Collision Energy Range Research Articles

Collision Energy Dependence of Particle Ratios and Freeze-out Parameters in Ultra Relativistic Nucleus Nucleus Collisions

This work investigates the thermo-chemical freeze-out condition of the multi-component hot and dense hadron resonance gas (HRG) formed in the ultra-relativistic nucleus-nucleus collisions (URNNC). The van der Waals (VDW) type model used in the present analysis incorporates the repulsive as well as attractive interactions among the hadrons. The baryons (antibaryons) are treated as incompressible objects. Using this theoretical approach the values of the model freeze-out parameters of the system are extracted over a wide range of collision energy by analyzing experimental data on like-mass antibaryon to baryon ratios. The same set of parameters is found to explain the energy dependence of several other particle ratios quite satisfactorily. We find that the horn-like structures seen in the ratios of strange particles to pions as a function of the collision energy cannot be explained by the VDW-HRG model alone without considering the strangeness imbalance effect in the system. We have compared our freeze-out line with those obtained earlier. The correlation between the p¯/p and K−/K+ ratios is also examined.

State-to-State Spin-Orbit Changing Collision Dynamics of Vibrationally Excited NO at Collision Energies from 1.4 eV to the Cold Regime.

State-to-state spin-orbit changing collisions of vibrationally excited nitric oxide (NO) with argon (Ar) were studied across a wide collision energy range from 3.5 to 11,200 cm-1 (0.43 meV to 1.4 eV) using two molecular beam geometries. Stimulated emission pumping (SEP) for precise initial state preparation and velocity map imaging (VMI) for detailed scattering image capture were employed. These methods enable the study of quantum-state-resolved differential cross sections (DCSs) and provide comprehensive insight into the collision dynamics over both quantum and classical regimes. Theoretical predictions using quantum mechanical close-coupling (QMCC) calculations based on high-level coupled cluster (CCSD(T)) and multireference configuration interaction (MRCI) potential energy surfaces (PESs) are compared with experimental results enabling the testing of both repulsive and attractive parts of the PESs. This study highlights the challenges in accurately modeling spin-orbit changing collisions and underscores the importance of precise experimental data for validating theoretical models, thereby advancing our understanding of nonadiabatic collision dynamics.

Automated potential energy surface development and quasi-classical dynamics for the F- + SiH3I system.

We report a potential energy surface (PES) development for the F- + SiH3I system to study its gas-phase reactions through quasi-classical dynamics simulations. The PES is represented by a full-dimensional permutationally invariant polynomial fitted to composite coupled cluster energy points obtained at the ManyHF-[CCSD-F12b + BCCD(T) - BCCD]/aug-cc-pVTZ(-PP) level of theory. The development was automated by Robosurfer, which samples the configurational space, manages abinitio calculations, and iteratively extends the fitting set. When selecting the abinitio method, we address two types of electronic structure calculation issues: first, the gold standard CCSD(T)-F12b is prone to occasional breakdown due to the perturbative (T) contribution, whereas CCSD-F12b + BCCD(T) - BCCD, with the Brueckner (T) term, is more robust; second, the underlying Hartree-Fock calculation may not always converge to the global minimum, resulting in highly erroneous energies. To mitigate this, we employed ManyHF, configuring the Hartree-Fock calculations with multiple initial guess orbitals and selecting the solution with the lowest energy. According to the simulations, the title system exhibits exceptionally high and diverse reactivity. We observe two dominant product formations: SN2 and proton abstraction. Moreover, SiH2F- + HI, SiHFI- + H2, SiH2FI + H-, SiH2 + FHI-, SiH2 + HF + I-, and SiHF + H2 + I- formations are found at lower probabilities. We differentiated inversion and retention for SN2, both being significant throughout the entire collision energy range. Opacity- and excitation functions are reported, and the details of the atomistic dynamics are visually examined via trajectory animations.

