Impact Parameter Collisions Research Articles

Analytical Framework for Space Debris Collision Avoidance Maneuver Design

An analytical formulation for collision avoidance maneuvers involving a spacecraft and a space debris is presented, including solutions for the maximum deviation and minimum collision probability cases. Gauss’s planetary equations and relative motion equations are used to map maneuvers at a given time to displacements at the predicted close approach. The model is then extended to map changes in state between two times, allowing one to propagate covariance matrices. The analytical formulation reduces the optimization problem to an eigenproblem, for both maximum deviation and minimum collision probability. Two maximum deviation cases, total deviation and impact parameter, are compared for a large set of spacecraft–debris conjunction geometries derived from European Space Agency’s Meteoroid and Space Debris Terrestrial Environment Reference (MASTER-2009) model. Moreover, the maximum impact parameter and minimum collision probability maneuvers are compared assuming covariances known at the maneuver time, to evaluate the net effect of lead time in collision probability. In all cases, solutions are analyzed in the b-plane to leverage its natural separation of phasing and geometry change effects. Both uncertainties and maximum deviation grow along the time axis for long lead times, limiting the reduction in collision probability.

Application of artificial intelligence in the determination of impact parameter in heavy-ion collisions at intermediate energies

The impact parameter is one of the crucial physical quantities of heavy-ion collisions, and can affect obviously many observables at the final state, such as the multifragmentation and the collective flow. Usually, it cannot be measured directly in experiments but might be inferred from observables at the final state. Artificial intelligence has had great success in learning complex representations of data, which enables novel modeling and data processing approaches in physical sciences. In this article, we employ two of commonly used algorithms in the field of artificial intelligence, the convolutional neural networks (CNN) and light gradient boosting machine (LightGBM), to improve the accuracy of determining impact parameter by analyzing the proton spectra in transverse momentum and rapidity on the event-by-event basis. Au + Au collisions with the impact parameter of 0 ⩽ b ⩽ 10 fm at intermediate energies (E lab = 0.2–1.0 GeV/nucleon) are simulated with the ultrarelativistic quantum molecular dynamics model to generate the proton spectra data. It is found that the average difference between the true impact parameter and the estimated one can be smaller than 0.1 fm. The LightGBM algorithm shows an improved performance with respect to the CNN on the task in this work. By using the LightGBM’s visualization algorithm, one can obtain the important feature map of the distribution of transverse momentum and rapidity, which may be helpful in inferring the impact parameter or centrality in heavy-ion experiments.

Hollowness effect and entropy in high energy elastic scattering

This paper presents a qualitative explanation for the hollowness effect based on the inelastic overlap function, claiming this result is a consequence of fundamental thermodynamic processes. Using the Tsallis entropy, one identifies the entropic index w with the ratio of the collision energy to critical one in the total cross-section. The integrated probability density function is replaced by the inelastic overlap function, which represents the probability of occurrence of an inelastic event depending on both the collision energy and impact parameter. The Coulomb potential, as well as the confinement potential, are used as naive approaches to describe the (internal) energy of the colliding hadrons. The Coulomb potential in the impact parameter picture is not able to furnish any reliable physical result near the forward direction. However, the confinement potential in the impact parameter space results in the hollowness effect shown by the inelastic overlap function near the forward direction.

Quantum interference of K capture in energetic Ge31+(1s)−Kr collisions

We have measured characteristic $K$ x rays in coincidence with the scattered particles from collisions of hydrogenlike Ge ions with Kr atoms. The ions were first accelerated to 8.6 MeV/amu, post-stripped to H-like charge state, and decelerated to around 2.5 MeV/amu. From the measurements the probabilities for K-shell to K-shell charge transfer as a function of collision impact parameters were obtained. The probabilities show an onset of oscillations which are interpreted as quantum interference between the $K$-shell to $K$-shell electron transfer amplitudes in two spatially separated coupling regions in the incoming and outgoing parts of the collision. The probabilities of $K$-shell vacancy distribution created by the collision are calculated within a relativistic independent electron model using the coupled-channel approach with atomlike Dirac-Fock-Sturm orbitals. A reasonable agreement between the theoretical results and the experimental data is found.

Double parton scattering in pA collisions at the LHC revisited

We consider the production of W-boson plus dijet, W-boson plus b-jets and same sign WW via double parton scattering (DPS) in pA collisions at the LHC and evaluate the corresponding cross sections. The impact of a novel DPS contribution pertinent to pA collisions is quantified. Exploiting the experimental capability of performing measurements differential in the impact parameter in pA collisions, we discuss a method to single out this novel DPS contribution. The method allows the subtraction of the leading twist (LT) single parton scattering background and it gives access in a very clean way to double parton distribution functions in the proton. We calculate leading twist and DPS cross sections and study the dependence of the observables on the cuts in the jets phase space. In the Wjj channel the observation of DPS is possible with data already accumulated in pA runs and the situation will greatly improve for the next high luminosity runs. For the Wb{bar{b}} final state, the statistics within the current data is too low, but there is possibility to observe DPS in this channel in future runs, albeit with much reduced sensitivity than in Wjj final state. Finally the DPS observation in the same sign WW channel will require either significant increase of integrated luminosity beyond that foreseen in next pA runs or improved methods for W reconstruction, along with its charge, in hadronic decay channels.

