influence of solvation energies of ions, which is based on influences of solvent and salt on the dielectric constant. Utilizing the Born term in electrolyte models is extensively debated, and it is often reasonably neglected in predominantly aqueous systems. Yet, it has a significant influence on transferability from aqueous to non-aqueous media i.e., systems with a large difference in polarity or permittivity compared to aqueous systems. In this work, a modified Born term was combined with electrolyte Perturbed-Chain Statistical Associating Fluid Theory (ePC-SAFT) by introducing additionally a salt concentration-dependent dielectric constant, henceforth called altered Born contribution. The new methodology was validated against infinite dilution properties for ion-solvent interactions: Gibbs energy of hydration and Gibbs energy of transfer of alkali halides from water to alcoholic solvents. Further, mean ionic activity coefficients (MIACs) of alkali halides in alcoholic solvents were quantitatively correct predicted with the advanced ePC-SAFT approach. Original ePC-SAFT parameters were applied for all predictions, and no further binary parameters were adjusted. Based on the success of the model predictions, the transferability of pure-ion ePC-SAFT parameters to organic solvents was verified and the incorporation of concentration-dependent dielectric constant into the altered Born contribution and Debye-Hückel theory was proven to be meaningful methods for the transfer of electrolyte thermodynamic models from aqueous to non-aqueous systems.

Anomalous Hall effect in semiconductor quantum wells in proximity to chiral p -wave superconductors

By using the gauge-invariant optical Bloch equation, we perform a microscopic kinetic investigation on the anomalous Hall effect in chiral p-wave superconducting states. Specifically, the intrinsic anomalous Hall conductivity in the absence of the magnetic field is zero as a consequence of Galilean invariance in our description. As for the extrinsic channel, a finite anomalous Hall current is obtained from the impurity scattering with the optically excited normal quasiparticle current even at zero temperature. From our kinetic description, it can be clearly seen that the excited normal quasiparticle current is due to an induced center-of-mass momentum of Cooper pairs through the acceleration driven by ac electric field. For the induced anomalous Hall current, we show that the conventional skew-scattering channel in the linear response makes the dominant contribution in the strong impurity interaction. In this case, our kinetic description as a supplementary viewpoint mostly confirms the results of Kubo formalism in the literature. Nevertheless, in the weak impurity interaction, this skew-scattering channel becomes marginal and we reveal that a novel induction channel from the Born contribution dominates the anomalous Hall current. This novel channel, which has long been overlooked in the literature, is due to the particle-hole asymmetry by nonlinear optical excitation. Finally, we study the case in the chiral p-wave superconducting state with a transverse conical magnetization, which breaks the Galilean invariance. In this situation, the intrinsic anomalous Hall conductivity is no longer zero. Comparison of this intrinsic channel with the extrinsic one from impurity scattering is addressed.

Development of intermolecular potential models for electrolyte solutions using an electrolyte SAFT-VR Mie equation of state

ABSTRACTWe present a theoretical framework and parameterisation of intermolecular potentials for aqueous electrolyte solutions using the statistical associating fluid theory based on the Mie interaction potential (SAFT-VR Mie), coupled with the primitive, non-restricted mean-spherical approximation (MSA) for electrolytes. In common with other SAFT approaches, water is modelled as a spherical molecule with four off-centre association sites to represent the hydrogen-bonding interactions; the repulsive and dispersive interactions between the molecular cores are represented with a potential of the Mie (generalised Lennard-Jones) form. The ionic species are modelled as fully dissociated, and each ion is treated as spherical: Coulombic ion–ion interactions are included at the centre of a Mie core; the ion–water interactions are also modelled with a Mie potential without an explicit treatment of ion–dipole interaction. A Born contribution to the Helmholtz free energy of the system is included to account for the process of charging the ions in the aqueous dielectric medium. The parameterisation of the ion potential models is simplified by representing the ion–ion dispersive interaction energies with a modified version of the London theory for the unlike attractions. By combining the Shannon estimates of the size of the ionic species with the Born cavity size reported by Rashin and Honig, the parameterisation of the model is reduced to the determination of a single ion–solvent attractive interaction parameter. The resulting SAFT-VRE Mie parameter sets allow one to accurately reproduce the densities, vapour pressures, and osmotic coefficients for a broad variety of aqueous electrolyte solutions; the activity coefficients of the ions, which are not used in the parameterisation of the models, are also found to be in good agreement with the experimental data. The models are shown to be reliable beyond the molality range considered during parameter estimation. The inclusion of the Born free-energy contribution, together with appropriate estimates for the size of the ionic cavity, allows for accurate predictions of the Gibbs free energy of solvation of the ionic species considered. The solubility limits are also predicted for a number of salts; in cases where reliable reference data are available the predictions are in good agreement with experiment.

