Physics

This work presents exchange potentials for specific orbitals calculated by inverting Hartree-Fock wavefunctions. This was achieved by using a Depurated Inversion Method. The basic idea of the method relies upon the substitution of Hartree-Fock orbitals and eigenvalues into the Kohn-Sham equation. Through inversion, the corresponding effective potentials were obtained. Further treatment of the inverted potential should be carried on. The depuration is a careful optimization which eliminates the poles and also ensures the fullfilment of the appropriate boundary conditions. The procedure developed here is not restricted to the ground state or to a nodeless orbital and is applicable to all kinds of atoms. As an example, exchange potentials for noble gases and term-dependent orbitals of the lower configuration of Nitrogen are calculated. The method allows to reproduce the input energies and wavefunctions with a remarkable degree of accuracy.

The usual derivations of the S and K matrices for two-particle reactions proceed through the Lippmann-Schwinger equation with formal definitions of the incoming and outgoing scattering states. Here we present an alternative derivation that is carried out completely in the Hamiltonian representation, using a discrete basis of configurations for the scattering channels as well as the quasi-bound configurations of the combined fragments. We use matrix algebra to derive an explicit expression for the K matrix in terms of the Hamiltonian of the internal states of the compound system and the coupling between the channels and the internal states. The formula for the K matrix includes explicitly a real dispersive shift matrix to the internal Hamiltonian that is easily computed in the formalism. That expression is applied to derive the usual form of the S matrix as a sum over poles in the complex energy plane. Some extensions and limitations of the discrete-basis Hamiltonian formalism are discussed in the concluding remarks and in the Appendix.

We present a combined ion imaging and density functional theory study of the dynamics of the desorption process of rubidium and cesium atoms off the surface of helium nanodroplets upon excitation of the perturbed 6s and 7s states, respectively. Both experimental and theoretical results are well represented by the pseudodiatomic model for effective masses of the helium droplet in the desorption reaction of m_eff/m_He~10 (Rb) and 13 (Cs). Deviations from this model are found for Rb excited to the 6p state. Photoelectron spectra indicate that the dopant-droplet interaction induces relaxation into low-lying electronic states of the desorbed atoms in the course of the ejection process.

The desorption dynamics of rubidium dimers (Rb_2) off the surface of helium nanodroplets induced by laser excitation is studied employing both nanosecond and femtosecond ion imaging spectroscopy. Similarly to alkali metal atoms, we find that the Rb_2 desorption process resembles the dissociation of a diatomic molecule. However, both angular and energy distributions of detected Rb_2^+ ions appear to be most crucially determined by the Rb_2 intramolecular degrees of freedom rather than by those of the Rb_2He_N complex. The pump-probe dynamics of Rb_2^+ is found to be slower than that of Rb^+ pointing at a weaker effective guest-host repulsion for excited molecules than for single atoms.

The electron-hole correlation length serves as an intrinsic length scale for analyzing excitonic interactions in semiconductor nanoparticles. In this work, the derivation of electron-hole correlation length using the two-particle reduced density is presented. The correlation length was obtained by first calculating the electron-hole cumulant from the pair density,and then transforming the cumulant into intracular coordinates, and finally then imposing exact sum-rule conditions on the radial integral of the cumulant. The excitonic wave function for the calculation was obtained variationally using the electron-hole explicitly correlated Hartree-Fock method. As a consequence, both the pair density and the cumulant were explicit functions of the electron-hole separation distance. The use of explicitly correlated wave function and the integral sum-rule condition are the two key features of this derivation. The method was applied to a series of CdSe quantum dots with diameters 1-20 nm and the effect of dot size on the correlation length was analyzed.

The use of powerful hydrogen cluster jet targets in storage ring experiments led to the need of precise data on the mean cluster velocity as function of the stagnation temperature and pressure for the determination of the volume density of the target beams. For this purpose a large data set of hydrogen cluster velocity distributions and mean velocities was measured at a high density hydrogen cluster jet target using a trumpet shaped nozzle. The measurements have been performed at pressures above and below the critical pressure and for a broad range of temperatures relevant for target operation, e.g., at storage ring experiments. The used experimental method is described which allows for the velocity measurement of single clusters using a time-of-flight technique. Since this method is rather time-consuming and these measurements are typically interfering negatively with storage ring experiments, a method for a precise calculation of these mean velocities was needed. For this, the determined mean cluster velocities are compared with model calculations based on an isentropic one-dimensional van der Waals gas. Based on the obtained data and the presented numerical calculations, a new method has been developed which allows to predict the mean cluster velocities with an accuracy of about 5%. For this two cut-off parameters defining positions inside the nozzle are introduced, which can be determined for a given nozzle by only two velocity measurements.

