Collision Calculations Research Articles

Phase diagram of the Polyakov–Nambu–Jona-Lasinio approach for finite chemical potentials

We extend the SU(3) (Polyakov) Nambu Jona-Lasinio in two ways: We introduce the next to leading order contribution (in $N_c$) in the partition function. This contribution contains explicit mesonic terms. We introduce a coupling between the gluon field and the quark degrees of freedom which goes beyond a simple rescaling of the critical temperature. With both these improvements we can reproduce, for vanishing chemical potentials, the lattice results for the thermal properties of a strongly interacting system like pressure, energy density, entropy density, interaction measure and the speed of sound. Also the expansion parameter towards small but finite chemical potentials agrees with the lattice results. Extending the calculations to finite chemical potentials (what does not require any new parameter) we find a first order phase transition up to a critical end point of $T_{CEP}= 110\ MeV$ and $\mu_q = 320\ MeV$. For very large chemical potentials, we find agreement with pQCD calculations. We calculate the mass of mesons and baryons as a function of temperature and chemical potential and the transition between the hadronic and the chirally restored phase. These calculations provide an equation of state in the whole $T,\mu$ plane an essential ingredient for dynamical calculations of ultra-relativistic heavy ion collisions but also for the physics of neutron stars and neutron star collisions.

An atomic-level study of the N2–N2 collision process at temperatures up to 2000 K

This article studies the mechanics of the N2–N2 collision process at temperatures up to 2000 K through an extensive set of classical trajectory calculations of binary collisions. It is found that key postcollision characteristics, namely, the deflection angle and the rotational–translational energy exchange rate, are significantly affected by precollision values of the rotational energies of the molecules, which is not addressed in commonly used collision models. On the macroscopic scale, such a behavior will lead to viscosity collision cross section and relaxation rate becoming dependent on both translational and rotational temperatures, as well as on the form of the nonequilibrium rotational energy distribution.

Elastic and inelastic low-energy electron collisions with PH2, PF2 and PCl2 radicals

Ab initio scattering calculations for low-energy electron collisions with PH2, PF2, and PCl2 are performed using the R-matrix method in this study. The elastic integral, differential, and momentum transfer cross sections and the excitation cross sections from the ground state to the five low-lying electron excited states are presented in the energy region of 0.01–15 eV. The target states are represented by including correlations via a configuration interaction technique. The resonant states are detected and identified. The sensitivity of the results to changes in the theoretical model is checked by comparing predictions from a variety of approximations including static exchange, one state close-coupling (CC), and many-state CC approximations. The similarities and differences among the resonances of these three radicals are discussed.

MQCT: User-ready program for calculations of inelastic scattering of two molecules

A program named MQCT is developed for calculations of rotationally and vibrationally inelastic scattering of molecules using the mixed quantum/classical theory approach. Calculations of collisions between two general asymmetric top rotors are now possible, which is a feature unavailable in other existing codes. Vibrational states of diatomic molecules can also be included in the basis set expansion, to carry out calculations of ro-vibrational excitation and quenching. Minimal input for the code assumes several defaults and is very simple, easy to set-up and run by non-experts. Multiple options, available for expert calculations, are listed in the Supplemental Information. The code is parallel and takes advantage of intrinsic massive parallelism of the mixed quantum/classical approach. A Monte-Carlo sampling procedure, implemented as option in the code, enables calculations for complicated systems with many internal states and large number of partial scattering waves. The coupled-states approximation is also implemented as an option. Integral and differential cross sections can be computed for the elastic channel. Rotational symmetry of each molecule, as well as permutation symmetry of two collision partners, are implemented. Potential energy surfaces for H2O + He, H2O + H2, and H2O + H2O are included in the code. Example input files are also provided for these systems. Program summaryProgram title: MQCTProgram files doi:http://dx.doi.org/10.17632/sg36r35njz.1Licensing provisions: GNU GPL v3.0Programming language: FORTRANSupplementary material: MQCT user guideNature of problem: Calculations of rotationally and vibrationally inelastic scattering of two molecules, with possible applications in astrophysics and atmospheric chemistry.Solution method: Mixed quantum/classical theory (MQCT) approachAdditional comments: This code can be used to simulate a collision of two asymmetric top rotors, such as H2O + H2O.