Relevance of two-boson exchange effect in quasi-elastic charged current neutrino–nucleon interaction

Two-boson exchange (TBE) correction in νn→l−p and ν¯p→l+n reactions is estimated. The TBE contribution is given by Wγ box diagrams. The calculations are performed for 1 GeV neutrinos and for the MiniBooNE and the T2K energy spectra. The TBE correction to the total cross section is of the order of 2–4% (with respect to the Born contribution) in the case of νe and ν¯e and 1–2% in the case of νμ and ν¯μ.

Thermodynamic properties of aqueous solutions of single and multiple salts using the Q-electrolattice equation of state

Thermodynamic property calculations of solutions containing electrolytes are relevant to design and optimize industrial process, among which water desalination. The conventional way of designing such processes relies on specific models or correlations for vapor pressure, density, osmotic coefficient, and mean ionic activity coefficient. Nonetheless, an equation of state (EOS) for electrolyte solutions enables, in principle, the evaluation of all of them. In previous work, the electrolattice EOS was presented, being composed by three terms: the Mattedi–Tavares–Castier (MTC) lattice-based contribution, the Born contribution, and an explicit mean spherical approximation (MSA) for ions of equal diameters. In the present work, an explicit MSA term suitable for ions of unequal diameters is used instead, along with new water parameters and two adjustable parameters per ion. The new expression for the Helmholtz energy, referred to as Q-electrolattice model, is used to correlate mean ionic activity coefficients and densities in strong 78 single-salt aqueous solutions. Additionally, calculations of vapor pressure, osmotic coefficient, and apparent molar volume of salt are performed. Predictions of thermodynamic properties for aqueous solutions containing multiple salts and seawater are also presented without using any additional adjustable parameter.

Calculation of phase behavior and chemical transformations in H2O-NH3-CO2 system using a modified hole quasichemical model

A technique for calculation of phase equilibria over a wide range of temperatures and pressures for fluid systems, where chemical interactions lead to the formation of ionic species, was developed. A hole quasichemical model was modified to account for chemical reactions and electrostatic interactions in the liquid phase. The densities and dielectric permittivity as function of a solution composition was taken into account in describing the electrostatic contribution to the Gibbs energy (Pitzer approximation) and Born contribution, that is required for thermodynamic consistency of simulation results. A method of assessing the appropriate relationships for mixtures of ammonia-water and ternary solutions was suggested. Calculations of the phase behavior of the H2O-NH3 system in the entire range of concentrations in the temperature interval 373–588 K at pressures up to 200 bar, and also of H2O-NH3-CO2 system containing NH3 to 30 mol% and CO2 up to 14 mol% in the temperature range 373–473 K at pressures to 88 bar gave satisfactory agreement with experimental data. Concentrations of the molecular and ionic individuals in the liquid phase, depending on the overall composition of the mixture were evaluated.

CP violation in Compton scattering

I consider Compton scattering off the nucleon in the presence of T violation. I construct the Compton tensor that possesses these features and consider low-energy expansion of the corresponding amplitudes. It allows separation of the Born contribution that depends only on the static properties of the nucleon, such as the electric charge, the mass, the magnetic moment, and the electric dipole moment. I introduce new structure constants, the T-odd nucleon polarizabilities that parametrize the unknown non-Born part. These constants describe the response of the T-violating content of the nucleon to the external quasistatic electromagnetic field. As an estimate, I provide a heavy-baryon ChPT calculation for these new polarizabilities and discuss the implications for the experiment.

Mechanical heterogeneity in nanoscale films of liquid silica

Molecular dynamics simulations are carried out for slabs of silica liquid with thicknesses between 1 and 3 nm . A local analysis of the Born contribution to the elastic modulus, CB, shows that the elasticity is not uniform throughout the slabs--CB is identical to that of bulk silica in the slab interior, but CB is larger at the slab edges. The larger CB at the slab edges is due to a distinct atomic level structure characterized by larger density, larger concentration of more highly coordinated ions, and smaller silica rings.