Features in the electron elastic scattering cross sections of atoms Sb, Xe and Bi, Rn

Abstract For atoms having pairwise similar electronic configurations, Sb([Cd]5p3), Xe([Cd]5p6) and Bi([Hg]6p3), Rn([Hg]6p6), features in the energy dependences of integral (ICSs) and differential (DCSs) cross sections of electron elastic scattering are considered theoretically. The positions of the Ramsauer-Townsend minimum (RT) and the low-energy maxima in the ICSs are calculated. The minima in the DCSs have been studied within the collision energy range from 0.1 (Sb, Xe, Bi) and 0.5 (Rn) eV up to 1000 (Sb), 2000 (Xe), 3000 (Bi) and 4000 (Rn) eV. The phase shifts, scattering amplitudes and cross sections have been calculated in the relativistic complex optical potential (OP) approximation. The results of the above OP calculation agree well with the experimental and the theoretical data. The energy dependences of the angular positions of the DCSs minima of these atoms are considered in detail. The energy and the angular positions of 15 (Sb), 17 (Xe and Bi) and 18 (Rn) critical minima (CM) in the DCSs have been found. The highest energy CM are located at: Sb – [727.6 eV; 131.89], Xe – [791.4 eV; 133.16], Bi – [1810.8 eV; 137.34], Rn – [1918.8 eV; 137.64]. A high-angle CM are located at: Sb – [233.6 eV; 151.08], Xe – [256.5 eV; 151.05], Bi – [180.3 eV; 157.30], Rn – [204.0 eV; 155.36].

Vibrational State-Resolved Differential Cross Sections of the F + CH4 → HF + CH3 Reaction at the Collision Energies of 3.1-13.8 kcal/mol.

We report a high-resolution crossed molecular beam experiment investigating the reaction dynamics of the F + CH4 → HF + CH3 reaction across a broad range of collision energies (3.1-13.8 kcal/mol). By using time-sliced velocity map imaging within the crossed molecular beam apparatus, we obtain correlated angular distributions and branching ratios for various product pairs (CH3(ν), HF(ν')). The resolved reactive rainbow-like features that display a distinct bulge in the angular distribution in different channels reveal the formation of vibrationally ground and excited states of the methyl radical accompanied by different rovibrationally excited HF products. These findings suggest distinct reaction dynamics for channels leading to vibrationally excited methyl radicals compared to those forming ground-state methyl radicals.

Construction of diabatic potential energy surfaces for the SiH2+ system and dynamics studies of the Si+(2P1/2, 3/2) + H2 reaction.

The construction of diabatic potential energy surfaces (PESs) for the SiH2+ system, related to the ground (12A') and excited states (22A'), has been successfully achieved. This was accomplished by utilizing high-level abinitio energy points, employing a neural network fitting method in conjunction with a specifically designed function. The newly constructed diabatic PESs are carefully examined for dynamics calculations of the Si+(2P1/2, 3/2) + H2 reaction. Through time-dependent quantum wave packet calculations, the reaction probabilities, integral cross sections (ICSs), and differential cross sections (DCSs) of the Si+(2P1/2, 3/2) + H2 reaction were reported. The dynamics results indicate that the total ICS is in excellent agreement with experimental data within the collision energy range studied. The results also indicate that the SiH+ ion is hardly formed via the Si+(2P3/2) + H2 reaction. The results from the DCSs suggest that the "complex-forming" reaction mechanism predominates in the low collision energy region. Conversely, the forward abstraction reaction mechanism is dominant in the high collision energy region.

Quantum Dynamics Studies of the Li + Na2 (V = 0, j = 0) → Na + NaLi Reaction on a New Neural Network Potential Energy Surface.

The ultracold reaction offers a unique opportunity to elucidate the intricate microscopic mechanism of chemical reactions, and the Na2Li system serves as a pivotal reaction system in the investigation of ultracold reactions. In this work, a high-precision potential energy surface (PES) of the Na2Li system is constructed based on high-level ab initio energy points and the neural network (NN) method, and a proper asymptotic functional form is adopted for the long-range interaction, which is suitable for the study of cold or ultracold collisions. Based on the new NN PES, the dynamics of the Li + Na2 (v = 0, j = 0) → Na + NaLi reaction are studied in the collision energy range of 10-7 to 80 cm-1. In the high collision energy range of 8 to 80 cm-1, the dynamics of the reaction is studied using the time-dependent wave packet method and the statistical quantum mechanical (SQM) method. Comparing the results of the two methods, it is found that the SQM method provides a rough description of the product ro-vibrational state distribution but overestimates the integral cross-section values. With the decrease of collision energy, the reaction differential cross section gradually changes from forward-backward symmetric scattering to predominant forward scattering. In the low collision energy range from 10-7 to 8 cm-1, the SQM method is used to study the reaction dynamics, and the rate constant in the Wigner threshold region is estimated to be 2.87 × 10-10 cm3/s.

