Particle-particle Correlations Research Articles

Extended quasiparticle random phase approximation at finite temperatures: Calculation of singleβ-decay Fermi transitions

The formalism of the quasiparticle random phase approximation, extended to include scattering terms in the equation of motion, is used to describe allowed single \ensuremath{\beta}-decay transitions of Fermi type at finite temperatures. The calculations were performed by using a realistic single particle basis and a separable two body interaction in the proton-neutron channel. The behavior of the Ikeda sum rule is studied and it is found that this sum rule is strictly conserved in the presence of particle-particle and hole-hole correlations. As an example on the validity of the formalism the case of Fermi transitions in ${}^{76}\mathrm{Ge}$ is considered.

Density expansion for particle-particle correlations in time-dependent physical clusters

We present a theory for the particle-particle correlations in physical clusters for which bonding between particles is determined by a connectivity distance and a permanency time. A generalized Mayer density expansion for the cluster pair correlation function is found, as well as an Ornstein-Zernike like relation. We can rely on this formalism to study clustering in realistic models by applying techniques of liquid state theory.

Structure-related diffusion under molecular confinement

Molecular diffusion under confinement by highly ordered nanoporous structures is subjected to a hierarchy of particle-particle correlations. These correlations result in a variety of peculiarities of molecular diffusion. Three examples are discussed in detail. As a consequence of the confinement by the host matrix, molecular displacements in different directions often intimately depend on each other, resulting in an interdependence of the principal elements of the diffusion tensor (correlation rule of diffusion anisotropy). If intracrystalline channel systems confine molecular propagation to one direction, molecules with diameters sufficiently exceeding the channel radii are subjected to single-file diffusion, whose spatial-temporal dependence significantly deviates from normal diffusion. In networks of intersecting single-file systems with different affinities to the reactant and product molecules, the interplay of diffusion and reaction leads to deviations from a homogeneous pore filling over the sample and to an enhanced output of reaction products in comparison with channel networks of equal adsorption affinities (reactivity enhancement by molecular traffic control). The presented theoretical concepts are compared with experimental results, in particular with the findings of pulsed field gradient (PFG) NMR diffusion studies.

On the Concentration Dependence of the Cluster Fractal Dimension in Colloidal Aggregation

We have undertaken the task to calculate, by means of extensive numerical simulations and by different procedures, the cluster fractal dimension (d) of colloidal aggregates at different initial colloid concentrations. Our first approach consists in obtaining d from the slope of the log-log plots of the radius of gyration versus size of all the clusters formed during the aggregation time. In this way, for diffusion-limited colloidal aggregation, we have found a square root type of increase of the fractal dimension with concentration, from its zero-concentration value: d = d0 f + a φβ, with d0 f = 1.80 ± 0.01, a = 0.91 ± 0.03 and β = 0.51 ± 0.02, and where φ is the volume fraction of the colloidal particles. In our second procedure, we get the d via the particle-particle correlation function gcluster(r) and the structure function Scluster(q) of individual clusters. We first show that the stretched exponential law gcluster(r) = Ard −3e−(r/ξ) gives an excellent fit to the cutoff of the g(r). Here, A, a and ξ are parameters characteristic of each of the clusters. From the corresponding fits we then obtain the cluster fractal dimension. In the case of the structure function Scluster (q), using its Fourier transform relation with gcluster(r) and introducing the stretched exponential law, it is exhibited that at high q values it presents a length scale for which it is linear in a log-log plot versus q, and the value of the d extracted from this plot coincides with the d of the stretched exponential law. The concentration dependence of this new estimate of d, using the correlation functions for individual clusters, agrees perfectly well with that from the radius of gyration versus size. It is however shown that the structure factor S(q) of the whole system (related to the normalized scattering intensity) is not the correct function to use when trying to obtain a cluster fractal dimension in concentrated suspensions. The log-log plot of S(q) vs. q proportions a value higher than the true value. Nevertheless, it is also shown that the true value can be obtained from the initial slope of the particle-particle correlation function g(r), of the whole system. A recipe is given on how to obtain approximately this g(r) from a knowledge of the S(q), up to a certain maximum q value.