Effect of impact-parameter-dependent electronic energy loss on reflected-ion spectra

Conventional theory and computation of the slowing-down of ions and associated radiation effects relies on a scheme proposed by Lindhard and Scharff, in which electronic energy losses enter as a friction force. We study limitations of this scheme, when the dependence of electronic losses on the impact parameter in individual atomic collisions is taken into account. We study this feature on the projected range – where it is found to be insignificant – and on reflected-ion spectra – where major changes are observed, dependent on ion energy and ion-target combination. Most sensitive are the position of the peak in the reflected-energy spectrum as well as the behavior near the maximum energy loss. Systems studied include He-Ag, Ne-Ag, B-Si and D-Pt.

Initial transverse-momentum broadening of Breit-Wheeler process in relativistic heavy-ion collisions

We calculate the cross section and transverse-momentum (P⊥) distribution of the Breit-Wheeler process in relativistic heavy-ion collisions and their dependence on collision impact parameter (b). To accomplish this, the Equivalent Photon Approximation (EPA) was generalized in a more differential way compared to the approach traditionally used for inclusive collisions. In addition, a lowest-order QED calculation with straightline assumption was performed as a standard baseline for comparison. The cross section as a function of b is consistent with previous calculations using the equivalent one-photon distribution function. Most importantly, the P⊥ shape from this model is strongly dependent on impact parameter and can quantitatively explain the P⊥ broadening observed recently by RHIC and LHC experiments. This broadening effect from the initial QED field strength should be considered in studying possible trapped magnetic field and multiple scattering in a Quark-Gluon Plasma (QGP). The impact-parameter sensitive observable also provides a controllable tool for studying extreme electromagnetic fields.

On the Centrality Determination with Forward Proton Detectors

The forward proton detectors, already installed at the Large Hadron Collider, are studied in the context of heavy-ion collisions. The potential of such detectors in measuring the nuclear debris coming from the spectator fragments is presented. The geometric acceptance of the forward proton detectors for different debris is estimated. The impact of experimental conditions and the Fermi motion on the acceptance is studied. A possibility of the collision impact parameter reconstruction from the measurement of nuclear fragments is discussed.

Classical and semiclassical simulations of differential single charge exchange in fast alpha-helium collisions

Within the framework of an independent particle model, the differential single charge transfer process in the collision of fast helium ions with neutral helium targets is theoretically studied by means of the classical trajectory Monte Carlo (CTMC) method. Also, the specified reactions are investigated using two semiclassical continuum distorted wave models with eikonal initial and final states. These theories are usually identified as CDW-EIS and CDW-EFS. Using the CTMC theory, both the electron capture and the excitation probabilities are estimated and discussed as functions of the collision impact parameter. Also, the distribution of the final projectile (n, l) states and the impact parameter dependence of the electron transfer to the final n levels are investigated. Using the theories, the projectile angular distribution of the fully differential cross-sections are calculated for several impact energies in the range of 60–630 keV/u for which the experimental data are available. The obtained results are compared to each other and to their corresponding experimental values. In most of the considered cases, comparisons show that the applied treatments are in qualitative agreement with the experimental data.

State-to-state quantum dynamics of the H + LiF → Li + HF reaction on an accurate ab initio potential energy surface

Quantum state-to-state dynamics calculations are reported for the H + LiF(vi, ji) → HF(vf, jf) + Li reaction on a recently reported ground state X̃2A′ potential energy surface. It was found that at low collision energies the title reaction is dominated by long-lived resonances, while the lifetimes of resonances become shorter at higher energies. The existence of resonances is also supported by the differential cross section, which has mostly forward and sideways bias. The integral cross section rises with collision energy slowly, and the opacity function suggests that the reaction is dominated by small impact parameter collisions. The HF product has cold vibrational state distributions in range of the collision energy studied here, although its rotational state distributions peak near the highest accessible rotational states. This early-barrier reaction shows some enhancement by translational energy, but internal excitations of the LiF reactant have more complex behaviors.

