Non-monotonic Potential Research Articles

Non-monotonic potential description of α+209Bi elastic scattering

The present work reports the analyses of the experimental angular distributions of α+209Bi elastic scattering at Eα=19−104 MeV using the non-monotonic (NM) potential in the framework of optical model (OM). The NM potential is a complex shallow potential with a soft repulsive core in its real part which has its root in the energy-density functional theory of Brueckner et al. (1968) [28]. The data are analyzed using the real NM potentials of unshifted Gaussian repulsive core with D1=0 (Set-1) and shifted repulsive core with D1≠0 (Set-2) in conjunction with the empirically adjusted imaginary potentials. For both sets, the volume integral per nucleon pair, JR/(4A) for the real potential decreases in magnitude with the incident energy for the energy range considered in this study. The χ2 values and almost similar quality of fits to the experimental data using both the potential sets show that the scattering of α-particles from the 209Bi target is dominated by the potential in the surface region, and the scattering is insensitive to the potential in the central region of the 209Bi nucleus.

16O + 16O cluster states and their fusion to 32S: A non-monotonic potential description

Non-monotonic (NM) nucleus-nucleus potential families rooted in the Pauli-compliant Energy Density Functional (EDF) theory and especially their behavior at higher energies have been investigated using experimental data for 16O + 16O elastic scattering in the range . At , the 16O + 16O NM potentials in a simple optical model (OM) are found to support five rotational bands of 16O + 16O bound and quasi-molecular states in 32S with the cluster global quantum numbers G = 24, 26, 28, 30 and 32. The lowest band in the experimental spectrum starting at , and having , 2+, 4+, 6+ and 8+, has been located for the first time. In the simple OM, the NM potentials are found to reproduce the experimental 16O + 16O fusion cross-sections in the energy range 12–31 MeV. The present work shows that both the 16O + 16O cluster bands and fusion cross-sections in the Coulomb barrier region can be reproduced using NM potentials.

Analytic solution for the electrostatic potential of the solar wind

Context. Some kinetic models of the solar wind, such as the exospheric ones, make certain assumptions about the solar plasma, which for modelling purposes is generally considered collisionless and quasi-neutral. They also assume specific distribution functions for the electron and proton populations from which the fundamental properties of the plasma, including the density, are calculated using the moment integrals. Imposing the quasi-neutrality condition leads to the presence of an ambipolar electrostatic field, which is responsible for the acceleration of the wind. Usually, the calculation of the moment integrals is complicated by the fact that most kinetic models assume different trajectories for the solar wind components, separating the integrals into chunks corresponding to the pitch angles defining the trajectories. Hence, up to now all these integrals and therefore the plasma fundamental quantities have been calculated numerically. Aims. A new model is presented that makes use of similar assumptions to other kinetic collisionless models but does not need to impose the separation of the populations in different trajectories for the calculation of the integrals. As a consequence, an analytic solution for the electrostatic potential of the solar wind valid for all distances is found. Methods. A kinetic collisionless approach was used to characterise the solar wind plasma. A single equation for the electrostatic potential function was found assuming certain distribution functions (Maxwellian or non-thermal such as Kappa), which include an unknown electrostatic potential, calculating the density integral for those distribution functions and making those densities equal for electrons and protons. Results. An analytic solution for the electrostatic potential as a function of radial distance is found (for the first time for all distances) and shown to produce a non-monotonic total potential, which is compatible with other models like the exospheric ones whose electrostatic potential drives the acceleration of the solar wind. This expression can now be used, in a straightforward way, to provide insight into the importance of the electron distribution functions to shape the electrostatic potential of thermal solar-like outflows.

