Resonances in Scattering. I. Basic Equations and Main Approximations

We describe the main features of resonances in scattering, determining the resonances in view of the theory of collisions in a two-body system, as well as the resonances emerging as a result of collisions in a few-body system. We analyze regularities in the emergence of such resonances and their characteristics. We discuss the results of calculations of the resonant processes occurring during collisions of electrons with diatomic molecules, in view of the quantum theory of scattering in a few-body system based on the Faddeev–Yakubovsky equations.     

Study of various few-body systems using Gaussian expansion method (GEM)

We review our calculation method, Gaussian expansion method (GEM), to solve accurately the Schrödinger equations for bound, resonant and scattering states of few-body systems. Use is made of the Rayleigh-Ritz variational method for bound states, the complex-scaling method for resonant states and the Kohn-type variational principle to S-matrix for scattering states. GEM was proposed 30 years ago and has been applied to a variety of subjects in few-body (3- to 5-body) systems, such as 1) few-nucleon systems, 2) few-body structure of hypernuclei, 3) clustering structure of light nuclei and unstable nuclei, 4) exotic atoms/molecules, 5) cold atoms, 6) nuclear astrophysics and 7) structure of exotic hadrons. Showing examples in our published papers, we explain i) high accuracy of GEM calculations and its reason, ii) wide applicability of GEM to various few-body systems, iii) successful predictions by GEM calculations before measurements. The total bound-state wave function is expanded in terms of few-body Gaussian basis functions spanned over all the sets of rearrangement Jacobi coordinates. Gaussians with ranges in geometric progression work very well both for shortrange and long-range behavior of the few-body wave functions. Use of Gaussians with complex ranges gives much more accurate solution than in the case of real-range Gaussians, especially, when the wave function has many nodes (oscillations). These basis functions can well be applied to calculations using the complex-scaling method for resonances. For the few-body scattering states, the amplitude of the interaction region is expanded in terms of those few-body Gaussian basis functions.     

Efimov Resonances in Ultracold Quantum Gases

Ultracold atomic gases have developed into prime systems for experimental studies of Efimov three-body physics and related few-body phenomena, which occur in the universal regime of resonant interactions. In the last few years, many important breakthroughs have been achieved, confirming basic predictions of universal few-body theory and deepening our understanding of such systems. We review the basic ideas along with the fast experimental developments of the field, focussing on ultracold cesium gases as a well-investigated model system. Triatomic Efimov resonances, atom-dimer Efimov resonances, and related four-body resonances are discussed as central observables. We also present some new observations of such resonances, supporting and complementing the set of available data.     

Collisions of electrons with molecules in excited vibrational-rotational states

Results are presented of calculations of cross sections for scattering of electrons by diatomic molecules in specific excited vibrational-rotational states. The calculations were made using an approximation based on a quantum theory of scattering in a system of several bodies which can be applied to calculations of direct reactions and reactions involving the formation of an intermediate transition complex. Results of calculations of cross sections for collisions of electrons with hydrogen, nitrogen, lithium, sodium, and hydrogen halide molecules are compared with existing experimental data and the results of calculations made by other authors.     

Mechanisms of resonant laser ionization

An experimental investigation and numerical simulation of resonant laser breakdown are performed. As a result, quantitative agreement between the experimental data on the parameters of a dense resonant plasma (the electron density and the electron temperature) and the results of calculations in the range of detunings of the laser radiation from resonance Δλ>2–2.5 nm, in which the spatial instability of the intense resonant laser beam and the absorption of radiation are minimal, is obtained for the first time. It is shown that the previously proposed mechanism of resonant breakdown associated with laser-induced associative ionization introduces only a small correction to the final extent of ionization of the resonant plasma and scarcely alters its temperature. The influence of quantum stimulated inverse bremsstrahlung processes, which are usually described as collisions of the second kind in the resonance case, on the energy gain by electrons is analyzed for the first time in reference to specific experimental findings. The numerical calculations show that at detunings of the order of the Rabi frequency, the mechanism by which electrons gain energy through the resonant system does not reduce to collisions of the second kind and can significantly increase the density of the resonant plasma. However, in this range of detunings the laser beam is still strongly perturbed by instability processes, precluding a proper comparison of the theory with experiment. At large Δλ the classical and quantum cases differ from one another only slightly, and the values of N _e calculated for both mechanisms lie within the measurement error. Zh. éksp. Teor. Fiz. 111, 1274–1296 (April 1997)     