Extraction of proton form factors in the timelike region from single-polarizede+e−→p→p¯events

We have performed numerical simulations of the single-polarized ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{p}\overline{p}$ process in kinematic conditions under discussion for a possible upgrade of the existing DAFNE facility. By fitting the cross section and spin asymmetry angular distributions with typical Born expressions, we can study the conditions for extracting information on moduli and phases of the proton electromagnetic form factors in the timelike region, which are poorly known and whose preliminary data show puzzling features. We have explored also non-Born contributions by introducing a further component in the angular fit, which is related to two-photon exchange diagrams. Using a dipole parametrization, we show that these corrections can be identified if larger than 5% of the Born contribution; we also explore the conditions for extracting information on the phase and, consequently, on the relative weight between their real and imaginary parts, which are presently unknown.

Extraction of proton form factors in the timelike region from unpolarizede+e−→pp¯events

We have performed numerical simulations of the unpolarized ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}p\overline{p}$ process in kinematic conditions under discussion for a possible upgrade of the existing DAFNE facility. By fitting the cross section angular distribution with a typical Born expression, we can extract information on the ratio $|{G}_{E}/{G}_{M}|$ of the proton electromagnetic form factors in the timelike region within a 5%--10% uncertainty. We have explored also non-Born contributions to the cross section by introducing a further component in the angular fit, which is related to two-photon exchange diagrams. We show that these corrections can be identified if larger than 5% of the Born contribution, and if relative phases of the complex form factors do not produce severe cancellations.

Energy of an ion crossing a low dielectric membrane: the role of dispersion self-free energy

The Born charging equation predicts that the permeability of a cell membrane to ions by the solubility-diffusion mechanism depends on the ionic radius and on the dielectric constant of the membrane. However, experiments, for example, on red blood cells and on lysosome membranes, show that the permeability depends strongly on the choice of salt anion in a way that cannot be accommodated by differences in ionic size. We demonstrate that one step towards understanding this ion specificity is to take account of the previously ignored dispersion self-free energy of the ion. This is the quantum electrodynamic analogue of the (electrostatic) Born self-energy of an ion. We show that the dispersion self-free energy contribution can be and often is of the same order of magnitude as the Born contribution. To understand the observed specificity, it is essential to take into account of both ionic size and ionic polarizability. In parallel and to reinforce these observations, we also give simple estimates for how self-free energy changes that occur when an ion moves into the air–water interface region (which has a density profile for water molecules) can influence the surface tension of salt solutions. Consistency can be found between the Hofmeister sequences observed in ion permeation and in surface tension of electrolytes when these previously ignored self-free energies are included properly.

Comparing phenomenological recipes with a microscopic model for the electric amplitude in strangeness photoproduction

Corrections to the Born approximation in photo-induced strangeness production off a proton are calculated in a semi-realistic microscopic model. The vertex corrections and internal contributions to the amplitude of the $\gamma p \to K^+ \Lambda$ reaction are included on the one-loop level. Different gauge-invariant phenomenological prescriptions for the modification of the Born contribution via the introduction of form factors and contact terms are discussed. In particular, it is shown that the popular minimal-substitution method of Ohta corresponds to a special limit of the more realistic approach.

Appearance and disappearance of the second Born effects in the(e,3e)reaction on He

We demonstrate, both experimentally and theoretically, clear manifestation of the second Born effects in the angular distributions of two ejected electrons produced by a 500 eV electron impact on the He atom in the so-called (e,3e) reaction. The second Born contribution, due to subsequent interaction of the projectile with the target, is most prominent for glancing collisions with small momentum transfer. However, these effects are absent for hard knock-out collisions with large momentum transfer.

Rescattering corrections in elastic scattering

A detailed study of the rescattering series is performed within a model, using a generalized procedure of eikonalization and fitted to the $pp$ and $\bar pp$ elastic scattering data. We estimate and compare the various rescattering corrections to be added to the Born contribution in the amplitude. We find that their number is finite, whereas it increases with the energy and the transfer, like does their importance. In the domain where data exist, we find also that a correct computation must include, at least, all two- and three-Reggeon exchanges and some four- and five-Reggeon exchanges. Any approximation aiming to reduce this (large) number of exchange would be hazardous, especially when extrapolating. We extend our estimates in the domain of future experiments.