Structure function and fractal dimension of diffusion-limited colloidal aggregates

On a three-dimensional lattice and at different concentrations we perform extensive numerical simulations of diffusion-limited colloidal aggregation (DLCA). In a previous work, we showed that the fractal dimension ${d}_{f}$ of the DLCA aggregates in the flocculation limit presents a square root type of dependence with the initial colloidal concentration. The ${d}_{f}$ was obtained from the slope of a standard log-log plot of the number of particles versus size of the formed aggregates. In this work we confirm the concentration dependency using the particle-particle correlation function $g(r)$ and the structure function $S(q)$ of individual aggregates. We demonstrate that the ${g(r)=Ar}^{{d}_{f}\ensuremath{-}3}{e}^{\ensuremath{-}(r/\ensuremath{\xi}{)}^{a}},$ where $A,$ $a,$ and \ensuremath{\xi} are parameters characteristic of the aggregates, and $a>1.$ This stretched exponential law gives an excellent fit to the cutoff of the $g(r).$ The structure function reveals the ${d}_{f}$ from the slope of a log-lot plot of $S(q)$ versus $q$ for high $q$ values. We also analyze $g(r)$ and $S(q),$ at different times during the reaction, for the whole aggregating system composed of many clusters of different sizes. We observe that the ${d}_{f}$ calculated from the $g(r)$ agrees well with that obtained from individual clusters. However, caution should be observed to extract a ${d}_{f}$ from the corresponding $S(q).$ Our results indicate that for finite concentrations a ${d}_{f}$ systematically larger than the true value is obtained from such analysis.

Mixing in reaction dynamics under enhanced diffusion conditions

We first review the Lévy-flight approach for the description of enhanced diffusion and then study the effects of mixing on the transient A + B → 0 reaction at stoichiometric conditions in d = 1−3 dimensions under enhanced diffusion conditions. The particles are assumed to follow Lévy walks, characterized by an index γ, which result in enhanced diffusion for 1 < γ < 2. Particle density decays and particle-particle correlation functions are calculated using deterministic reaction diffusion equations and computer simulations of this multi-particle problem. We concentrate on the segregation phenomenon and demonstrate that, depending on γ, segregation may disappear in d = 3 dimensions under enhanced diffusion conditions. Hence, Lévy walks lead to an efficient mixing of reacting particles.

Competition between particle-hole and particle-particle correlations in forbidden electron capture: The case of123Te

The K-electron capture half-life of $^{123}$Te has been recently measured to be $t^K_{exp}=2.4\times 10^{19}$ yr, and constitutes the longest half-life ever measured in a single $\beta$-transition of any nuclear species. We have calculated this second unique forbidden transition within the framework of the proton-neutron quasi-particle random phase approximation, making use of Skyrme-type effective interactions. A strong cancellation effect between particle-hole and particle-particle correlations is found. The model, without any renormalization of the force, provides a lower limit for the K-electron capture half-life of $\sim 10^{17}$ yr, which unambiguously rules out the old experimental values of $10^{13} - 10^{14}$ yr. A few percent increase of the particle-particle matrix elements of the Skyrme interaction allows to reproduce the experimental findings.

Magnetic phases near the Van Hove singularity ins- andd-band Hubbard models

We investigate the magnetic instabilities of the nondegenerate (s-band) and a degenerate (d-band) Hubbard model in two dimensions using many-body effects due to the particle-particle diagrams and Hund's rule local correlations. The density of states and the position of Van Hove singularity change depending on the value of next-nearest neighbor hopping t'. The Stoner parameter is strongly reduced in the s-band case, and ferromagnetism survives only if electron density is small, and the band is almost flat at small momenta due to next-nearest neighbor hopping. In contrast, for the d-band case the reduction of the Stoner parameter which follows from particle-particle correlations is much smaller and ferromagnetism survives to a large extent. Inclusion of local spin-spin correlations has a limited destabilizing effect on the magnetic states.

Angular dependence of particle correlations in pp collisions at 400 GeV/ c

The angular dependence of the particle-particle correlation (PPC) and its asymmetry (PPCA) has been studied by using the experimental data of multiplicity production for pp collisions at 400 GeV/ c. The results differ strongly from the overall behavior of e +e − data, but agree with the results obtained by NA22 Collaboration quite well.

Breakdown of Ovchinnikov-Zeldovich Segregation in the A+B-->0 Reaction under Lévy Mixing.