Neutron Resonances in Few-Body Systems and the EOS of Neutron Star Crust

The effective interactions formed by neutron rescattering between the nuclei fixed in nodes of the crystalline lattice of neutron star crusts have been considered. In the case of two-body resonances in neutron–nucleus subsystems new neutron resonances of few-body nature come into existence in the overdense crystal under certain conditions. The energies and widths of new resonances get additional dependence on the lattice parameters. The effective interactions result in nonlinear correction to the equation of state determined by the balance of gravitational, Coulomb and nuclear resonance forces. This leads to resonant oscillations of density in the accordant layers of crusts that are accompanied by oscillations of gamma radiation. The phenomena may clarify some processes connected with few-body neutron resonances in neutron star crusts, that have influence on the microstructure of pulsar impulses.     

Index of refraction for cold lithium- and diatomic sodium waves traveling through cold noble gases

In the present paper we propose to measure the index of refraction for diatomic sodium molecules traveling through a cold helium gas. Theoretical calculations of the index of refraction for this system are presented as a function of the molecule velocity and atom gas temperature. Whereas previous theoretical efforts to compute the refractive index have been concerned with atomic systems and atomic matter waves, we extend the investigation to diatomic molecules in the present work. To enable such calculations the potential energy surface for the atom-molecule interaction is calculated ab initio, along with the long range dispersion coefficients for the atom-molecule system. The full close-coupled equations, describing the atom-molecule collisions, are solved numerically to work out the influence of the collisions on the matter waves. We investigate the sensitivity of the results upon changes and inaccuracies in the potential energy surface. Several molecular rotational levels are included in the present study, and the index of refraction is found to depend on the rotational state. In addition, the index of refraction for atomic lithium matter waves traveling through the cold noble gases helium and argon are computed, motivated by a recent experiment with atomic lithium matter waves. Different resonances (glory- and scattering resonances) are identified from the results. Such resonances offer an important opportunity for the comparison of experiment and theory.     

Dynamics of low-energy electron attachment to formic acid

Low-energy electrons (<2 eV) can fragment gas phase formic acid (HCOOH) molecules through resonant dissociative attachment processes. Recent experiments have shown that the principal reaction products of such collisions are formate ions (HCOO-) and hydrogen atoms. Using first-principles electron scattering calculations, we have identified the responsible negative ion state as a transient pi* anion. Symmetry considerations dictate that the associated dissociation dynamics are intrinsically polyatomic: a second anion surface, connected to the first by a conical intersection, is involved in the dynamics and the transient anion must necessarily deform to nonplanar geometries before it can dissociate to the observed stable products.     

磁场下量子点的电子态

原子和核结构的少体理论方法改进后用以研究磁场下包含三个电子的二维量子点的电子性质。我们首先解析地证明了对应于三电子系统基态的幻数角动量的存在起源于量子力学对称性的要求。基于少体理论方法的计算确认了上述理论分析的正确性,计算同时显示出磁场强度和约束势对三电子系统基态的影响。 关键词：     

Electron-molecule and atom-molecule scattering within the few-body approximation

A quantum theory of few-body scattering based on the Faddeev-Yakubovsky equations is applied to the calculation of cross sections of electron and atom scattering by diatomic molecules in specified excited rovibrational states. The results of the calculations are compared with the available experimental data and other calculations.     

Mechanisms of molecular manipulation with the scanning tunneling microscope at room temperature: chlorobenzene/si(111)-(7 x 7)

We report a systematic experimental investigation of the mechanism of desorption of chlorobenzene molecules from the Si(111)-(7 x 7) surface induced by the STM at room temperature. We measure the desorption probability as a function of both tunneling current and a wide range of sample bias voltages between -3 V and +4 V. The results exclude field desorption, thermally induced desorption, and mechanical tip-surface effects. They indicate that desorption is driven by the population of negative (or positive) ion resonances of the chemisorbed molecule by the tunneling electrons (or holes). Density functional calculations suggest that these resonant states are associated with the pi orbitals of the benzene ring.     