Two photons plus jet at LHC: the NNLO contribution from the gg initiated process

The production of the Standard Model Higgs boson of mass ≈100–140 GeV at the LHC likely gives clear signals in the γγ (1) and in the γγ jet (2) channels. The quantitative evaluation of the background to channel (1) is very hard since the next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) QCD corrections are large. In particular, the contributions of the NNLO QCD subprocess gg→ γγ to inclusive γγ production is comparable to the contribution of the leading order subprocess q q ̄ →γγ . The quantitative description of the background to channel (1), therefore, requires to calculate all corrections up to the NNNLO level. In this letter we present results on the contribution of the NNLO QCD subprocess gg→ gγγ to the production rate of channel (2). We have found that in this case this NNLO contribution is less than 20% of the Born contribution. Since the NNLO contributions will likely be dominated by this subprocess one can argue that in the case of channel (2) – contrary to the case of channel (1) – a quantitative description of the background can be achieved already at next-to-leading order accuracy.

Production of e+e− pairs to all orders in Zα for collisions of high-energy muons with heavy nuclei

The e + e − pair production in collisions of muons with atoms is considered to all orders in the parameter Zα. We obtain the energy distribution of e + and e − as well as the energy loss of muons passing through matter with heavy atoms. The found corrections to the Born contribution do not depend on the details of the target properties except of a simple factor. For the considered example of Pb target the muon energy loss corrections vary from −65% to −10% depending on the pair energy.

Polarization asymmetry zero in heavy quark photoproduction and leptoproduction

We demonstrate two novel features of the sea-quark contributions to the polarized structure functions and photoproduction cross sections, a zero sum rule and a zero crossing point of the polarization asymmetry, which can be traced directly to the dynamics of the perturbative tree-graph gluon-splitting contributions. In particular, we show that the Born contribution of massive quarks arising from photon-gluon fusion gives zero contribution to the logarithmic integral over the polarization asymmetry $\int {d\nu \over \nu}\Delta \sigma(\nu,Q^2)$ for any photon virtuality. The vanishing of this integral in the Bjorken scaling limit then implies a zero gluon-splitting Born contribution to the Gourdin-Ellis-Jaffe sum rule for polarized structure functions from massive sea quarks. The vanishing of the polarization asymmetry at or near the canonical position predicted by perturbative QCD provides an important tool for verifying the dominance of the photon-gluon fusion contribution to charm photoproduction and for validating the effectiveness of this process as a measure of the gluon polarization $\Delta G(x,Q^2)$ in the nucleon. The displacement of the asymmetry zero from its canonical position is sensitive to the virtuality of the gluon in the photon-gluon fusion subprocess, and it can provide a measure of intrinsic and higher-order sea quark contributions.

QCD corrections to heavy quark pair production in polarized gamma gamma collisions and the intermediate-mass Higgs boson signal.

Perturbative QCD one-loop corrections to the cross sections of the $b\bar b$ $(c\bar c)$ quark pair production in polarized photon-photon collisions, as well as cross sections of the radiative processes photon-photon ->$b\bar b g$,$c\bar c g$ leading to two- and three-jet final states are calculated. It is shown that the signal from the intermediate mass Higgs boson is observable and precise measurements of the Higgs boson two-photon width are possible at a photon-photon collider, although the statistical significance is substantially reduced with respect to the tree level calculations. We demonstrate that virtual corrections are of the same order or larger than the Born contribution in the $J_z=0$ channel at high energy for small values of the cutoff $y_{cut}$, separating two-jet from three-jet topologies. The nature of these large corrections is elucidated. For $b\bar b$ pair production at $\sqrt{s_{\gamma\gamma}}\sim 100$~GeV and for small values of $y_{cut}\leq 0.04$ the higher order resummation of double logarithmic terms ${\cal O}\left(\alpha_s m_b^2/s\ln^2(s/m_b^2)\right)$ is needed.

Calculating QCD corrections to single top production in hadronic interactions

We give a detailed exposé on the calculation of O( α s ) corrections to the cross section for the semiweak production of single top quarks in hadronic interactions. After introducing the different sub-processes and defining their kinematics, we briefly recall the computation of the O(α 2) qb → q′t and O(α sα 2) qg → q′t b Born amplitudes squared. Next, the calculation of virtual and bremsstrahlung corrections is presented. We adopt a massive quark and massive gluon regularisation scheme. We explicitly demonstrate cancellations among various radiative corrections and we describe the procedure of absorbing remaining singularities in the parton density distribution functions. Finally, numerical results are given. We find a cross-section enhancement of roughly 30% (for m t ≈ 174 GeV/ c 2) with respect to the Born contribution. We observe good agreement between the exact calculation and the approach where the mass singularity is subtracted from the sum of the O( α 2) and O( α s α 2) tree-level expressions.