Convergent close-coupling calculations of positron collisions with the hydrogen negative ion

SynopsisConvergent close-coupling method has been applied to positron scattering by the hydrogen negative ion. Internal consistency of the method and convergence of the cross sections are achieved with use of both the single- and two-centre approaches. Calculations were performed using accurate target wave functions obtained with the multi-core approach.

Double-continuum R-matrix theory and codes for many-electron atoms: ionizing electron collisions and time-dependent laser-induced double-ionization

SynopsisAn extension of ab initio many-electron R-matrix theory is described which is relevant both to the time-dependent description of excitation and single and double ionization of atoms in laser pulses, and to time-independent calculation of intermediate energy electron collisions where ionized states of the target atom can be excited. Corresponding general many-electron ‘inner region’ code modules have been developed for use in combination with existing R-matrix method codes for diverse applications with up to two electrons explicitly described by a continuum orbital basis.

From Transition Electromagnetic Form Factors \(\gamma ^* \gamma ^* \eta _c(1S,2S)\) to the Production of \(\eta _c(1S,2S)\) at the LHC

We review our recent results for production of $\eta_c(1S)$ and $\eta_c(2S)$ in the $\gamma^* \gamma^* \to \eta_c(1S,2S)$ fusion and in proton-proton collisions via gluon-gluon fusion. The quarkonium wave functions are calculated by solving Schr\"odinger equation for different $c \bar c$ potentials. Using Terentev prescription the light-cone wave functions are obtained. The light-cone wave functions are used then to calculate $\gamma^* \gamma^* \to \eta_c$ transition form factors. The theoretical results are compared to the Belle experimental data for $\eta_c(1S)$. In addition we discuss our results for two-photon decay width. We present also results of our calculations for proton-proton collisions obtained within $k_T$-factorization approach for different unintegrated gluon distributions. The results for hadroproduction of $\eta_c(1S)$ are compared to the LHCb experimental data.

Effect of isotope on state-to-state dynamics for reactive collision reactions and in ground state 12A″ and first excited 12A′ potential energy surfaces**Project supported by the National Natural Science Foundation of China (Grant No. 11504206) and the Shandong Jiaotong University PhD Research Start-up Fund, China.

We carry out quantum scattering dynamics and quasi-classical trajectory (QCT) calculations for the reactive collision in the ground (12A″) and first excited (12A′) potential energy surface. We calculate the reaction probabilities of and reaction for total angular momentum J = 0. The results calculated by QCT are consistent with those from quantum mechanical wave packet. Using the QCT method, we generate in the center-of-mass frame the product state-resolved integral cross-sections (ICSs); two commonly used generalized polarization-dependent differential cross-sections (PDDCSs), (2π/σ)(dσ00/dωt), (2π/σ)(dσ20/dωt); and three angular distributions of the product rotational vectors, P(θr), P(ϕr), and P(θr, ϕr). We discuss the influence on the scalar and vector properties of the potential energy surface, the collision energy, and the isotope mass. Since there are deep potential wells in these two potential energy surfaces, their kinetic characteristics are similar to each other and the isotopic effect is not obvious. However, the well depths and configurations of the two potential energy surfaces are different, so the effects of isotopic substitution on the integral cross-section and the rotational polarization of product are different.

Electron capture and ionization cross-section calculations for proton collisions with methane and the DNA and RNA nucleobases

Net ionization and net capture cross-section calculations are presented for proton collisions from methane molecules and the DNA/RNA nucleobases adenine, cytosine, guanine, thymine, and uracil. We use the recently introduced independent-atom-model pixel counting method to calculate these cross sections in the 10 keV to 10 MeV impact energy range and compare them with results obtained from the simpler additivity rule, a previously used complete-neglect-of-differential-overlap method, and with experimental data and previous calculations where available. It is found that all theoretical results agree reasonably well at high energies, but deviate significantly in the low-to-intermediate energy range. In particular, the pixel counting method which takes the geometrical overlap of atomic cross sections into account is the only calculation that is able to describe the measurements for capture in proton-methane collisions down to 10 keV impact energy. For the nucleobases it also yields a significantly smaller cross section in this region than the other models. New measurements are urgently required to test this prediction.

