Repulsive Core Research Articles

Marchenko method with incomplete data and singular nucleon scattering

We apply the Marchenko method of quantum inverse scattering to study nucleon scattering problems. Assuming a $\beta/r^2$ type repulsive core and comparing our results to the Reid93 phenomenological potential we estimate the constant $\beta$, determining the singularity strength, in various spin/isospin channels. Instead of using Bargmann type S-matrices which allows only integer singularity strength, here we consider an analytical approach based on the incomplete data method, which is suitable for fractional singularity strengths as well.

Random phase approximation for the non-uniform Yukawa fluid

Mean-field density functional theory can be used to estimate the free energy of non-uniform fluids. The second functional derivative with respect to density of the free energy is related to the direct correlation function of the fluid and, in principle, this can be inverted to find an improved approximation for the pair correlation function and hence the free energy, the so-called ‘random phase approximation’. If the repulsive molecular interaction is approximated by the local density approximation and the attractive interaction is assumed to be of the Yukawa form, the problem reduces to that of finding the eigenvalues of Schrödinger-like equations, which, for certain models (such as the ‘Φ4 model’), can be done analytically in the planar case. The relationship between this approach and field theoretical treatment of the vapour-liquid interface is discussed. The ultraviolet divergence of the expression can be eliminated by separating the first term in the expansion, although quantitative results still depend on the behaviour of the attractive potential in the repulsive core. In the case of a spherical droplet of radius R, correction terms to the free energy involving lnR appear due to (i) cluster translational invariance, (ii) the unstable mode corresponding to droplet growth, and (iii) capillary waves. The net effect of these terms is to modify the classical expression for the nucleation rate by a factor proportional to R4/3.

Assessing Pair Interaction Potentials of Nanoparticles on Liquid Interfaces.

The pair interaction potentials of polymer-grafted silica nanoparticles (NPs) at liquid surfaces were determined by scanning electron microscopy, exploiting the nonvolatility of ionic liquids to stabilize the specimens against microscope vacuum. Even at near contact, individual, two-dimensionally well-dispersed NPs were resolved. The potential of mean force, reduced to the pair interaction potential for dilute NPs, was extracted with good accuracy from the radial distribution function, as both NP diameter and grafted polymer chain length were varied. While NP polydispersity somewhat broadened the core repulsion, the pair potential well-approximated a hard sphere interaction, making these systems suitable for model studies of interfacially bound NPs. For short (5 kDa) poly(ethylene glycol) ligands, a weak (< kB T) long-range attraction was discerned, and for ligands of identical length, pair potentials overlapped for NPs of different diameter; the attraction is suggested to arise from ligand-induced menisci. To understand better the interactions underlying the pair potential, NP surface-binding energies were measured by interfacial tensiometry, and NP contact angles were assessed by atomic force microscopy and transmission electron microscopy.

The Induced Surface Tension Contribution for the Equation of State of Neutron Stars

Abstract We apply a novel equation of state (EoS) that includes the surface tension contribution induced by interparticle interaction and asymmetry between neutrons and protons, to the study of neutron star (NS) properties. This elaborated EoS is obtained from the virial expansion applied to multicomponent particle mixtures with hard core repulsion. The considered model is in full concordance with all the known properties of normal nuclear matter, provides a high-quality description of the proton flow constraints, hadron multiplicities created during the nuclear–nuclear collision experiments, and equally is consistent with astrophysical data coming from NS observations. The analysis suggests that the best model parameterization gives the incompressibility factor K 0, symmetry energy J, and symmetry energy slope L at normal nuclear density equal to 200 MeV, 30 MeV, and 113.28–114.91 MeV, respectively. The mass–radius relations found for NSs computed with this EoS are consistent with astrophysical observations.

Microscopic Theory of Two-Step Yielding in Attractive Colloids.

Attractive colloids display two distinct amorphous solid phases: the attractive glass due to particle bonding and the repulsive glass due to the hard-core repulsion. By means of a microscopic mean field approach, we analyze their response to a quasistatic shear strain. We find that the presence of two distinct interaction length scales may result in a sharp two-step yielding process, which can be associated with a hysteretic stress response or with a reversible but nonmonotonic stress-strain curve. We derive a generic phase diagram characterized by two distinct yielding lines, an inverse yielding and a critical point separating the hysteretic and reversible regimes. Our results should be applicable to a large class of glassy materials characterized by two distinct interaction length scales.

