A path integral approach has been generalized for the non-relativistic electron charge transfer processes. The charge transfer - the capture of an electron by an ion passing another atom or more generally the problem of rearrangement collisions is formulated in terms of influence functionals. It has been shown that the electron charge transfer process can be treated either as electron transition problem or as elastic scattering of ion and atom in the some effective potential field. The first-order Born approximation for the electron charge transfer cross section has been reproduced to prove the adequacy of the path integral approach for this problem.
Abstract We present Feynman’s path integral derivation of the Schrödinger equation. The van Hove formulation of non-relativistic scattering is presented. We then give a full quantum mechanical treatment of non-relativistic scattering. Both the interaction of the beams with the apparatus and the scattering process itself are treated quantum mechanically. In the spirit of Schrödinger, particle trajectories do not appear, with all of the physics being contained in the phases of the wave function.
The simulation of ion-atom collisions remains a formidable challenge due to the complex interplay between electronic and nuclear degrees of freedom. We present a hybrid quantum-classical computing framework for simulating time-dependent ion-atom collision dynamics, within which two variational quantum time evolution algorithms are implemented. To validate our framework, we simulate the charge-transfer dynamics and compute the corresponding cross sections for the proton-hydrogen collision system across an energy range 1--25 keV. Our results accurately reproduce the charge-transfer dynamics with high fidelity and exhibit very good agreement with available experimental and theoretical cross-section data across the entire energy range. These results highlight the accuracy and applicability of our hybrid quantum-classical framework for scattering cross-section calculations. Our work demonstrates an effective approach for mapping time-dependent many-body collision problems onto near-term quantum computing devices, and also provides promising directions for practical applications of universal quantum computing in the noisy intermediate-scale quantum era.
The collision between two positronium (Ps) atoms is a four-body Coulomb problem with all the particles of equal masses. It is very difficult to compute the Born-Oppenheimer (BO) scattering amplitude involving the nine-dimensional integrals with four Coulomb interaction terms between the atoms. It is extremely difficult in the electron-electron correlation term to include the exchange or antisymmetry between two system electrons exactly. Earlier the Ps and H system was easily approximated as a three-body problem, due to the light mass of Ps the center of mass of the system was confined in the H-nucleus. A simple substitution of variables using no approximation has enabled to evaluate the electron-electron Coulomb exchange-correlation term exactly in such a four-center problem in the center of mass frame involving a nine dimensional integral. The present code of Ps-Ps collision using an ab-initio and exact static-exchange model (SEM) that uses the BO amplitude as input, can reproduce exactly the same data of Ps and H system just by using the appropriate atomic parameters and reduced mass of the system. The s-wave elastic phase shifts and the corresponding partial cross sections are calculated for both the singlet and triplet channels. In addition, we calculate the integrated /total elastic cross section ( ) and the quenching cross section ( q ); an augmentedBorn method is used to evaluate more accurately. The effective range theory is applied to get the scattering length and the effective range. The SEM can include only the non-adiabatic short-range effects but no long-range interaction. Now it is easy to extend the basis of a coupled-channel method to include the excitation and continuum channels exactly for better accuracy following the present prescription and avoiding the approximation tools. PACS 03.65.Nk – Scattering theory PACS 36.10.Dr – Positronium PACS 34.50.Cx – Elastic; ultracold collisions
Electronic structure, spectroscopy, cold ion-atom elastic collision properties and photoassociation formation prediction of (MgCs)
+ molecular ion
Studies on the interactions between an alkali atom and an alkaline earth ion at low energy are important in the field of cold chemistry. In this paper we, extensively, study the structure, interactions, and dynamics of (MgCs)
+ molecular ion. We use an ab initio approach based on the formalism of non-empirical pseudo-potential for Mg
2+ and Cs
+ cores, large Gaussian basis sets and full valence configuration interaction. In this context, the (MgCs)
+ cation is treated as an effective two-electron system. Potential energy curves and their spectroscopic constants for the ground and the first 41 excited states of
1,3Σ+,
1,3Π and
1,3Δ symmetries are determined. Furthermore, we identify the avoided crossings between the electronic states of
1,3Σ+ and
1,3Π symmetries. These crossings are related to the charge transfer process between the two ionic limits Mg/Cs
+ and Mg
+/Cs. In addition, vibrational-level spacings, the transition and permanent dipole moments are presented and analysed. Using the produced potential energy data, the ground-state scattering wave functions and elastic cross sections for a wide range of energies are performed. Furthermore, we predict the formation of translationally and rotationally cold molecular ion (MgCs) + in the ground state electronic potential energy by stimulated Raman type process aided by ion-atom cold collision. In the low energy limit (< 1 mK), elastic scattering cross sections exhibit Wigner law threshold behaviour; while in the high energy limit the cross sections as a function of energy E go as E
−1/3. A qualitative discussion about the possibilities of forming the cold (MgCs)
+ molecular ions by photoassociative spectroscopy is presented.