Cross sections, stopping power and Bragg peak range calculation of proton collisions with the DNA base adenine

Passage of ionizing radiation into the biological medium plays an important role in a variety of chemical modifications, directly or indirectly of the four DNA bases. However, up to now proton collisions on DNA bases remain experimentally approached and a theoretical model for total cross section, stopping cross section and Bragg peak calculation are poorly characterized. In this current work, we restricted our study on the interaction of energetic ion proton beams with DNA base adenine (C5H5N5). The total cross section produced by high energy impact of protons are here analytically investigated via a novel model combining two methods—the Rudd semi-empirical formulas to calculate the ionization and the analytic method based on the similitude between the electron energy loss in adenine and liquid water to calculate the excitation and charge-transfer—these cross sections used to describe the total stopping cross section of adenine molecule by protons including the nuclear stopping powers. We give in this work an estimation of the Bragg peak profile and position with impact energies ranging from 1 to 20 MeV/amu. The results are compared to the available experimental, theoretical and Monte-Carlo results, and reasonable agreements are generally observed especially for the ionization. The proposed method is useful as an alternative to traditional approaches, and is useful for studies of various radiation effects in other biological material.

Energy levels, oscillator strengths, radiative transition probabilities, level lifetimes and electron-impact excitation rate coefficients for Ne-like Mo XXXIII

The energy levels, oscillator strengths, radiative decay rates, lifetimes, collision strengths, direct and resonance electron-impact excitation rate coefficients have been computed for the 257 fine-structure levels arising from 1s22s22p5nl and 1s22s2p6n′l′ configurations belonging to the Mo32+ ion with n≤7, l≤4 and n′≤5, l′≤4. The model-potential approach is used for the target ion structure calculations. Additionally, we employ the multiconfiguration Dirac–Hartree–Fock method to further assess the energy levels and transition probabilities. The collision strengths for the electron-impact direct excitation are computed within the relativistic distorted-wave approximation at 34, 135, 680, 1700, 5436, and 12,740 eV scattered electron energy values. We also perform collision calculations at 85, 175, and 450 keV electron energies using the plane-wave approximation and interpolate the reduced cross section within Fano plots, thus accounting for relativistic effects at asymptotic energies. This assures the convergence of Maxwellian integration for effective collision strengths calculation at electron temperatures up to 80 keV. The resonance contribution to the excitation rates is accounted for within the independent process isolated resonance approximation by including Na-like Mo31+ doubly excited autoionization states arising from the 1s227nln′l′ configurations with n≤7,l≤4,n′≤20,l′≤8. Contributions from high n′≥21 Rydberg states to the excitation rate coefficients are included by employing the n′−3 extrapolation law for radiative and autoionization decay rates. Radiative decay of resonances to lower autoionization states followed by autoionization cascade as well as radiative damping via core transitions are included in our model. The highest rate coefficients corresponding to ground state excitations are the 2p–3d allowed and 2p–3p electric monopole transitions, respectively. Intercombination and generally higher-order electric multipole transitions amount to lower excitation rate coefficients but are not to be neglected. Magnetic transitions are only relevant for low electron temperatures since both their direct and resonance contributions to excitation significantly decrease with increasing electron energy. Present results compare well with existing data from literature. The resonance contributions play an important role in the accuracy of rate coefficients, especially for weak forbidden transitions at low electron temperatures. These results may be useful in fusion related plasmas, astrophysics and fundamental physics.

Collision and Radiative Rates for Infrared to Extreme Ultraviolet Lines of S iii

Abstract Electron excitation collision strengths for a wide range of transitions giving rise to infrared, optical, ultraviolet, and extreme ultraviolet lines of S iii have been calculated using the B-spline Breit–Pauli R-matrix method. The term-dependent non-orthogonal orbitals have been employed for the accurate representation of target wave functions and the electron plus S iii target scattering system. The multiconfiguration Hartree–Fock method has been utilized for the calculation of 198 S iii fine-structure level energies belonging to the , , , and 3s3p 25s configurations. The transition probabilities between fine-structure levels have also been calculated and compared with available other calculations. The close-coupling expansion includes these 198 fine-structure levels of S iii in the electron collision calculations. The effective collision strengths are calculated at electron temperatures in the range of 103–106 K for all possible transitions between the 198 fine-structure levels. The present calculation includes a larger number of levels in the close-coupling expansion and improved target description than previous calculations and should be useful for the analysis of measured spectra from various astrophysical objects. Comparison with other calculations is used to assess likely uncertainties in the existing collision and radiative rates for S iii. The collision and radiative rates are estimated to be accurate to about 20% or better for most main transitions of astrophysical importance.