A Schrödinger Potential Conditionally Integrable in Terms of the Hermite Functions

We introduce a biconfluent Heun potential well for the one-dimensional stationary Schrodinger equation which is composed of a confining fraction-power term and a repulsive centrifugal-barrier core. This is a conditionally integrable potential in that the strength of the centrifugal barrier is fixed to a constant. The potential supports a countable infinite number of bound states. We present the general solution of the Schrodinger equation, deduce the exact equation for the energy spectrumand derive a highly accurate approximation for energy levels. The bound state wave functions are written as irreducible linear combinations with constant coefficients of two Hermite functions of a scaled and shifted argument.

Improved nucleus–nucleus folding potential with a repulsive core due to the change of intrinsic kinetic energy

The change in the internal kinetic energy (KE) of two interacting nuclei grows by increasing their density overlap. We investigated to what extent the double-folding potential based on the density dependent M3Y nucleon–nucleon interaction can be improved by considering this repulsive KE. We adopted the α-decay of , the 24Ne decay of 232U, and the fusion cross section as examples of reactions involving density redistribution. We performed the α and cluster decay calculations based on solving the Schrödinger equation to find the wavefunction and the penetration probability. Upon normalizing the calculated KE by applying the Bohr–Sommerfeld quantization condition, the necessary missed pocket is physically developed in the internal region of the total folding potential. The folding potential improved by considering the pivotal repulsive KE reduced the uncertainty inherent in the decay calculations at small internuclear distances. The calculated fusion cross section is substantially improved and its steep falloff at sub-barrier energies is reasonably reproduced.

Neutron–proton scattering and singular potentials

We consider a Bargmann-type rational parametrization of the nucleon scattering phase shifts. Applying Marchenko’s method of quantum inverse scattering we show that the scattering data suggest a singular repulsive core of the potential of the form 2/r2 and 6/r2 in natural units, for the and channels, respectively. The simplest solution in the channel contains three parameters only but reproduces all features of the potential and bound state wave function within one percent error. We also consider the – coupled channel problem with the coupled channel Marchenko inversion method.

Role of Solute Attractive Forces in the Atomic-Scale Theory of Hydrophobic Effects.

The role that van der Waals (vdW) attractive forces play in the hydration and association of atomic hydrophobic solutes such as argon (Ar) in water is reanalyzed using the local molecular field (LMF) theory of those interactions. In this problem, solute vdW attractive forces can reduce or mask hydrophobic interactions as measured by contact peak heights of the ArAr correlation function compared to reference results for purely repulsive core solutes. Nevertheless, both systems exhibit a characteristic hydrophobic inverse temperature behavior in which hydrophobic association becomes stronger with increasing temperature through a moderate temperature range. The new theoretical approximation obtained here is remarkably simple and faithful to the statistical mechanical LMF assessment of the necessary force balance. Our results extend and significantly revise approximations made in a recent application of the LMF approach to this problem and, unexpectedly, support a theory of nearly 40 years ago.

How to simulate patchy particles⋆.

Patchy particles is the name given to a large class of systems of mesoscopic particles characterized by a repulsive core and a discrete number of short-range and highly directional interaction sites. Numerical simulations have contributed significantly to our understanding of the behaviour of patchy particles, but, although simple in principle, advanced simulation techniques are often required to sample the low temperatures and long time-scales associated with their self-assembly behaviour. In this work we review the most popular simulation techniques that have been used to study patchy particles, with a special focus on Monte Carlo methods. We cover many of the tools required to simulate patchy systems, from interaction potentials to biased moves, cluster moves, and free-energy methods. The review is complemented by an educationally oriented Monte Carlo computer code that implements all the techniques described in the text to simulate a well-known tetrahedral patchy particle model.

Recent theoretical advances regarding α-spectroscopy

We present an overview of a unified description of the structure and α-emission properties of even-even nuclei. The low-energy spectrum relevant for α-emission is described within the framework of the Coherent State Model (CSM). The treatment of the α-emission process is based on an α-daughter interaction containing a monopole component, calculated through a double folding procedure with a M3Y interaction plus a repulsive core simulating the Pauli principle, and a quadrupole-quadrupole (QQ) interaction. The decaying states are identified with the lowest narrow outgoing resonances obtained through the coupled channels method. The α-branching ratio to the first excited state is reproduced by means of the QQ strength. Simultaneously, a reasonable agreement is obtained for the α-branching ratios to the second and third excited states.

A Conditionally Integrable Bi-confluent Heun Potential Involving Inverse Square Root and Centrifugal Barrier Terms

Abstract We present a conditionally integrable potential, belonging to the bi-confluent Heun class, for which the Schrödinger equation is solved in terms of the confluent hypergeometric functions. The potential involves an attractive inverse square root term ~x −1/2 with arbitrary strength and a repulsive centrifugal barrier core ~x −2 with the strength fixed to a constant. This is a potential well defined on the half-axis. Each of the fundamental solutions composing the general solution of the Schrödinger equation is written as an irreducible linear combination, with non-constant coefficients, of two confluent hypergeometric functions. We present the explicit solution in terms of the non-integer order Hermite functions of scaled and shifted argument and discuss the bound states supported by the potential. We derive the exact equation for the energy spectrum and approximate that by a highly accurate transcendental equation involving trigonometric functions. Finally, we construct an accurate approximation for the bound-state energy levels.