Dynamic electron correlations with charge order wavelength along all directions in the copper oxide plane

In strongly correlated systems the strength of Coulomb interactions between electrons, relative to their kinetic energy, plays a central role in determining their emergent quantum mechanical phases. We perform resonant x-ray scattering on Bi2Sr2CaCu2O8+δ, a prototypical cuprate superconductor, to probe electronic correlations within the CuO2 plane. We discover a dynamic quasi-circular pattern in the x-y scattering plane with a radius that matches the wave vector magnitude of the well-known static charge order. Along with doping- and temperature-dependent measurements, our experiments reveal a picture of charge order competing with superconductivity where short-range domains along x and y can dynamically rotate into any other in-plane direction. This quasi-circular spectrum, a hallmark of Brazovskii-type fluctuations, has immediate consequences to our understanding of rotational and translational symmetry breaking in the cuprates. We discuss how the combination of short- and long-range Coulomb interactions results in an effective non-monotonic potential that may determine the quasi-circular pattern.

Non-monotonic nucleus-nucleus potential and incompressibility of infinite cold nuclear matter

A novel method for the determination of the yet not well-known quantity of nuclear incompressibility, K is presented. Non-monotonic (NM) nucleus-nucleus potentials from the energy-density functional (EDF) theory including the Pauli principle have been considered for K in the range 188-266 MeV. The experimental cross sections of 16O+16O elastic scattering over the 31-350 MeV incident energies have been analyzed in the optical model using the NM potentials. Sensitivity of K on the elastic scattering data is studied and its value for infinite cold nuclear matter deduced to be 222 ± 5 MeV

Non-monotonic shallow nucleus-nucleus potential for heavy-ion elastic scattering2

‘Goldberg criterion’ [Goldberg and Smith, Phys. Rev. Lett. 29 (1972) 500] tells that at sufficiently high energies, where pronounced refractive scattering with nuclear rainbow oscillations are followed by an ‘exponential-type falloff’ in the angular distribution, discrete ambiguities are eliminated for the deep monotonic potential. The criterion is also confirmed in the work of Bartnitzky et al. [Phys. Lett. B 365 (1996) 23] on the 16O+16O elastic scattering in the energy range of 250 - 704 MeV. However, their finding ‘using model-independent potentials’ suggests that heavy-ion elastic scattering data unambiguously favour deep potentials. The Goldberg criterion is examined in our work for non-monotonic shallow potentials using the 16O+16O elastic scattering at energy region up to 350 MeV.

Non-monotonic potential description of alpha-40Carefractive elastic scattering

Experimental differential cross sections of elastic scattering by 40Ca, over a wide range of incident energies, have been analyzed in terms of non-monotonic (NM) potentials, generated from the energy density functional (EDF) theory using a realistic two-nucleon potential coupled with an appropriate consideration of the Pauli principle. The Airy structure of the nuclear rainbow scattering data in the energy range of 36.1–42.6 MeV is well accounted for the first time by the shallow NM potential.

Non-monotonic potential description of the cross-section, vector and tensor analyzing powers of the 6Li+12C elastic scattering at 30 and 50 MeV†

This work illustrates, for the first time, the analysis of tensor analyzing powers (T 20, T 21, T 22) along with the differential cross-section (CS) and the vector analyzing power iT 11 for the 6Li+12C elastic scattering at 30 and 50 MeVwithin the framework of an optical model (OM) using microscopic shallow non-monotonic (NM) potentials. The NM potential is generated from the energy density functional formalism (EDF) [Brueckner et al., Phys. Rev., 168 (1968) 1184] using a realistic two-nucleon interaction incorporating Pauli Exclusion principle. The shallow NM potential can describe the experimental angular distributions of CS and analyzing powers of the elastic scattering data. The OM analysis of the data at this energy does not indicate their sensitivity on the nuclear matter incompressibility K.

Cross-section, vector and tensor analyzing powers of the 6Li + 12C elastic scattering at 30 and 50 MeV: a non-monotonic potential description

This work reports, for the first time, the analysis of tensor analyzing powers (T20, T21, T22) along with the differential cross-section (CS) and the vector analyzing power iT11 for the 6Li + 12C elastic scattering at 30 and 50 MeV within the framework of an optical model (OM) using microscopic shallow non-monotonic (NM) potentials. The NM potential is generated from the energy density functional formalism (EDF) (Brueckner et al (1968) Phys. Rev. 168 1184) using a realistic two-nucleon interaction incorporating the Pauli exclusion principle. The shallow NM potential can describe the experimental angular distributions of CS and analyzing powers of the elastic scattering data. The OM analysis of the data at 30 and 50 MeV does not indicate their sensitivity on the nuclear matter incompressibility K.

