Coalescence Radius Research Articles

Light hypernuclei in heavy-ion collisions

Prediction for hyper nuclei multiplicities from GSI to LHC energies from the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model combined with a final state coalescence approach is presented and compared to the thermal model. The influence of the coalescence radius on the collision energy and centrality dependence of the Λ3H/Λ ratio is discussed.

Effect of viscoelasticity on the foaming behaviour of long-chain branched polypropylene with different branching degrees analysed by using bubble-growth modelling

Long-chain branched polypropylene (LCB-PP) was generated by a melt grafting reaction with trimethylolpropane triacrylate (TMPTA) as the grafting monomer and zinc dimethyldithiocarbamate (ZDMC) or styrene (St) as the co-monomers. High-temperature size exclusion chromatography (HT-SEC) was used to characterize the molecular mass, molecular mass distribution and branching degree of the modified PP. Subsequently, linear and nonlinear viscoelasticity data were obtained by a small amplitude oscillatory shear (SAOS) test and uniaxial extensional viscosity measurement. The pressure balanced bubble-growth (PBB) model was used to calculate the critical coalescence radius (CCR) curves for PP to quantitatively correlate the viscoelasticity and foamability and evaluate the foamability of PP combined with batch foaming. It is shown that with increasing branching degree, the foam shows a better resistance to bubble coalescence, resulting in a more regular bubble structure and a higher expansion ratio. Moreover, viscosity should be controlled over an appropriate range for realising good foamability; otherwise, excessive viscosity can suppress bubble growth and limit the expansion ratio. MPPZ4 modified with 4 wt% TMPTA and 0.4 wt% ZDMC showed the best foamability. A combination of the PBB model and batch foaming experiment is used to quantitatively explain the contribution of LCB to foaming.

Evaluating melt foamability of LLDPE/LDPE blends with high LLDPE content by bubble coalescence mechanism

Bubble coalescence mechanism was introduced to evaluate the melt foamability of polymer blends. Linear low-density polyethylene (LLDPE), with excellent mechanical properties but poor foamability, was blended with small amounts of low-density polyethylene (LDPE), which was expected to impart the desired foaming-related properties to LLDPE. The presence of LDPE in LLDPE matrix provided only a small improvement in linear viscoelasticity under small deformations, but a significantly large improvement in nonlinear behavior under large deformations. A critical coalescence radius curve was simulated using a pressure-balanced bubble growth model to evaluate bubble coalescence and foamability of the blends, taking into account the linear and non-linear behaviors. It was found that the steep stress growth caused by LDPE addition can dramatically increase the pressure of large bubbles and then effectively inhibit the coalescence of adjacent bubbles, thus improving the foamability of LLDPE/LDPE blends. The theoretical predictions derived from the bubble coalescence mechanism were also confirmed by experiments.

Analysis of bubble coalescence and determination of the bubble radius for long‐chain branched poly(ethylene terephthalate) melt foaming with a pressure balanced bubble‐growth model

AbstractA pressure balanced bubble‐growth (PBB) model was proposed to analyze bubble coalescence and determine the bubble radius for the melt foaming of long‐chain branched poly(ethylene terephthalate) (LCB‐PET). The key for the PBB model calculation was to determine the bubble inner pressure composed of additional pressure induced by interface tension, and molecular stress, that is, the biaxial tensile stress of the polymer cell wall calculated with the molecular stress function model. LCB‐PET was generated by reactive extrusion, and the molecular structure and viscoelasticity were well characterized. Batch melt‐foaming experiments with CO2 were conducted for the LCB‐PET. The critical coalescence radius curve was calculated with the PBB model to dynamically describe the bubble coalescence and evaluate the melt foamability. The PBB model was also used to determine the bubble size of LCB‐PET foam. Both the evaluation of the melt‐foamability and the determination of the bubble radius agreed well the experimental results.