Dynamics of the HCl + C2H5 Multichannel Reaction on a Full-Dimensional Ab Initio Potential Energy Surface.

We report a full-dimensional ab initio analytical potential energy surface (PES), which accurately describes the HCl + C2H5 multichannel reaction. The new PES is developed by iteratively adding selected configurations along HCl + C2H5 quasi-classical trajectories (QCTs), thereby improving our previous Cl(2P3/2) + C2H6 PES using the Robosurfer program package. QCT simulations for the H'Cl + C2H5 reaction reveal hydrogen-abstraction, chlorine-abstraction, and hydrogen-exchange channels leading to Cl + C2H5H', H' + C2H5Cl, and HCl + C2H4H', respectively. Hydrogen abstraction dominates in the collision energy (Ecoll) range of 1-80 kcal/mol and proceeds with indirect isotropic scattering at low Ecoll and forward-scattered direct stripping at high Ecoll. Chlorine abstraction opens around 40 kcal/mol collision energy and becomes competitive with hydrogen abstraction at Ecoll = 80 kcal/mol. A restricted opening of the cone of acceptance in the Cl-abstraction reaction is found to result in the preference for a backward-scattering direct-rebound mechanism at all energies studied. Initial attack-angle distributions show mainly side-on collision preference of C2H5 for both abstraction reactions, and in the case of the HCl reactant, H/Cl-side preference for the H/Cl abstraction. For hydrogen abstraction, the collision energy transfer into the product translational and internal energy is almost equally significant, whereas in the case of chlorine abstraction, most of the available energy goes into the internal degrees of freedom. Hydrogen exchange is a minor channel with nearly constant reactivity in the Ecoll range of 10-80 kcal/mol.

Low-lying Negative Ion States Probed in Potassium - Ethanol Collisions.

Dissociative electron transfer in collisions between neutral potassium atoms and neutral ethanol molecules yields mainly OH-, followed by C2H5O-, O-, CH3 - and CH2 -. The dynamics of negative ions have been investigated by recording time-of-flight mass spectra in a wide range of collision energies from 17.5 to 350 eV in the lab frame, where the branching ratios show a relevant energy dependence for low/intermediate collision energies. The dominant fragmentation channel in the whole energy range investigated has been assigned to the hydroxyl anion in contrast to oxygen anion from dissociative electron attachment (DEA) experiments. This result shows the relevant role of the electron donor in the vicinity of the temporary negative ion formed allowing access to reactions which are not thermodynamically attained in DEA experiments. The electronic state spectroscopy of such negative ions, was obtained from potassium cation energy loss spectra in the forward scattering direction at 205 eV impact energy, showing a prevalent Feshbach resonance at 9.36±0.10 eV with character, while a less pronounced contribution assigned to a shape resonance has been obtained at 3.16±0.10 eV. Quantum chemical calculations for the lowest-lying unoccupied molecular orbitals in the presence of a potassium atom have been performed to support the experimental findings.

Thermodynamic signatures and phase transitions in high-energy Au–Au collision

In this study, we systematically investigate the dynamics of various hadrons namely π +, π −, K +, K −, p, p¯ , Λ, Λ¯ , Ξ− and Ξ¯+ produced in central Au–Au collisions. We analyze data of AGS and RHIC, which span a broad range of collision energies, ranging from sNN = 1.9 to 200 GeV. To analyze the transverse momentum (p T ) and transverse mass (m T ) distributions, we employ a two-component standard distribution function, achieving a very good representation of the experimental data across these energy regimes. We extract key thermodynamic parameters, including the effective temperature T, the mean transverse momentum 〈p T 〉, and the initial temperature T i , and analyze their dependence on the values of collision energy and particle mass. Our findings reveal a distinct transition behaviour around sNN=19.6GeV . Below sNN=19.6GeV , the values of T, 〈p T 〉, and T i increase monotonically for all hadrons due to higher energy transfer into the system. Above this energy threshold, these extracted parameters plateau, suggesting that the additional energy is utilized as latent heat for phase transition rather than increasing the system’s temperature. These observations delineate two distinct regions: a hadron-dominated region at lower energies and a parton-dominated region at higher energies, each potentially indicative of different phases of matter, with the latter possibly signalling the onset of a quark–gluon plasma. The study thus provides critical insights into the complex interplay of thermodynamics, phase transitions, and particle interactions in high-energy Au–Au collisions.