Recently we have proposed an effective Hartree-Fock (EHF) theory for the electrons of the muonic molecules that is formally equivalent to the HF theory within the context of the Nuclear-Electronic Orbital theory [Phys. Chem. Chem. Phys. 20, 4466 (2018)]. In the present report we extend the muon-specific effective electronic structure theory beyond the EHF level by introducing the effective second order Muller-Plesset perturbation theory (EMP2) and the effective coupled-cluster theory at single and double excitation levels (ECCSD) as well as an improved version including perturbative triple excitations (ECCSD(T)). These theories incorporate electron-electron correlation into the effective paradigm and through their computational implementation, a diverse set of small muonic species is considered as a benchmark at these post-EHF levels. A comparative computational study on this set demonstrates that the muonic bond length is in general non-negligibly longer than corresponding hydrogenic analogs. Next, the developed post-EHF theories are applied for the muoniated N-Heterocyclic carbene/silylene/germylene and the muoniated triazolium cation revealing the relative stability of the sticking sites of the muon in each species. The computational results, in line with previously reported experimental data demonstrate that the muon generally prefers to attach to the divalent atom with carbeneic nature. A detailed comparison of these muonic adducts with the corresponding hydrogenic adducts reveals subtle differences that have already been overlooked.

A sputter ion source with a solid graphite target has been used to produce dianions with a focus on carbon cluster dianions, C 2− n , with n=7−24 . Singly and doubly charged anions from the source were accelerated together to kinetic energies of 10 keV per atomic unit of charge and injected into one of the cryogenic (13 K) ion-beam storage rings of the Double ElectroStatic Ion Ring Experiment facility at Stockholm University. Spontaneous decay of internally hot C 2− n dianions injected into the ring yielded C − anions with kinetic energies of 20 keV, which were counted with a microchannel plate detector. Mass spectra produced by scanning the magnetic field of a 90 ∘ analyzing magnet on the ion injection line reflect the production of internally hot C 2− 7 − C 2− 24 dianions with lifetimes in the range of tens of microseconds to milliseconds. In spite of the high sensitivity of this method, no conclusive evidence of C 2− 6 was found while there was a clear C 2− 7 signal with the expect isotopic distribution. An upper limit is deduced for a C 2− 6 signal that is two orders-of-magnitue smaller than that for C 2− 7 . In addition, C n O 2− and CsCu 2− dianions were detected.

We have recorded the coherent diffraction images of individual xenon clusters with intense extreme ultraviolet pulses to elucidate the influence of light-induced electronic changes on the diffraction pattern. Using the FLASH free-electron laser we tuned the wavelength to specific xenon atomic and ionic resonances. The data show the emergence of a transient core-shell structure within the otherwise homogeneous sample. Simulations indicate that ionization and nanoplasma formation result in a cluster shell with strongly altered refraction. The presented resonant scattering approach enables imaging of ultrafast electron dynamics on their natural time scale.

The bound states of two identical dipoles in a harmonic waveguide are investigated. In the regime of weak dipole-dipole interactions, the local frame transformation (LFT) method is applied to determine the spectrum of dipolar confinement-induced bound states analytically. The accuracy of the LFT approach is discussed by comparing the analytical results with the numerical ones based on a solution of the close-coupling equations. It is found that close to the threshold energy in the waveguide, the LFT method needs to include more partial wave states to obtain accurate bound state energies. As the binding energy increases, the LFT method using a single partial wave state becomes more accurate. We also compare the bound states in waveguides and in free space. For the bosonic case, the s-wave dominated bound state looks like a free-space state when its energy is below a certain value. For the fermionic case, the p-wave dominated bound state energies in waveguides and in free-space coincide even close to zero energy.