Impact parameter smearing effects on isospin sensitive observables in heavy ion collisions

The validity of impact parameter estimation from the multiplicity of charged particles at low-intermediate energies is checked within the framework of ImQMD model. The simulations show that the multiplicity of charged particles cannot estimate the impact parameter of heavy ion collisions very well, especially for central collisions at the beam energies lower than $\sim$70 MeV/u due to the large fluctuations of the multiplicity of charged particles. The simulation results for the central collisions defined by the charged particle multiplicity are compared to those by using impact parameter b=2 fm and it shows that the charge distribution for $^{112}$Sn +$^{112}$Sn at 50 MeV/u is different evidently for two cases; and the chosen isospin sensitive observable, the coalescence invariant single neutron to proton yield ratio, reduces less than 15\% for neutron-rich systems $^{124,132}$Sn +$^{124}$Sn at $E_{beam}$=50 MeV/u, while the coalescence invariant double neutron to proton yield ratio does not have obvious difference. The sensitivity of the chosen isospin sensitive observables to effective mass splitting is studied for central collisions defined by the multiplicity of charged particles. Our results show that the sensitivity is enhanced for $^{132}$Sn+$^{124}$Sn relative to that for $^{124}$Sn+$^{124}$Sn, and this reaction system should be measured in future experiments to study the effective mass splitting by heavy ion collisions.

Procedure for event characterization in Pb-Pb collisions at 40AGeV in the NA49 experiment at the CERN SPS

The time evolution of the strongly interacting matter created in a heavy-ion collision depends on the initial geometry and the the centrality of the collision. Thus an experimental determination of the collision geometry is required. This paper discusses a procedure for event classification and estimation of the geometrical parameters in inelastic Pb+Pb collisions at a beam energy of 40A GeV recorded with the fixed target experiment NA49 at the CERN SPS. In the NA49 experiment, event classes can be defined using the measured multiplicity of particles in the Time Projection Chambers (TPC) or the energy of projectile spectators deposited in the forward Veto or Ring calorimeters. Using the Monte-Carlo Glauber model, these event classes can be related to average values of the geometric quantities such as impact parameter or number of nucleon-nucleon collisions. The implementation of this procedure within a software framework of the future CBM experiment was adopted for event classification in the NA49 experiment. In future, this procedure will be used for analysis of the new Pb+Pb data collected by the NA61/SHINE experiment and for comparison with the results previously obtained by STAR at RHIC and NA49 at the CERN SPS.

On the star-forming ability of Molecular Clouds

The star-forming ability of a molecular cloud depends on the fraction of gas it can cycle into the dense-phase. Consequently, one of the crucial questions in reconciling star-formation in clouds is to understand the factors that control this process. While it is widely accepted that the variation in ambient conditions can alter significantly the ability of a cloud to spawn stars, the observed variation in the star-formation rate in nearby clouds that experience similar ambient conditions, presents an interesting question. In this work we attempted to reconcile this variation within the paradigm of colliding flows. To this end we develop self-gravitating, hydrodynamic realisations of identical flows, but allowed to collide off-centre. Typical observational diagnostics such as the gas-velocity dispersion, the fraction of dense-gas, the column density distribution ({\small N-PDF}), the distribution of gas mass as a function of $K$-band extinction and the strength of compressional/solenoidal modes in the post-collision cloud were deduced for different choices of the impact parameter of collision. We find that a strongly sheared cloud is terribly inefficient in cycling gas into the dense phase and that such a cloud can possibly reconcile the sluggish nature of star-formation reported for some clouds. Within the paradigm of cloud-formation via colliding flows this is possible in case of flows colliding with a relatively large impact parameter. We conclude that compressional modes - though probably essential - are insufficient to ensure a relatively higher star-formation efficiency in a cloud.

Direct mapping of the angle-dependent barrier to reaction for Cl + CHD3 using polarized scattering data.

The transition state, which gates and modulates reactive flux, serves as the central concept in our understanding of activated reactions. The barrier height of the transition state can be estimated from the activation energy taken from thermal kinetics data or from the energetic threshold in the measured excitation function (the dependence of reaction cross-sections on initial collision energies). However, another critical and equally important property, the angle-dependent barrier to reaction, has not yet been amenable to experimental determination until now. Here, using the benchmark reaction of Cl + CHD3(v1 = 1) as an example, we show how to map this anisotropic property of the transition state as a function of collision energy from the preferred reactant bond alignment of the backward-scattered products-the imprints of small impact-parameter collisions. The deduced bend potential at the transition state agrees with ab initio calculations. We expect that the method should be applicable to many other direct reactions with a collinear barrier.