Density fluctuations in the transient $A+B\ensuremath{\rightarrow}0$ reaction, at stoichiometric conditions, cause the Ovchinnikov-Zeldovich segregation which slows down the reaction process. Continuous mixing that homogenizes the reactants can suppress the role of the fluctuations. L\'evy walks which lead to an anomalous diffusion provide such a mixing mechanism. For L\'evy walks with the number of steps distributed as $P(n)\ensuremath{\sim}{n}^{\ensuremath{-}1\ensuremath{-}\ensuremath{\gamma}},n&gt;0,1&lt;\ensuremath{\gamma}&lt;2$, we demonstrate that segregation disappears in $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$ dimensions for $\ensuremath{\gamma}&lt;3/2$. Particle densities and particle-particle correlation functions are presented. The erosion of the segregation is an example of L\'evy mixing.

Reducibility and Thermal and Mass Scaling in Angular Correlations from Multifragmentation Reactions.

Intermediate-mass-fragment (IMF, 3 {le} Z {le} 20) emission probabilities and IMF charge distributions were recently shown to be reducible to the corresponding one fragment quantities. Furthermore, a strong thermal scaling was shown to control the energy dependence of the same quantities. The multifragmentation scenario painted by these experimental observations is that of a process controlled by a largely independent emission of individual fragments, which, in turn is dominated by phase space. Fragment-fragment angular correlations have been used to study the space-time extension of the emitting source. In particular, small angle repulsion (the Coulomb hole) has been interpreted in terms of the Coulomb repulsion of fragments emitted near each other, both in space and time. We will show in this paper that, except at small angles, the particle-particle angular correlations and their dependence on excitation energy are interpretable in terms of nearly independently emitted fragments whose angular distributions are controlled by phase space. Thus we show that the angular correlations are reducible and thermally scalable. A mass scaling of the angular correlations will also be demonstrated and its possible implications discussed.

Driven granular media in one dimension: Correlations and equation of state.

We study a one-dimensional granular system in which each particle is excited by white noise, with inelastic interactions between the particles. When the coefficient of restitution, $\ensuremath{\eta}$, is one, the particles are uncorrelated. As $\ensuremath{\eta}$ decreases, long-range correlations between the particles develop. A computer simulation of the system shows a steady-state, power-law particle-particle correlation function, which depends strongly on $\ensuremath{\eta}$. We give simple analytic arguments for the correlations. We also present an "equation of state" for the system of particles, which relates the noise amplitude to the particle density and the average particle speed.

Correlations in quantum plasmas. II. Algebraic tails.

For a system of point charges that interact through the three-dimensional electrostatic Coulomb potential (without any regularization) and obey the laws of nonrelativistic quantum mechanics with Bose or Fermi statistics, the static correlations between particles are shown to have a $\frac{1}{{r}^{6}}$ tail, at least at distances that are large with respect to the length of exponential screening. After a review of previous work, a term-by-term diagrammatic proof is given by using the formalism of paper I, where the quantum particle-particle correlations are expressed in terms of classical-loop distribution functions. The integrable graphs of the resummed Mayer-like diagrammatics for the loop distributions contain bonds between loops that decay either exponentially or algebraically, with a $\frac{1}{{r}^{3}}$ leading term analogous to a dipole-dipole interaction. This reflects the fact that the charge-charge or multipole-charge interactions between clusters of particles surrounded by their polarization clouds are exponentially screened, as at a classical level, whereas the multipole-multipole interactions are only partially screened. The correlation between loops decays as $\frac{1}{{r}^{3}}$, but the spherical symmetry of the quantum fluctuations makes this power law fall to $\frac{1}{{r}^{5}}$, and the harmonicity of the Coulomb potential eventually enforces the correlations between quantum particles to decay only as $\frac{1}{{r}^{6}}$. The coefficient of the $\frac{1}{{r}^{6}}$ tail at low density is planned to be given in a subsequent paper. Moreover, because of Coulomb screening, the induced charge density, which describes the response to an external infinitesimal charge, is shown to fall off as $\frac{1}{{r}^{8}}$, while the charge-charge correlation in the medium decreases as $\frac{1}{{r}^{10}}$. However, in spite of the departure of the quantum microscopic correlations from the classical exponential clustering, the total induced charge is still essentially determined by the exponentially screened charge-charge interactions, as in classical macroscopic electrostatics.

Observation of large momentum phononlike modes in glasses.