Prospects for thermalization of microwave-shielded ultracold molecules

Toward more efficient schemes for achieving deeply degenerate molecular Fermi gases, we study anisotropic thermalization in dilute gases of microwave shielded polar molecular fermions. For collision energies above the threshold regime, we find that thermalization is suppressed due to a strong preference for forward scattering and a reduction in total cross section with energy, significantly reducing the efficiency of evaporative cooling. We perform close-coupling calculations on the effective potential energy surface derived by Deng [] to obtain accurate two-body elastic differential cross sections across a range of collision energies. We use Gaussian process regression to obtain a global representation of the differential cross section over a wide range of collision angles and energies. The route to equilibrium is then analyzed with cross-dimensional rethermalization experiments, quantified by a measure of collisional efficiency toward achieving thermalization. Published by the American Physical Society 2024

The influence of stereodynamical control on the nonadiabatic effects in the D + HD (v = 1, j = 2) → D2 + H reaction.

Stereodynamics is a field that studies the influence of the alignment or orientation of colliding partners on the results of collisions. At present, the intersection of nonadiabatic effects and stereodynamics remains to be explored. In this study, we theoretically demonstrate significant stereodynamical effects in the D + HD (v = 1, j = 2) → D2 + H reaction within the collision energy range of 0.01-2.99eV by using the time-dependent wave packet method. It is found that the stereodynamical control not only facilitates the reaction but also allows precise control of the products over a range of different scattering angles. The analysis at the state-to-state level reveals that the nonadiabatic effects are stronger in the parallel configuration than in the perpendicular configuration. By topological approach to separate the two reaction pathways at the conical intersection, the scattering amplitude of the roaming pathway in the parallel configuration is larger than that of the perpendicular configuration, which leads to more dramatic nonadiabatic features in the collision with parallel configuration.

Transport cross sections and collision integrals for N(4S)–O(3P) and N(4S)–O(1D) interactions in high-temperature air plasmas

Collisions between nitrogen (N) and oxygen (O) play a crucial role in determining transport coefficients in high-temperature atmospheres of Earth and planetary. In this study, the momentum transfer, viscosity, third-moment, and fourth-moment transport cross sections for the N(4S)–O(3P) and N(4S)–O(1D) interactions are reported in the collision energy range of 10−6–10 Hartree based on the classical and semiclassical methods. The new and accurate potential energy curves for N–O interactions, which are used to provide the input for calculations of the cross sections, are calculated based on the state-of-the-art ab initio method. The classical and semiclassical collision integrals are provided at 300–50 000 K, and the results support the calculation of transport coefficients in a third-order approximation. In particular, the collision data for the N(4S)–O(1D) interaction based on ab initio points are reported for the first time. The calculated transport cross sections and collision integrals are helpful for studies of modeling the high-temperature air plasmas.

Quantum State-Resolved Nonadiabatic Dynamics of the H+NaF → Na+HF Reaction

The H + NaF reaction is investigated at the quantum state-resolved level using the time-dependent wave-packet method based on a set of accurate diabatic potential energy surfaces. Oscillatory structures in the total reaction probability indicate the presence of the short-lived intermediate complex, attributed to a shallow potential well and exothermicity. Ro-vibrational state-resolved integral cross sections reveal the inverted population distributions of the product. The HF product favors an angular distribution in the forward hemisphere of 30°–60° within the collision energy range from the threshold to 0.50 eV, which is related to the nonlinear approach of the H atom to the NaF molecule. Quantum generalized deflection functions show that the low-J partial waves contribute primarily to the backward scattering, while the high-J partial waves govern the forward scattering. The correlation between the partial wave J and the scattering angle ϑ proves that the reaction follows a predominant direct reaction mechanism.