Temperature of intermediate mass fragments in simulated 40Ca + 40Ca reactions around the Fermi energies by AMD model

The primary fragments in 40Ca + 40Ca reactions at 35, 50, 80, 100, 140, and 300 MeV/u were simulated using the antisymmetrized molecular dynamics model, in the phase space at t = 300 fm/c with a coalescence radius Rc = 5 fm. The standard Gogny interactions g0, g0as, and g0ass were adopted in simulating the collisions at an impact parameter of b = 0 fm. It was found, using an isobaric yield ratio method, that temperature of the primary fragment depends on the incident energy and hardness of the interaction potential. The temperature obtained in this work agrees with the results by the self-consistent fitting method.

Isobaric yield ratio difference between the140AMeVNi58+Be9andNi64+Be9reactions studied by the antisymmetric molecular dynamics model

Background: The isobaric yield ratio difference (IBD) method is found to be sensitive to the density difference of neutron-rich nucleus induced reaction around the Fermi energy.Purpose: An investigation is performed to study the IBD results in the transport model.Methods: The antisymmetric molecular dynamics (AMD) model plus the sequential decay model gemini are adopted to simulate the $140A$ MeV ${}^{58,64}\mathrm{Ni}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}^{9}\mathrm{Be}$ reactions. A relative small coalescence radius ${R}_{c}=$ 2.5 fm is used for the phase space at $t=$ 500 fm/c to form the hot fragment. Two limitations on the impact parameter ($b1=0--2$ fm and $b2=0--9$ fm) are used to study the effect of central collisions in IBD.Results: The isobaric yield ratios (IYRs) for the large-$A$ fragments are found to be suppressed in the symmetric reaction. The IBD results for fragments with neutron excess $I=$ 0 and 1 are obtained. A small difference is found in the IBDs with the $b1$ and $b2$ limitations in the AMD simulated reactions. The IBD with $b1$ and $b2$ are quite similar in the AMD + GEMINI simulated reactions.Conclusions: The IBDs for the $I=0$ and 1 chains are mainly determined by the central collisions, which reflects the nuclear density in the core region of the reaction system. The increasing part of the IBD distribution is found due to the difference between the densities in the peripheral collisions of the reactions. The sequential decay process influences the IBD results. The AMD + GEMINI simulation can better reproduce the experimental IBDs than the AMD simulation.

Dropwise condensation theory revisited Part II. Droplet nucleation density and condensation heat flux

An improved dropwise condensation heat transfer model modified from previous models is proposed in this paper. The critical radius for onset of droplet condensation is determined in the preceding paper (Part I), leading to a more accurate determination of droplet nucleation density and the coalescence radius in this paper (Part II). Effects of subcooling, contact angle, thickness and thermal conductivity of the coating layer on droplet nucleation density, condensation heat flux, and critical condensation heat transfer rate for onset of droplet condensation are illustrated. The predicted droplet nucleation density and dropwise condensation heat flux are shown in excellent agreement with existing experimental data.

Coalescence in semiconcentrated emulsions in simple shear flow

The coalescence frequency in emulsions containing droplets with a low viscosity (viscosity ratio approximately 0.005) in simple shear flow has been investigated experimentally at several volume fractions of the dispersed phase (2%-14%) and several values of the shear rate (0.1-10 s(-1)). The evolution of the size distribution was monitored to determine the average coalescence probability from the decay of the total number of droplets. Theoretically models for two-droplet coalescence are considered, where the probability is given by P(c)=exp(-tau(dr)tau(int)). Since the drainage time tau(dr) depends on the size of the two colliding droplets, and the collision time tau(int) depends on the initial orientation of the colliding droplets, the calculated coalescence probability was averaged over the initial orientation distribution and the experimental size distribution. This averaged probability was compared to the experimentally obtained coalescence frequency. The experimental results indicate that (1) to predict the average coalescence probability one has to take into account the full size distribution of the droplets; (2) the coalescence process is best described by the "partially mobile deformable interface" model or the "fully immobile deformable interface" model of Chesters [A. K. Chesters, Chem. Eng. Res. Des. 69, 259 (1991)]; and (3) independent of the models used it was concluded that the ratio tau(dr)tau(int) scales with the coalescence radius to a power (2+/-1) and with the rate of shear to a power (1.5+/-1). The critical coalescence radius R(o), above which hardly any coalescence occurs is about 10 microm.