Mesoscopic modeling and parameter estimation of a lithium-ion battery based on LiFePO4/graphite

A novel numerical model for simulating the behavior of lithium-ion batteries based on LiFePO4(LFP)/graphite is presented. The model is based on the modified Single Particle Model (SPM) coupled to a mesoscopic approach for the LFP electrode. The model comprises one representative spherical particle as the graphite electrode, and N LFP units as the positive electrode. All the SPM equations are retained to model the negative electrode performance. The mesoscopic model rests on non-equilibrium thermodynamic conditions and uses a non-monotonic open circuit potential for each unit. A parameter estimation study is also carried out to identify all the parameters needed for the model. The unknown parameters are the solid diffusion coefficient of the negative electrode (Ds,n), reaction-rate constant of the negative electrode (Kn), negative and positive electrode porosity (εn&εn), initial State-Of-Charge of the negative electrode (SOCn,0), initial partial composition of the LFP units (yk,0), minimum and maximum resistance of the LFP units (Rmin&Rmax), and solution resistance (Rcell). The results show that the mesoscopic model can simulate successfully the electrochemical behavior of lithium-ion batteries at low and high charge/discharge rates. The model also describes adequately the lithiation/delithiation of the LFP particles, however, it is computationally expensive compared to macro-based models.

Comprehensive Study of the Polarization Behavior of LiFePO4 Electrodes Based on a Many-Particle Model

The unique polarization behavior of LiFePO4 electrodes was investigated using mathematical simulations with a many-particle model, which have a non-monotonic potential profile for each LiFePO4 particle, and analyzed by the active population concept. The present simulations reveal two known polarization behaviors, namely the memory effect and path dependence. Notably, a hitherto unknown polarization behavior, the so-called relaxation-induced polarization (RIP), was also identified. The memory effect requires, at a minimum, a sequential four-step operation. By comparison, RIP is triggered only by a one-step operation, namely a long rest. In effect, the polarization associated with the memory effect and RIP was caused by a reduction of the active particles in the two-phase region via relaxation during a rest. The path-dependence mechanism was attributed to kinetically inhomogeneous reactions for each particle. We further found that narrowing the particle size distribution was an effective means to reduce polarization viz. the memory effect and path dependence of LiFePO4 electrodes. However, RIP could not be suppressed by narrowing the particle size distribution. A comprehensive understanding of these polarization behaviors with our model provides a more accurate way to estimate the state of charge in Li-ion batteries with LiFePO4 electrodes.

Kinetic features of collisionless sheaths around polarized cylindrical emitters from the orbital motion theory

The kinetic features of the sheath around a cylindrical emitter immersed in collisionless plasma at rest are analysed. After finding self-consistently the electric potential by applying the Orbital Motion Theory to the Vlasov-Poisson system, the local distribution functions are reconstructed and the radial profiles of important macroscopic quantities (plasma densities, currents, and temperatures) are then computed. It is found that there can only be three kinds of holes that are bound by three different boundaries—two related to the constraints from orbital effects and the other due to the electric potential barrier. The results are presented for three regimes: negative probe bias with monotonic and non-monotonic potential and positive probe bias with non-monotonic potential. To understand the variation of macroscopic-quantity radial profiles, three diagrams are presented for kinetic features: the ϵl-diagram for the integration domains of the two orbital invariants, the effective potential, and the local ...

One-dimensional plasma sheath model in front of the divertor plates

A new model of the stationary electrostatic plasma sheath in front of divertor plates is developed, which takes into account strong inelastic processes. Using particle-in-cell simulations and analytic estimates it is demonstrated, that the properties of the tokamak divertor plasma sheath can significantly deviate from the properties of the classical sheath model. The most significant deviations are the increased energy flux to the plates and non-monotonic potential and ion velocity profiles in the presheath. Two main reasons for these deviations are identified: strong inelastic collisionality of the plasma presheath and the presence of super-thermal plasma particles originating from the upstream scrape-off layer.