Microscopic dynamics simulations of multinucleon transfer inKr86+Ni64at 25 MeV/nucleon

Multi-nucleon transfer in $^{86}$Kr+$^{64}$Ni at an incident energy of 25 MeV/nucleon is for the first time investigated with a microscopic dynamics model: improved quantum molecular dynamics (ImQMD) model. The measured isotope distributions are reasonably well reproduced by using the ImQMD model together with a statistical code (GEMINI) for describing the secondary decay of fragments. The reaction mechanism is explored with the microscopic dynamics simulations from central to peripheral collisions. In central collisions there exists a strong competition among fusion, deep-inelastic scattering and multi-fragmentation at such an incident energy. In semi-peripheral collisions, binary scattering together with nucleon transfer is dominant, and the probability of elastic+inelastic scattering events increases rapidly with impact parameter in peripheral collisions and approaches to one when $b>14$ fm. The mass-TKE distribution in central collisions due to the competition is quite different from those in peripheral collisions and the distribution of total kinetic energy loss (TKEL) for binary events with nucleon transfer is much more broader than those without transfer.

Maximal efficiency of the collisional Penrose process

The center of mass (CM) energy in a collisional Penrose process - a collision taking place within the ergosphere of a Kerr black hole - can diverge under suitable extreme conditions (maximal Kerr, near horizon collision and suitable impact parameters). We present an analytic expression for the CM energy, refining expressions given in the literature. Even though the CM energy diverges, we show that the maximal energy attained by a particle that escapes the black hole's gravitational pull and reaches infinity is modest. We obtain an analytic expression for the energy of an escaping particle resulting from a collisional Penrose process, and apply it to derive the maximal energy and the maximal efficiency for several physical scenarios: pair annihilation, Compton scattering, and the elastic scattering of two massive particles. In all physically reasonable cases (in which the incident particles initially fall from infinity towards the black hole) the maximal energy (and the corresponding efficiency) are only one order of magnitude larger than the rest mass energy of the incident particles. The maximal efficiency found is ~ 13.92 and it is obtained for the scattering of an outgoing massless particle by a massive particle.

Colliding nuclei to colliding galaxies: Illustrations using a simple colliding liquid-drop apparatus

A simple apparatus suitable for observing the collisions between drops of fluids of various properties is described. Typical results are shown for experiments performed by undergraduate students using various types of fluids. The collisions take place under free-fall (zero-g) conditions, with analysis employing digital video. Two specific types of collisions are examined in detail, head-on collisions and peripheral, grazing collisions. The collisions for certain fluids illustrate many types of nuclear collisions and provide useful insight into these processes, including both fusion and non-fusion outcomes, often with the formation of exotic shapes or emission of secondary fragments. Collisions of other liquids show a more chaotic behavior, often resembling galactic collisions. As expected, the Weber number associated with a specific collision impact parameter is found to be the important quantity in determining the initial outcome of these colliding systems. The features observed resemble those reported by others using more elaborate experimental techniques.

Study of ion-atom ionization using dressed ions and effective projectiles charge state

SynopsisIn this report, we present a study of dressed ion projectile impact ionization of He and Ne atoms in the double differential cross section level. A large deviation from the q2-scaling of the DDCS was observed even for large impact parameter collisions. Different q-dependence (i.e. qn, n differs from 2) was found from which we calculated the effective projectile charge state. It also indicates the projectile screening mechanism which varies with impact parameter of the collision. For theoretical calculation we used GSZ model potential in the CDW-EIS framework, which gives an excellent agreement

State-to-state quantum dynamics of the N(4S) + H2(X1Σ+) → NH(X3Σ−) + H(2S) reaction and its reaction mechanism analysis**Project supported by the National Natural Science Foundation of China (Grant No. 11074151) and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2014AM022).

Quantum state-to-state dynamics of the N(4S) + H2 (X1Σ+) → NH(X3Σ−) + H(2S) reaction is reported in an accurate novel potential energy surface constructed by Zhai et al. (2011 J. Chem. Phys. 135 104314). The time-dependent wave packet method, which is implemented on graphics processing units, is used to calculate the differential cross sections. The influences of the collision energy on the product state-resolved integral cross sections and total differential cross sections are calculated and discussed. It is found that the products NH are predominated by the backward scattering due to the small impact parameter collisions, with only minor components being forward and sideways scattered, and have an inverted rotational distribution and no inversion in vibrational distributions; both rebound and stripping mechanisms exist in the case of high collision energies.

Separation Criteria for Off-Axis Binary Drop Collisions

Off-axis collisions of two equal size droplets are investigated numerically. Various governing processes in such collisions are discussed. Several commonly used theoretical models that predict the onset of separation after collision are evaluated based on the processes observed numerically. A separation criterion based on droplet deformation is found. The numerical results are used to assess the validity of some commonly used phenomenological models for drop separation after collision. Also, a critical Weber number for the droplet separation after grazing collision is reported. The effect of Reynolds number is investigated and regions of permanent coalescence and separation are plotted in a Weber-Reynolds number plane for high impact parameter collisions.