Flux of light antimatter nuclei near Earth, induced by cosmic rays in the Galaxy and in the atmosphere

The fluxes of light antinuclei $A\ensuremath{\le}4$ induced near Earth by cosmic ray interactions with the interstellar matter in the Galaxy and with the Earth's atmosphere are calculated in a phenomenological framework. The hadronic production cross section for antinucleons is based on a recent parametrization of a wide set of accelerator data. The production of light nuclei is calculated using coalescence models. For the standard coalescence model, the coalescence radius is fitted to the available experimental data. The nonannihilating inelastic scattering process for the antideuterons is discussed and taken into account for the first time via a more realistic procedure than used so far for antiprotons.

Antideuteron production in 158A GeV/c Pb + Pb collisions

The invariant cross section as a function of transverse momentum for antideuterons produced in 158A GeV/c per nucleon Pb+Pb central collisions has been measured by the NA44 experiment at CERN. This measurement, together with a measurement of antiprotons, allows for the determination of the antideuteron coalescence parameter. The extracted coalescence radius is found to agree with the deuteron coalescence radius and radii determined from two particle correlations.

D/pandt/pratios in nucleon-nucleus and heavy ion reactions: Can entropy be determined?

The relative yields of high energy deuterons and tritons as compared to protons have been measured in p+Kr, 16O+Kr and 20Ne+Ar reactions with a continuously varying beam energy up to 500A(400A) MeV. Statistical (expanding) evaporation models are not able to reproduce these d/p or t/p ratios, which for high particle energy (>30 MeV) increase smoothly with beam energy. Models that contain nucleon-nucleon scattering, like cascade or nuclear molecular dynamics models, can only reproduce the ratios if a final-state interaction is introduced via the coalescence prescription. The coalescence radius that best fit the data is rather constant over wide beam energy intervals. Entropy can, however, not be directly determined from these ratios.Received 3 December 1998DOI:https://doi.org/10.1103/PhysRevC.60.024601©1999 American Physical Society

In Situ Diagnostics of Vuv Laser Cvd of Semiconductor Interfaces by Ftir Spectroscopy and Spectroscopic Ellipsometry

ABSTRACTThe growth of high quality amorphous hydrogenated semiconductor films was explored with different in situ spectroscopic methods. Nucleation of ArF laser-induced CVD of a-Ge:H on different substrates was investigated by real time ellipsometry, whereas the F2 laser (157nm) deposition of a-Si:H was monitored by FTIR transmission spectroscopy. The ellipsometric studies reveal a significant influence of the substrate surface on the nucleation stage, which in fact determines the electronic and mechanical properties of the bulk material. Coalescence of initial clusters occurs at a thickness of 16 Å for atomically smooth hydrogen-terminated c-Si substrates, whereas on native oxide covered c-Si substrates the bulk volume void fractions are not reached until 35 Å film thickness. For the first time we present a series of IR transmission spectra with monolayer resolution of the initial growth of a-Si:H. Hereby the film thickness was measured simultaneously using a quartz crystal microbalance with corresponding sensitivity. The results give evidence for cluster formation with a coalescence radius of about 20 Å. Difference spectra calculated for layers at different depths with definite thickness reveal that the hydrogen-rich interface layer stays at the substrate surface and does not move with the surface of the growing film. The decrease of the Urbach energy switching from native oxide to H-terminated substrates suggests a strong influence of the interface morphology on the bulk material quality.

Coalescence model for deuterons and antideuterons in relativistic heavy-ion collisions.