Existence of a virtual cathode close to a strongly electron emissive wall in low density plasmas

The interaction between an electron emissive wall, electrically biased in a plasma, is revisited through a simple fluid model. We search for realistic conditions of the existence of a non-monotonic plasma potential profile with a virtual cathode as it is observed in several experiments. We mainly focus our attention on thermionic emission related to the operation of emissive probes for plasma diagnostics, although most conclusions also apply to other electron emission processes. An extended Bohm criterion is derived involving the ratio between the two different electron densities at the potential minimum and at the background plasma. The model allows a phase-diagram analysis, which confirms the existence of the non-monotonic potential profiles with a virtual cathode. This analysis shows that the formation of the potential well critically depends on the emitted electron current and on the velocity at the sheath edge of cold ions flowing from the bulk plasma. As a consequence, a threshold value of the governing parameter is required, in accordance to the physical nature of the electron emission process. The latter is a threshold wall temperature in the case of thermionic electrons. Experimental evidence supports our numerical calculations of this threshold temperature. Besides this, the potential well becomes deeper with increasing electron emission, retaining a fraction of the released current which limits the extent of the bulk plasma perturbation. This noninvasive property would explain the reliable measurements of plasma potential by using the floating potential method of emissive probes operating in the so-called strong emission regime.

Non-monotonic potentials above the day-side lunar surface exposed to the solar radiation

Basic equations describing stable non-monotonic altitude profiles of the electric potential arising near the Moon׳s surface due to the joint action of solar ultraviolet radiation and interactions with the plasma environment are obtained for two cases: the surface is in the solar wind and the surface is exposed to the terrestrial plasma sheet. The influence of the solar wind on the non-monotonic potential is investigated in a wide range of drift velocities for different values of the photoelectron density. It is found that for any photoelectron density the surface potential reaches its minimum value for a slow solar wind. This effect is most pronounced for the lunar regolith regions not enriched with hydrogen. When the Moon is exposed to both solar radiation and the terrestrial plasma sheet, the surface potential and the potential minimum are calculated as functions of the ion and electron temperatures for different values of the photoelectron density. It is shown that both potentials depend strongly on the temperature of plasma sheet populations, particularly in the range where the ratio of the ion temperature to the electron temperature is less than three.

The Delithiation Behavior of LiFePO4 Particles with Broad Particle Size Distribution during Chemically Delithiation

LiFePO4 is the most promising cathode material, especially for electric vehicle (EV) because of its inexpensive cost, superior thermal and structural safety, and non-toxicity. Although LiFePO4 has been believed to be poor conductor due to its low electronic conductivity and 1D lithium diffusion, nano-sized LiFePO4 shows the fastest electrochemical reaction during charge and discharge.To understand these intriguing behaviors, we have to consider delithiation behavior of particles in the electrode which consists of 1010 ~ 1017 particles in addition to the transport properties in the material because a particle has a non-monotonic chemical potential[1]. The non-monotonic chemical potential of single particle in multi-particle electrode leads to characteristic electrochemical behaviors such as a flat potential in voltage curve of the electrode and a sequential phase transformation between particles. Thus, delithiation behaviors in a particle in the electrode should be understood.In this study, we will explore delithiation behaviors of LiFePO4 with broad particle size distribution. For this purpose, chemical delithiation and followed centrifuge method were applied to understand the delithiation behavior of LiFePO4 depending on particle size. This simple method shows phase transformation behaviors more directly. We synthesized LiFePO4 with broad particle size distribution by solid state reaction. And then, we can easily separate chemically delithiated small and large particles by centrifuge method. In this talk, we will introduce simple centrifuge method and will discuss about delithiation behavior of LiFePO4 with broad particle size distribution during chemical delithiation.[1] W. Dreyer et al 2010 The thermodynamic origin of hysteresis in insertion batteries Nature Mat. 9, 448.