Scattering of diatomic molecules from graphite

In the last years, state-to-state molecular dynamics simulations of some basic elementary processes, occurring at the gas–surface interface in a wide range of temperatures and collision energies, have been performed by adopting new potential energy surfaces. In this contribution, our attention is mostly addressed to the role of long-range forces, determining the physisorption of gaseous molecules on the surface. Such forces, formulated in terms of the improved Lennard–Jones interaction potential model, control the formation of precursor or pre-reactive state that plays a crucial role in the dynamical evolution of molecules impinging on the surface in the range of low–intermediate collision kinetic energies. The study focuses on the collisions of H2, O2, N2 and CO, initially in their ground and excited vibro-rotational levels, on a graphite surface. The resulting dispersion coefficients, which control the capture of impinging molecules, are compared and found in good agreement with those available in the literature. New selectivity and peculiarities of scattered molecules, crucial to control the kinetics of elementary chemical processes occurring at the gas–surface interfaces under thermal and sub-thermal conditions, of interest in different applied fields, are highlighted.Graphic abstract

Quantum dynamics study of C—H stretching vibrational excitation in the F+CHD<sub>3</sub> → HF+CD<sub>3</sub> reaction

In recent decades, significant progress has been made in the precise theoretical investigation of gas-phase chemical reactions. Presently, a major challenge in the field of quantum dynamics is to develop the precise methodologies for studying chemical reactions involving more than four atoms. As a typical multi-atomic reaction system, the F+CH<sub>4</sub> reaction and its isotopic substitution reactions have attracted widespread attention from both experimental and theoretical perspectives in recent years. Experimental studies on the reaction of F+CHD<sub>3</sub> have revealed that the stretching vibration excitation of the C—H bond inhibits the bond dissociation, favoring the formation of DF+CHD<sub>2</sub> product channels. In this study, we use a seven-dimensional quantum time-dependent wave packet method to investigate the dynamics of the F+CHD<sub>3</sub> reaction in both the reactant vibrational ground state and the first stretching excited state of the C—H bond. In this work, the reaction probabilities under different vibrational conditions are analyzed, showing that when the collision energy is below 0.06 eV, the reaction probability curves exhibit numerous fast-oscillating peaks, supporting the experimentally suggested phenomena of dynamic resonance. In a collision energy range from 0.06 eV to 0.3 eV, the reaction probability for the HF product channel in the vibrational excited state is lower than that in the ground state, which is consistent with experimental observation. Through the analysis of the time-independent wave functions of product channels under low-energy collision conditions, it is found that for reactions involving vibrational ground states, the HF products in the product asymptotic region and the reaction transition state region are in the <i>v'</i> = 2 excited state and <i>v'</i> = 3 excited state of stretching vibration, respectively, which are consistent with previous experimental observations and six-dimensional quantum wave packet simulations. For reactions involving the first excited state of C—H stretching vibration, the HF products in the product asymptotic region and the reaction transition state region are both in the <i>v'</i> = 3 excited state of stretching vibration, which are consistent with the results obtained based on energy analysis. Simulation results indicate that in the case of low-energy collisions, the time-independent wave function for the C—H stretching vibrational excited state tends to be closer to the D atom side in the transition state region. This phenomenon is attributed to the more significant energy advantage of the vibrational excited state potential energy surface in the large collision angle region, explaining the inhibitory effect of stretching vibration excitation on the HF product channel. This study offers important theoretical support for explaining experimental results and contributes to a more in-depth understanding of the influence of vibrational mode excitations on the dynamical processes in poly-atomic reactions.

Exotic particles and nuclei

Light nuclei, antinuclei and hypernuclei constitute a laboratory to study the mechanisms of formation of bound states in proton-proton and nucleus-nucleus collisions over a broad range of collision energies, providing insights into the nuclear structure as well as into the strong interaction. In this contribution, a selection of the experimental results and latest developments presented at the Quark Matter 2023 conference is reviewed.

Detailed quasiclassical dynamics of the F- + SiH3Cl multi-channel reaction.