Existing formulations of the coalescence model for the formation of small nuclear clusters in nuclear collisions cannot distinguish between particle and antiparticle clusters and ignore the interactions of the cluster constituents with the other particles in the interaction region. Furthermore none of these models is kinematically fully consistent since the problem of energy conservation in the coalescence process is not dealt with directly, but buried in a phenomenological parameter, the ``coalescence radius.'' Studying the simplest case of (anti)deuteron formation, we include the effects on the coalescence rate from interactions with the medium, which allow for off-shell propagation and thus for energy conservation during coalescence, via effective medium-dependent masses for the cluster constituents. Instead of the conceptually ill-defined ``coalescence radius'' the width of the mass distributions is introduced as a fundamental parameter which, through the scattering rate in the medium, can be related to the temperature of the collision fireball. The freeze-out condition for the created clusters relates the thermodynamical parameters of the fireball to its geometric size at freeze-out and thus provides a deeper understanding of the role of the phenomenological ``coalescence radius'' in previous formulations. It automatically predicts different radius parameters and coalescence probabilities for deuterons and antideuterons. A detailed comparison of our new formulation with previous approaches is given.

On the graph approach to the coalescence model

The graph approach is used to explain the universality of the coalescence radius p 0 for the formation of various light fragments (d, t, 3He, 4He) and to study the tendency for a decrease of p 0 with mass number of the parent nucleus.

On the dynamical basis for the coalescence model

A quantitative analysis, using realistic deuteron wavefunctions, shows that the simplest Feynman graph corresponding to the several nucleon fusion idea can serve as a basis for the coalescence model. The coalescence radius is expressed in terms of the slope parameter of inclusive nucleon spectrum. An adequate description is obtained for the transverse momentum distribution of alpha-particles from the interactions of relativistics nuclei.

A refined coalescence model for intermediate-energy heavy-ion collisions. Application to deuteron spectra

The coalescence model for complex-particle emission is modified by introducing corrections for the Coulomb barrier and the binding energy of the ejectile. The model is applied to the analysis of deuteron spectra for various projectile-target combinations at incident energies of 15-25 MeV/nucleon. The results, together with those of a previous analysis of alpha -particle spectra for the same colliding systems, show that the extracted coalescence radii decrease regularly with increasing Ap/(Ap+AT) for both the weakly bound deuterons and the strongly bound alpha particles.

Fragment production in intermediate energy heavy ion reactions.

The emission of intermediate rapidity fragments with Aless than or equal to14 has been studied in 42 to 151 MeV/nucleon Ar- and Ne-induced reactions on Al, Ca, and Au targets. The energy spectra were fitted assuming emission from a single source moving with a velocity intermediate between that of the projectile and target. The extracted temperatures were independent of fragment mass, indicating that the fragments had a common source. The spectra for fragments as heavy as nitrogen were also well described using the coalescence model and the resulting coalescence radii were independent of fragment mass. The observed fragment production cross sections were fitted with a quantum statistical model from which the entropy produced was extracted. This entropy was found to be much less than that derived from d/p ratios and higher than the entropy displayed by target-like fragments. The light particle spectra were compared to a model utilizing a solution of the Boltzmann equation incorporating mean field and Pauli blocking effects to describe the proton spectra from Ar + Ca. Nuclear fluid dynamics calculations agreed reasonably well with the higher energy data but could not describe the 42 MeV/nucleon data.

Coalescence of complex fragments.

The production of intermediate rapidity complex fragments up to A = 14 from the reactions of Ar incident on Au and Ca targets at 92 and 137 MeV/nucleon has been described using the coalescence model. The resulting coalescence radii are independent of observed fragment mass which indicates that these fragments are emitted from a common source. Extracted interaction region radii agree with recent proton-proton correlation results.

The coalescence phenomenon and the Pauli quenching in high-energy heavy ion collisions

Calculating the proton and deuteron spectra of high-energy heavy ion reactions by means of the cascade model it is argued that the effective account of the nuclear medium on the deuteron-like bound-state wave function requires a smaller coalescence radius of the respective momentum sphere compared with that obtained by using a deuteron wave function of two isolated nucleons.

Composite particle emission in relativistic heavy ion collisions

Inclusive spectra of d, t, and 3He have been measured over a wide range of fragment angles and energies. The observed spectra are well reproduced by the “coalescence model” with a coalescence radius p 0 which is independent of beam energies and which decreases as the sizes of the target-projectile combinations increase. The sizes of the interaction regions have been derived from these p 0 values. The experimental cross sections generally deviate from predictions of the firestreak model.