Non-monotonic potential description of alpha–Zr refractive elastic scattering

Experimental differential cross sections of α elastic scattering by 90Zr in the 15.0–141.7 MeV range of the bombarding energies have been analysed within the framework of an optical model using non-monotonic (NM) potentials. These potentials are generated from the energy-density functional theory using a realistic two-nucleon potential coupled with an appropriate consideration of the Pauli principle. The NM nature of the real part of the potential seems to be gradually diminishing at energies beyond 118.0 MeV. The Airy structure of the nuclear rainbow scattering data in the energy range of 79.5–141.7 MeV is for the first time well accounted for by the shallow NM potential. Two potential families, which are located in the real part, bear a linear variation of a volume integral in the energy range 25.0–141.7 MeV with a threshold anomaly at the lower energies. The potential contains an interior repulsive part that, with energy, shifts towards the surface and gradually weakens until it is almost lost in the nuclear surface. The requirement of a deep attractive real part of the nuclear potential seems to be generally non-stringent for describing the nuclear rainbow oscillations. Some discrete ambiguities in the potentials seem to persist even when the ‘exponential falloff’ in the angular distribution following the ‘rainbow angle’ is well reproduced in this investigation using the NM real part of the optical potentials.

Non-monotonic potentials for 6Li elastic scattering at 88 MeV

This work compares the performance of the traditional phenomenological Woods–Saxon (WS) and squared WS (SWS) potentials with that of a non-monotonic (NM) potential, for 6Li elastic scattering by targets of a wide range, namely 24,25,26Mg, 27Al, 40,44Ca, 59Co, 60Ni, 197Au and 206,208Pb at an incident energy of 88 MeV. The real part of this NM potential is derived microscopically using the energy-density functional (EDF) formalism, from a realistic two-nucleon potential, that includes the Pauli principle. The experimental differential cross sections (DCSs) for the 6Li elastic scattering are well accounted for using this raw EDF-generated real part along with an empirical imaginary part, referred to as the NM-1 potential, which needs no renormalization. To make this potential more consistent in terms of the variations of the volume integrals per nucleon pair of its real part with the target mass numbers, a completely empirical NM potential, referred to as the NM-2 potential, is derived that fits the data more satisfactorily. The DCS data are also well described by the SWS and WS potentials. However, the SWS potential is found to be inconsistent in terms of the above-mentioned criterion and the NM-2 potential has an edge over all the potentials.

Dynamics of levitating dust particles near asteroids and the Moon

Using a numerically modeled nonmonotonic potential profile plasma sheath, we identify the equilibrium height and charge of levitating dust particles for nanometer to 10 µm sized particles over a five order of magnitude variation in the gravity of an airless central body. The stability and time scales of the dust particle motion about the equilibria are computed. The range of initial velocities that results in levitation of a dust particle is dominated by the particle size and is relatively insensitive to the mass of the central body and the particle's charge. By studying the dynamics of levitating dust particles, we are able to move beyond the point solutions that have been previously considered. This work enables more complete evaluations of the importance of dust levitation in the evolution of airless bodies and the hazard that levitating dust particles pose to exploration vehicles.

Analysis of pattern formation in systems with competing range interactions

We analyzed pattern formation and identified various morphologies in a system of particles interacting through a non-monotonic potential with a competing range interaction characterized by a repulsive core (r < rc) and an attractive tail (r > rc), using molecular-dynamics simulations. Depending on parameters, the interaction potential models the inter-particle interaction in various physical systems ranging from atoms, molecules and colloids to vortices in low κ type-II superconductors and in recently discovered ‘type-1.5’ superconductors. We constructed a ‘morphology diagram’ in the plane ‘critical radius rc–density n’ and proposed a new approach to characterizing the different types of patterns. Namely, we elaborated a set of quantitative criteria in order to identify the different pattern types, using the radial distribution function (RDF), the local density function and the occupation factor.