We report a detailed quasiclassical trajectory study on the F- + SiH3Cl multi-channel reaction using a full-dimensional ab initio analytical potential energy surface. Reaction probabilities, cross sections, initial attack and scattering angle distributions as well as product relative translational, internal, vibrational, and rotational energy distributions are obtained in the collision energy range of 1-40 kcal mol-1 for the following channels: SiH3F + Cl-, SiH2Cl- + HF, SiH2F- + HCl, SiH2FCl + H-, SiH2 + FHCl-, and SiHFCl- + H2. All the channels are translationally cold indicating indirect mechanisms, except proton transfer (SiH2Cl- + HF), which shows mixed direct-indirect character. The angular distributions vary depending on collision energy and inversion/retention for SiH3F + Cl-. In the case of SiH2Cl- + HF front-side/back-side attack backward-forward/forward scattering preference is found at low/high collision energy. SiH2F- + HCl is formed with isotropic scattering and the preferred angle of attack is similar to the SiH3F + Cl- channel. SiH2FCl + H-/SiH2 + FHCl- favors back-side attack and isotropic/backward scattering, whereas SiHFCl- + H2 does not show significant angular preference.

Quantum dynamics study of reaction H+SiH using a new potential energy surface of SiH<sub>2</sub>(1<sup>1</sup>A′)

Initial state-selected and energy-resolved reaction probabilities, integral cross sections(ICSs), and thermal rate constants of the <inline-formula><tex-math id="M3">\begin{document}$ \text{H}{(}^{2}\text{S})+S\text{iH}({\text{X}}^{2}\Pi; \nu = 0\text{ },j = 0)\to \text{Si}{(}^{1}\text{D})+{\text{H}}_{2}({\text{X}}^{1} \Sigma_{g}^{+}) $\end{document}</tex-math></inline-formula> reaction are calculated within the coupled state(CS) approximation and accurate calculation with full Coriolis coupling(CC) by a time-dependent wave packet propagation method (Chebyshev wave packet method). Therefore, a new ab initio global potential energy surface (PES) of the electronic ground state (1<sup>1</sup>A′) of the system, which was recently reported by Li et al. [<ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://pubs.rsc.org/en/content/articlelanding/2022/cp/d1cp05432e"> <i>Phys. Chem. Chem. Phys.</i> 2022 <b>24</b> 7759</ext-link>], is employed. The contributions of all partial waves to the total angular momentum <i>J</i> = 80 for CS approximation and <i>J</i> = 90 for CC calculation are considered to obtain the converged ICSs in a collision energy range of 1.0 ×10<sup>–3</sup>－1.0 eV. The calculated probabilities and ICSs display a decreasing trend with the increase of the collision energy and show an oscillatory structure due to the SiH<sub>2</sub> well on the reaction path. The neglect of CC effect will lead to underestimation of the ICS and the rate constant due to the formation of an SiH<sub>2</sub> complex supported by the stationary points of the SiH<sub>2</sub>(1<sup>1</sup>A′) PES. In addition, the results of the exact calculation including CC effect are compared with those calculated in the CS approximation. For the reaction probability, CC and CS calculations change with similar tends, shown by their observations at small total angular momentum <i>J</i> = 10, 20 and 30, and the CC results are larger than the CS results almost in the whole considered energy range at large total angular momentum <i>J</i> = 40, 50, 60 and 70. The gap between CS and CC probability get more pronounced with increasing of <i>J</i>, which reveals that Coriolis coupling effects become more and more important with <i>J</i> increasing for the title reaction<i>.</i> Moreover, the exact quantum-wave calculations show that the thermal rate constant between 300 K and 1000 K for the title reaction shows a similar temperature independent behavior to that for the H + CH reaction, but the value of the rate constant for the H + SiH reaction is an order of magnitude larger than that for the H + CH reaction.

Directed flow and hyperon polarization at RHIC BES from multi-fluid dynamics

We present directed flow of protons and pions, as well as mean polarization of Λ and ¯Λ hyperons computed for Au-Au collisions at √SNN = 5 … 19.6 GeV in MUFFIN model. MUlti Fluid simulation for Fast IoN collisions, or MUFFIN, is a state-of-the-art 3-fluid dynamic model for simulating heavy-ion collisions in the region from a few to a hundred GeV center-of-mass energy. Whereas MUFFIN succeeds to reproduce basic observables in the collision energy range of interest, the slope of the directed flow at mid-rapidity is much steeper as compared to the data, it has unclear EoS dependence and final-state hadronic cascade affects this observable significantly. The excitation function of the Λ polarization shows a significant splitting between polarizations of Λ and ¯Λ, which challenges a widespread interpretation that the splitting is affected mainly by the late-stage magnetic field.