We report here the first time-dependent wave packet dynamics study for an ultracold four-atom reaction. Our calculations provide accurate integral cross sections and rate constants all the way down to the Bethe–Wigner threshold regime for the benchmark OH + H 2 ( v = 2, j = 0) → H 2 O + H reaction, indicating that the time-dependent wave packet method is a powerful tool for studying ultracold four-atom reactions.
We report here the first time-dependent wave packet dynamics study for an ultracold four-atom reaction. Our calculations provide accurate integral cross sections and rate constants all the way down to the Bethe–Wigner threshold regime for the benchmark OH + H 2 ( v = 2, j = 0) → H 2 O + H reaction, indicating that the time-dependent wave packet method is a powerful tool for studying ultracold four-atom reactions.
Because the de Broglie wavelength of ultracold molecules is very large, the cross sections for collisions of molecules at ultracold temperatures are always computed by the time-independent quantum scattering approach. Here, we report the first accurate time-dependent wave packet dynamics calculation for reactive scattering of ultracold molecules. Wave packet dynamics calculations can be applied to molecular systems with more dimensions and provide real-time information on the process of bond rearrangement and/or energy exchange in molecular collisions. Our work thus makes possible the extension of rigorous quantum calculations of ultracold reaction properties to polyatomic molecules and adds a new powerful tool for the study of ultracold chemistry.
We describe a method for obtaining the scattering matrix for nuclear or chemical reactions on a finite lattice. Aside from the preparation of the initial and final states as wave packets, the only other operation required is unitary time evolution, making this approach ideal for simulations on quantum hardware. The central quantity is a time-dependent overlap between incoming and outgoing wave packets whose Fourier transform corresponds to the scattering matrix at fixed energy, from which one can calculate elastic and inelastic cross sections for reactions involving two interacting clusters. Working in Cartesian coordinates enables an efficient encoding of the problem on quantum hardware via the first quantization mapping, with favorable qubit scaling for describing asymptotic scattering states. Within this framework, we describe a quantum algorithm for probing the scattering amplitude through different angles, including the forward direction, which provides access to the total cross section via the optical theorem. We demonstrate our methods through a series of numerical examples, for both elastic and inelastic processes, comparing against exact calculations. The techniques we describe can more readily be extended to a large number of constituent particles than other existing approaches, once fault-tolerant quantum hardware becomes available.
We have calculated accurate quantum reactive and elastic cross sections for the prototypical barrierless reaction D++H2(v=0,j=0) using a modified hyperspherical scattering method. The considered kinetic energy ranges from the ultracold to the Langevin regimes. A reaction rate coefficient practically constant in no less than eight orders of magnitude is obtained. The availability of accurate results for this system allows one to test the quantum theory by Jachymski et al. [K. Jachymski, M. Krych, P. S. Julienne, and Z. Idziaszek, Phys. Rev. Lett. 110, 213202 (2013)] in a nonuniversal case. The short-range reaction probability is rationalized using statistical model assumptions and related to a statistical factor. This provides a means to estimate one of the parameters that characterizes ultracold processes from first principles.
Non-relativistic quantum scattering theory informs our broad understanding of nuclear collision processes. However, detailed theoretical insights into the dynamics of fusion, whereby the colliding nuclei form a compound nucleus, remain elusive with conventional approaches. Fundamentally, understanding the complex dissipative processes inherent to compound nucleus formation and when they occur during the collision remains challenging. This, for example, prevents a consistent description of heavy-ion fusion over a wide range of collision energies and hinders searches for new super-heavy elements. To understand these dynamics, we need time-dependent approaches to nuclear collisions. In this thesis, a non-relativistic, time-dependent wave packet theory for potential scattering of charged quantum particles (such as nuclei) has been developed. It formally extends the application of Tannor and Weeks's (1993) formulation of the scattering matrix theory to systems containing the long-range Coulomb potential, by utilising Dollard's (1964) Møller operators. Using the asymptotic localisation of wave packets, analytical theorems have been formulated that allow convenient numerical application of this method. Numerical tests illustrating the theory mark the first rigorous application of this method in nuclear physics. Further insights are gained through a novel analysis of the wave packet time-correlation function (which underlies the theory) to understand how different dynamical processes, such as the formation of long-lived, quasi-bound states, during scattering contribute to the scattering matrix. This provides guidance on using the time-correlation function to obtain fusion observables, along with the associated challenges. Furthermore, this analysis showed that time-correlation functions can be obtained from static calculations, opening numerous new possibilities for studying the dynamics of nuclear reactions, in general, using this approach. This work opens new avenues for studying the dynamics of compound nucleus formation and other dissipative processes in nuclear reactions.
Ultracold hydrogen-exchange reactions have long provided a key platform for identifying subtle quantum mechanical effects in triatomic systems. The long-range interactions, diagonal Born-Oppenheimer correction (DBOC), and geometric phase (GP) have been predicted to influence such reactions, yet their individual effects have not been investigated. Here, we investigate the D + H2(v = 4, j = 0) → H + HD reaction using time-dependent wave packet calculations that incorporate a newly constructed long-range potential, DBOC, and a diabatic GP treatment. The inclusion of the accurate long-range interactions substantially alters the cold reaction dynamics by removing spurious short-range barriers and strongly modifying partial-wave resonances, including a pronounced shift and nearly 70% enhancement of the J = 2 resonance. The DBOC produces a modest overall reduction in the reaction rate, whereas the GP introduces the dominant suppression and governs the interference pattern in both total and state-resolved rates. These results demonstrate that the accurate inclusion of long-range interactions, DBOC, and GP is essential for reliably describing ultracold hydrogen-deuterium exchange reactions, clarifying the distinct roles each contribution plays in the reaction dynamics.
Abstract We report a quantum dynamics study of the Li + HF → LiF + H reaction at low temperatures of interest to cooling and trapping experiments. Contributions from non-zero partial waves are analyzed and results show narrow resonances in the energy dependence of the cross section that survive partial wave summation. The computations are performed using the ABC code and a simple modification of the ABC code that enables separate energy cutoffs for the reactant and product rovibrational energy levels is found to dramatically reduce the basis set size and computational expense. Results obtained using two ab initio electronic potential energy surfaces for the LiHF system show strong sensitivity to the choice of the potential. In particular, small differences in the barrier heights of the two potential surfaces are found to dramatically influence the reaction cross sections at low energies. Comparison with recent measurements of the reaction cross section (Bobbenkamp et al 2011 J. Chem. Phys. 135 204306 ) shows similar energy dependence in the threshold regime and an overall good agreement with experimental data compared to previous theoretical results. Also, usefulness of a recently introduced method for ultracold reactions that employ the quantum close-coupling method at short-range and the multichannel quantum defect theory at long-range, is demonstrated in accurately evaluating product state-resolved cross sections for D + H2 and H + D2 reactions.