Effect of a core-softened O–O interatomic interaction on the shock compression of fused silica

Isotropic soft-core potentials have attracted considerable attention due to their ability to reproduce thermodynamic, dynamic, and structural anomalies observed in tetrahedral network-forming compounds such as water and silica. The aim of the present work is to assess the relevance of effective core-softening pertinent to the oxygen-oxygen interaction in silica to the thermodynamics and phase change mechanisms that occur in shock compressed fused silica. We utilize the MD simulation method with a recently published numerical interatomic potential derived from an ab initio MD simulation of liquid silica via force-matching. The resulting potential indicates an effective shoulder-like core-softening of the oxygen-oxygen repulsion. To better understand the role of the core-softening we analyze two derivative force-matching potentials in which the soft-core is replaced with a repulsive core either in the three-body potential term or in all the potential terms. Our analysis is further augmented by a comparison with several popular empirical models for silica that lack an explicit core-softening. The first outstanding feature of shock compressed glass reproduced with the soft-core models but not with the other models is that the shock compression values at pressures above 20 GPa are larger than those observed under hydrostatic compression (an anomalous shock Hugoniot densification). Our calculations indicate the occurrence of a phase transformation along the shock Hugoniot that we link to the O–O repulsion core-softening. The phase transformation is associated with a Hugoniot temperature reversal similar to that observed experimentally. With the soft-core models, the phase change is an isostructural transformation between amorphous polymorphs with no associated melting event. We further examine the nature of the structural transformation by comparing it to the Hugoniot calculations for stishovite. For stishovite, the Hugoniot exhibits temperature reversal and associated phase transformation, which is a transition to a disordered phase (liquid or dense amorphous), regardless of whether or not the model accounts for core-softening. The onset pressures of the transformation predicted by different models show a wide scatter within 60-110 GPa; for potentials without core-softening, the onset pressure is much higher than 110 GPa. Our results show that the core-softening of the interaction in the oxygen subsystem of silica is the key mechanism for the structural transformation and thermodynamics in shock compressed silica. These results may provide an important contribution to a unified picture of anomalous response to shock compression observed in other network-forming oxides and single-component systems with core-softening of effective interactions.

Initial Stage of Aerosol Formation from Oversaturated Vapors

The formation of aerosol particles from oversaturated vapor was considered assuming that the stable nuclei of the new phase contain two (dimers) or three (trimers) condensing vapor molecules. Exact expressions were derived and analyzed for the partition functions of the dimer and trimer suspended in a carrier gas for the rectangular well and repulsive core intermolecular potentials. The equilibrium properties of these clusters and the nucleation rate of aerosol particles were discussed. The bound states of clusters were introduced using a limitation on their total energy: molecular clusters with a negative total energy were considered to exclude configurations with noninteracting fragments.

Metal–ligand bond directionality in the M2–NH3 complexes (M = Cu, Ag and Au)

ABSTRACTThe metal–ligand bonds in the M2–NH3 complexes (M = Au, Ag and Cu) are directional and the M–M–N angles tend to be linear. Natural energy decomposition analysis (NEDA) and localised molecular orbital energy decomposition analysis (LMOEDA) approaches indicate that the metal-ligand bonds in these complexes are mainly electrostatic in nature, however, the electrostatic is not the cause of the linearity of M–M–N arrangements. Instead, NEDA shows that the charge transfer and core repulsion are mainly responsible for the directionality of these bonds. In the LMOEDA point of view, the repulsion term is the main reason for the linearity of these complexes. Interacting quantum atoms (IQA) analysis shows that inter-atomic and inter-fragment interactions favour the nonlinear arrangements; however, these terms are compensated by the atomic self-energies, which stabilise the linear structure.

Hydrophobicity Varying with Temperature, Pressure, and Salt Concentration.

Temperature-, pressure-, and salt-concentration-induced variations in the solubility of small nonpolar solutes in aqueous solution and the corresponding variations in the solvent-induced pair attraction between such solute molecules are investigated. The variations in the solvation free energy of a solute and those in the solvent-induced pair attraction are well reproduced by a mean-field approximation in which the repulsive cores of solute molecules are treated as hard spheres and the mean-field energy of a solute molecule is taken to be the average potential energy that the solute molecule feels in solution. The mechanisms of variation in the solvation free energy and those of variation in the solvent-induced pair potential, with increasing temperature, pressure, and salt concentration, are clarified. Correlations between the solvation free energy and the solvent-induced pair potential at a contact distance in temperature, pressure, and salt concentration variations are near linear in any mode of variation, but the slope of the linear relation is dependent on the mode of variation and is determined by a ratio of the solvation thermodynamic quantities characteristic of each mode of variation.