Flow‐Induced Coalescence Involving Attractive Interparticle Forces

Coalescence is one of mechanisms of increasing average size of droplets dispersed in a matrix. Extensional‐flow‐induced coalescence where the motion can be described using two coordinates, distance and angle, and shear‐flow‐coalescence described in three dimensions have been studied. Unlike approaches in most of our previous papers where trajectories are solved as dependence of distance on angle or of distance and polar angle on azimuth, parallel integration of all spatial coordinates with respect to time is employed here, which allowed also more correct solution of coalescence including attractive forces. In contrast to previous studies, where interdroplet interaction is neglected till their close approach, this paper is based on the switch between equations describing hydrodynamic interactions between droplets at their moderate distance and equations for matrix drainage between close droplets. The results have been compared for zero and finite critical distance with and without considering van der Waals forces. For droplets keeping spherical shape during coalescence, non‐zero critical distance plays qualitatively the same role as attractive forces in calculation of collision. On the other hand, the critical distance cannot be omitted in models considering droplets flattening where the motion equations diverge for zero intersurface distance.

Systematic Study of Neutron-Rich Rare Isotope Production in Peripheral Heavy-Ion Collisions at Beam Energies 15–25 MeV/nucleon

The production cross sections of projectile-like fragments from collisions of 86Kr projectiles with 64,58Ni and 124,112Sn targets at 15 and 25 MeV/nucleon are studied systematically with emphasis on the neutron-rich isotopes. Our recent experimental data are compared with calculations for the above collisions employing a hybrid approach. The dynamical stage of the projectile-target interaction was described with either the phenomenological deep-inelastic transfer (DIT) model or with the the microscopic constrained molecular dynamics model (CoMD). Subsequently, for the de-excitation of the projectile-like fragments, the statistical multifragmentation model (SMM) or the binary-decay code GEMINI were employed. An overall good agreement with the experimental results was obtained. We point out that our current understanding of the reaction mechanism at beam energies below the Fermi energy suggests that such nuclear reactions, involving peripheral nucleon exchange, can be exploited as a novel route to access extremely neutron-rich rare isotopes toward the r-process path and the hard-to-reach neutron drip-line. For this purpose, we believe that the use of re-accelerated neutron-rich radioactive beams may offer unique and exciting opportunities toward unexplored regions of the nuclear landscape.

Coarsening Behavior of Particles in Fe-O-Al-Ca Melts

The characteristics of particles greatly affect the microstructure and performance of metallic materials, especially their sizes. To provide insight into coarsening phenomena of particles in metallic melts, Fe-O-Al-Ca melt with calcium aluminate particles was selected as a model system. This study uses HT-CSLM, SEM detections and stereological analysis to probe the behavior of particles and their characteristics including size, number density, volume fraction, spreading of particle size, inter-surface distance and distribution of particles. Based on the experimental evidence and calculation of collision, we demonstrate that the coarsening of inclusion particles is not only dependent on the Ostwald growth as studied in previous study, but also on the particle coagulation, and floatation. The collision of particles affects the maximum size of the particles during whole deoxidation process and dominates the coarsening of particles at later stage of deoxidation under the condition without external stirring in Fe-O-Al-Ca melts. The factors influencing collision behaviors and floating properties were also analyzed, which is corresponding to coarsening behavior and change of particle characteristic in the melts with different amounts of Ca addition. Such coarsening mechanism may also be useful in predicting the size of particles in other metallic materials.

R -matrix calculations of electron collisions with a lithium atom at low energies

$R$-matrix calculations of the electron collisions with lithium atom at energies below the $3s$ excitation threshold are presented. The $^1S^e$, $^3S^e$ and $^1P^o$ phase shifts calculated in the near-threshold energy range are in excellent agreement with previous theoretical studies. The threshold behavior of the $^3P^o$ phase shift is accurately analyzed along with the resonance located at the scattering energy $\sim60$ meV. The phase shifts and cross sections calculated here show two resonances below the $3s$ threshold that have not been previously reported.