Rotational Feshbach resonances in ultracold molecular collisions

In collisions at ultralow temperatures, molecules will possess Feshbach resonances, foreign to ultracold atoms, whose virtual excited states consist of rotations of the molecules. We estimate the mean spacing and mean widths of these resonant states, exploiting the fact the molecular collisions at low energy display chaotic motion. As examples, we consider the experimentally relevant molecules O2, OH, and PbO. Especially for polar species, the density of s-wave resonant states is quite high, implying potentially disastrous consequences for trapped molecules.     

Spectrum and dynamics of the BCS-BEC crossover from a few-body perspective

The spectrum of two spin-up and two spin-down fermions in a trap is calculated using a correlated Gaussian basis throughout the range of the BCS-BEC crossover. These accurate calculations provide a few-body solution to the crossover problem. This solution is used to study the time evolution of the system as the scattering length is changed, mimicking experiments with Fermi gases near Fano-Feshbach resonances. The structure of avoiding crossings in the spectrum allow us to understand the dynamics of the system as a sequence of Landau-Zener transitions. Finally, we propose a ramping scheme to study atom-molecule coherence.     

Resonance multiplicities in a hadron transport approach

In this article we focus on the multiplicities of resonances, ratios of resonant over non-resonant states and rescattering processes in heavy ion collisions. Therefore we utilize a hadron transport model (UrQMD v1.3). We find that rescattering of decay particles is of great importance when studying resonances in a hadronic medium.     

Population processes in high-pressure inert-gas-mixture lasers

Working-level-population processes are analyzed on the basis of detailed investigations of the amplitude-time structure of the laser and spontaneous emission following a pulsed electric discharge in the mixtures He + R (R = Ar, Kr, Xe), Ar + Xe. Account is taken in the analysis of excitation by electrons (direct and stepwise) and of population as a result of relaxation processes (collisions of second kind with electrons; radiative cascades, recombination processes; collisions with the atoms of the working and buffer gases; excitation transfer from helium molecules). It is concluded that under optimum efficiency conditions inversion is produced in the lasers considered as a result of direct electron collision with the working atoms (Ar, Kr, Xe), which are in the ground state.Translated from Lazernye Sistemy, pp. 15–34, 1982.     

Dispersive interactions between matter qubits and bright squeezed light

The damage induced by radiation in cells is currently described via low-energy attachment of electrons produced in the biological medium by the primary radiation. Therefore the corresponding metastable anionic states are obtained in this work from multichannel quantum calculations which, in the present study, involve β-D-ribose and β-D-deoxyribose molecular fragments from RNA and DNA structures. The scattering attributes associated with the resonant processes are derived from the computed total, elastic cross sections by means of a high-level Breit-Wigner analysis of the calculated phase shifts. The present procedure is shown to provide a powerful tool for extracting the resonance parameters from the scattering data even in the presence of broad, overlapping resonances which typically occur in the resonant dynamics of complicated biosystems after electron attachment effects.     

Application of the time-dependent close-coupling approach to few-body atomic and molecular ionizing collisions

We review the recent progress made in applying the time-dependent close-coupling approach to ionizing collisions of electrons, photons, and ions with small atoms and molecules. The last twenty years have seen a proliferation of non-perturbative approaches applied to fundamental atomic and molecular scattering processes. Such processes form the building blocks of describing the dynamics of plasmas over a wide range of temperatures and densities, and also provide insight into the long-range Coulomb interactions between charged particles. Studies of the few-body Coulomb problem presented in electron, photon, or ion-impact ionization of small atoms and molecules, by direct solution of the time-dependent Schr?dinger equation, are particularly useful because the complicated three-body boundary conditions of more than one continuum particle in a Coulomb potential are not required. With the continuing growth and increasing availability of high-performance computing resources, such methods can now be applied to a wide variety of scattering processes. The recent progress made using such a time-dependent approach is described in this colloquium. In this paper, we focus on the recent results obtained for one-, two-, and three-electron systems, thus building on a previous review of the time-dependent close-coupling method [M.S. Pindzola et?al., J. Phys. B 40, R39 (2007)], which also described the application to multi-electron targets.