Symmetric cumulants as a probe of the proton substructure at LHC energies

We present a systematic study of the normalized symmetric cumulants, NSC(n,m), at the eccentricity level in proton-proton interactions at s=13TeV within a wounded hot spot approach. We focus our attention on the influence of spatial correlations between the proton constituents, in our case gluonic hot spots, on this observable. We notice that the presence of short-range repulsive correlations between the hot spots systematically decreases the values of NSC(2,3) and NSC(2,4) in mid- to ultra-central collisions while increases them in peripheral interactions. In the case of NSC(2,3) we find that, as suggested by data, an anti-correlation of ε2 and ε3 in ultra-central collisions, i.e. NSC(2,3)<0, is possible within the correlated scenario while it never occurs without correlations when the number of gluonic hot spots is set to three. We attribute this fact to the decisive role of correlations on enlarging the probability of interaction topologies that reduce the value of NSC(2,3) and, eventually, make it negative. Further, we explore the dependence of our conclusions on the number of hot spots, the values of the hot spot radius and the repulsive core distance. Our results add evidence to the idea that considering spatial correlations between the subnucleonic degrees of freedom of the proton may have a strong impact on the initial state properties of proton-proton interactions [1].

Self-assembly of model short triblock amphiphiles in dilute solution.

In this work, a molecular theory is used to study the self-assembly of short diblock and triblock amphiphiles, with head-tail and head-linker-tail structures, respectively. The theory was used to systematically explore the effects of the molecular architecture and the affinity of the solvent for the linker and tail blocks on the relative stability of the different nanostructures formed by the amphiphiles in dilute solution, which include spherical micelles, cylindrical fibers and planar lamellas. Moreover, the theory predicts that each of these nanostructures can adopt two different types of internal organization: (i) normal nanostructures with a core composed of tail segments and a corona composed of head segments, and (ii) nanostructures with a core formed by linker segments and a corona formed by tail and head segments. The theory predicts the occurrence of a transition from micelle to fiber to lamella when increasing the length of the tail or the linker blocks, which is in qualitative agreement with the geometric packing theory and with experiments in the literature. The theory also predicts a transition from micelle to fiber to lamella as the affinity of the solvent for the tail or linker block is decreased. This result is also in qualitative agreement with experiments in the literature but cannot be explained in terms of the geometric packing theory. The molecular theory provides an explanation for this result in terms of the competition between solvophobic attractions among segments in the core and steric repulsions between segments in the corona for the different types of self-assembled nanostructures.

On the Mechanism of Nucleon-Nucleon Attraction by Pion Exchange

A formula is derived for the central nucleon-nucleon potential, based on an analysis of the physical origin of the nucleon-nucleon attraction by pion exchange. The decrease of the dynamical mass of the interaction field, exchanged pion in this case, is the principal mechanism responsible for the nuclear attraction in a similar way that the decrease of the kinetic energy of the exchange electron in the diatomic molecule is directly responsible for the covalent molecular attraction. The minimum value of this central nucleon-nucleon potential and the position of the minimum are similar with the values reported in literature for a potential calculated by lattice QCD, which shares the features of the phenomenological nucleon-nucleon potentials. The Schrodinger equation with this central nucleon-nucleon potential was solved numerically for different values of the pion mass. The binding energy increases with the decrease of the pion mass. For masses higher than the real pion mass the nucleon-nucleon system is unbound. We discuss on the two pion exchange and hard core repulsion. The minimum value of the potential for two pion exchange is comparable with the minimum value of the CD Bonn potential. For a hard core radius of 0.5 fm the binding energy is equal to the deuteron binding energy.

Critical parameters, thermodynamic functions, and shock Hugoniot of aluminum fluid at high energy density

We present estimates of the critical properties, thermodynamic functions, and principal shock Hugoniot of hot dense aluminum fluid as predicted from a chemical model for the equation-of-state of hot dense, partially ionized and partially degenerate plasma. The essential features of strongly coupled plasma of metal vapors, such as multiple ionization, Coulomb interactions among charged particles, partial degeneracy, and intensive short range hard core repulsion are taken into consideration. Internal partition functions of neutral, excited, and multiply ionized species are carefully evaluated in a statistical-mechanically consistent way. Results predicted from the present model are presented, analyzed and compared with available experimental measurements and other theoretical predictions in the literature.