Towards quantitative LEIS with alkali metal ions

Nowadays low-energy ion scattering (LEIS) is known as a technique with the best surface sensitivity. In this paper we consider the surface composition analysis of metallic samples by means of LEIS with alkali metal ions. We review several LEIS experiments and show that widely used method of the elemental sensitivity factors calibration against reference samples does not correctly account ions neutralization, which leads to wrong results. Further, we discuss two ways to improve the accuracy of LEIS by accounting/calculating alkali metal ion neutralization. The first one is the correction of the reference samples method results, which accounts ion neutralization. Such correction can be done by using available experimental data or by calculating the neutralization probability. The second option is the direct calculation of the elemental sensitivity factors, which consists of calculation of scattering cross section by means of the binary collision model and calculation of the neutralization probability. To calculate the neutralization probability of alkali metal ion we use theoretical method, developed in previous studies. Despite the scope of the direct calculation of the elemental sensitivity factors is limited to relatively simple surfaces nowadays, in some cases, e.g. for metallic compounds, this method allows to reduce the number of experimental measurements by at least three times.

Calculation of naval collisions with general use finite element software

Collisions and groundings are contributing significantly to the structural damage of ships causing almost half of the total losses of ships. The capacity of computers and software made it possible to analyse collision cases as integrated formulation where movement equations are solved for ships’ structures and for the surrounding waters by applying general numerical methods such as the finite element method. In order to ascertain the quality of software used in collision calculations, generally there are used relatively simple structures made of stiffened plates which are very similar to the structure of vessel’s side plate. In this research, for collision calculus the software ANSYS which offers two main interfaces, ADPL and WORKBENCH. It was used a procedure of explicit dynamic calculus and ANSYS software is greeting the user and requesting only the input of total time of calculus/simulation. For the explicit dynamic calculus it was used the LS-DYNA software within ANSYS, which is a very reliable and fast solution. We are using calculations and measurements of a structure from the available literature and as a conclusion, we will note that there is a good correspondence between the three categories of results: measured, calculated in the literature and the one calculated with own means.

Factorization of two-particle distributions in AMPT simulations of Pb–Pb collisions at TeV

The flow ansatz states that the single-particle distribution of a given event can be described in terms of the complex flow coefficients Vn. Multi-particle distributions can therefore be expressed as products of these single-particle coefficients; a property commonly referred to as factorization. The amplitudes and phases of the coefficients fluctuate from event to event, possibly breaking the factorization assumption for event-sample averaged multi-particle distributions. Furthermore, non-flow effects such as di-jets may also break the factorization assumption. The factorization breaking with respect to pseudorapidity η provides insights into the fluctuations of the initial conditions of heavy ion collisions and can simultaneously be used to identify regions of the phase space which exhibit non-flow effects. These proceedings present a method to perform a factorization of the two-particle Fourier coefficients VnΔ(ηa, ηb) which is largely independent of detector effects. AMPT model calculations of Pb-Pb collisions at TeV are used to identify the smallest |Δη|-gap necessary for the factorization assumption to hold. Furthermore, a possible Δη-dependent decorrelation effect in the simulated data is quantified using the empirical parameter . The decorrelation effect observed in the AMPT calculations is compared to results by the CMS collaboration for Pb-Pb collisions at TeV.

Measurement and evaluation for head injury of pedestrian impact using high-speed digital image correlation

This paper presents the use of the high-speed digital image correlation (DIC) method for measurement of the head injury of a pedestrian in a vehicle–pedestrian collision experiment. Two simultaneous high-speed cameras captured the images of the impact process between the head-simulator and the car hood. The DIC method can achieve comprehensive analysis of the impact and help to reconstruct the impact process, from which not only the velocity, acceleration of the headform impactor, and the head injury criterion (HIC) but also the angular velocity and acceleration can be calculated. The possibility of using DIC to calculate of the neck injury criterion (NIC) is also discussed in this paper. Furthermore, the quantitative calculation of the full-field deformation of the car hood during the collision can also be achieved with the DIC method, which is of great practical value in optimizing automobile design and collision protection. A vehicle–pedestrian collision experiment is carried out, and the comprehensive results show that the DIC method can obtain accurate and comprehensive data in the calculation of human and vehicle collision.