The dynamical properties of disordered systems are not well established in the intermediate, mesoscopic, timespace domain. Here, they are not properly described either by a macroscopic thermodynamical picture or by a microscopic single particle dynamics. The concept of propagating collective modes implies the existence of a simple relation between the energy and the momentum of specific excitations. This occurs as a consequence of translational invariance, and is typical in crystals and free particles. In liquids and glasses, this concept may lose its physical significance when local interparticle interactions start to dominate and the topological disorder does not allow one to derive some kind of quasiparticle and its excitation spectrum [1]. In opposition to this picture, however, one may argue that the translational invariance becomes an increasingly less important aspect at large energies and momentum transfers, because one samples particle-particle correlations on a very short time and space scale. Therefore, if local properties become dominant over long range correlations among particles, the differences in the dynamics of liquid, glass, and crystalline states may disappear. An example is provided by recent inelastic x-ray scattering measurements in water: a propagating collective dynamics is shown to exist in the liquid up to a momentum transfer Q › 14 nm 21 [2], and, in the mesoscopic wavelength region from 0.5 to 3 nm, the velocity of sound of these acoustic excitations is found to be equivalent in the liquid and in the crystalline solid (ice Ih) [3]. In glasses, the collective dynamics at these high frequencies, and its propagating or localized nature, has not yet been established experimentally [1].

Particle-hole and particle-particle correlations in neodymium isotopes

Abstract Excited states in 140, 142, 144, 146 Nd nuclei, up to an excitation energy of about 5 MeV, were investigated by (p,t) experiments performed with a good energy resolution. These data, together with proton and deuteron scattering data from a previous experiment, are compared with Quasi-Particle Phonon Model evaluations, in which the competition between particle-hole and particle-particle residual interactions is considered. The B (Eλ) distributions are satisfactorily reproduced. The 146, 148 Nd(p,t) reaction data are well accounted for, while difficulties are found in reproducing those for 142, 144 Nd(p,t). Limitations and improvements of the model are discussed.

AZIMUTHALLY ANISOTROPIC EMISSION OF UNSTABLE LIGHT NUCLEI IN NUCLEUS-NUCLEUS COLLISIONS

The in-plane and out-of-plane emission of unstable light nuclei was measured in the reaction of ４０Ａｒ＋１９７Ａｕ at energy 25MeV/u by means of extensive particle-particle correlation. An in-plane enhancement is observed for mid-rapidity unstable light nuclei, indicating a rotational effect exists in this reaction system. This in-plane enhanced emission becomes stronger with increasing of impact parameter, but becomes a little weaker with increasiong of energy of the excited state.

Simulation of Ostwald Ripening in Two Dimensions: Spatial and Nearest Neighbor Correlations

Recent experimental results on late stage coarsening (Ostwald ripening) in two dimensions were reinvestigated by means of numerical simulation using the Cahn-Hilliard equation (model B). We determine the spatial particle-particle and charge-charge correlation functions according to the experimental results of Krichevsky and Stavans. We find that our numerical results correspond well with these experiments. We also investigate particle-particle correlations between nearest neighbors (defined by the Voronoi diagram of particle centroids) following the experiments of Seul, Morgan and Sire and compare our numerical results with their Maximum Entropy model of Ostwald ripening.

Angular dependence of particle correlations in [formula omitted] eractions at 250 GeV/ c

A sample of non-diffractive π +p and K +p collisions at s =22 GeV is used to investigate the angular dependence of the particle-particle correlation (PPC) and its asymmetry (PPCA) for soft hadronic data. The results differ strongly from the overall behavior in e +e − data, but agree with that expected for e +e − 2-jet data. For the hadronic collisions, the effect depends strongly on the charge configuration of the pairs and on the rapidity range covered. The FRITIOF Monte Carlo model gives qualitative agreement with the trend of the overall data when Bose-Einstein correlations are included, but differs considerably in the central rapidity region.

Evidence for gluon interference in hadronic Z decays

We present evidence for soft gluon interference, as required by QCD. This interference is expected to manifest itself in an angular ordering of the gluons radiated within a jet. Using hadronic decays of the Z boson in the L3 detector at LEP, we compare variables sensitive to such an angular ordering, namely the energy-energy correlation asymmetry and the newly introduced particle-particle correlation asymmetry, with the predictions of various parton shower models. Only those models which incorporate the expected interference agree with the data.

Azimuthal correlation functions and the energy of vanishing flow in nucleus-nucleus collisions

A method is proposed for estimating the energy of vanishing flow (also called balance energy, E bal) without reconstructing the reaction plane. This method is based on the shapes of experimental particle-particle azimuthal correlation functions. It is used for determining E bal for three systems: Ar + Al, Zn + Ti, Zn + Ni. The results are compared with estimations using flow-parameter analysis and with theoretical expectations.