Grazyna Staszewska

Convergence of L2 methods for scattering problems

We compare 35 different methods for calculating reactance matrix elements from L2 basis sets. By systematically classifying the methods, we are able to draw conclusions about several lines of approach. For example, the explicit subtraction of unscattered waves or the least‐squares minimization of the iterative correction do not lead to significant improvements in accuracy. However, expansions of the amplitude density are systematically more rapidly convergent than expansions of the wave function. The most efficient methods are variational methods based on expanding the amplitude density, but the method of moments for the amplitude density may also be useful since it leads to reasonable accuracy with smaller programming effort.

Complex optical potential model for electron–molecule scattering, elastic scattering, and rotational excitation of H2 at 10–100 eV

We report nonempirical calculations for differential and integral elastic scattering cross sections, absorption cross sections (accounting for electronic inelasticity), and total scattering cross sections for electron–H2 scattering at 10–100 eV. The calculations are based on a complex, energy‐dependent effective potential consisting of four terms: A static potential calculated from ab initio extended‐basis‐set Hartree–Fock (EBSHF) wave functions, a polarization potential calculated from an ab initio EBSHF adiabatic polarization potential modified by the local‐kinetic‐energy semiclassical polarization model to account for nonadiabatic effects, an exchange potential calculated from the EBSHF static electron density and static potential by the semiclassical exchange approximation, and an imaginary absorption potential calculated from the EBSHF static electron density and static potential by the quasifree scattering model with Pauli blocking. We obtain good agreement with all available experimental data at im...

Rapid convergence of discrete-basis representations of the amplitude density for quantal scattering calculations

Abstract We show that an expansion of the amplitude density in a square-integrable basis set leads to much faster convergence of the reactance matrix than a square-integrable expansion of the wavefunction for a quantum mechanical scattering problem. The computational savings for large-scale calculations may be very great.

Non-empirical model for the imaginary part of the optical potential for electron scattering

The authors propose a new kind of model for absorption of flux from the elastic scattering channel in electron-atom or electron-molecule collisions. It is a non-empirical model so it predicts the absorption cross section as well as the elastic scattering wavefunction and elastic differential cross sections. They have tested the model for electron scattering by He, Ne and Ar at impact energies 30-400 eV. Agreement with experiment is very good for both the absorption cross sections and elastic differential cross sections.

Tight-Binding Configuration Interaction (TBCI): A Noniterative Approach to Incorporating Electrostatics into Tight Binding.

We present a new electronic structure approximation called Tight Binding Configuration Interaction. It uses a tight-binding Hamiltonian to obtain orbitals that are used in a configuration interaction calculation that includes explicit charge interactions. This new method is better capable of predicting energies, ionization potentials, and fragmentation charges than the Wolfsberg-Helmholz Tight-Binding and Many-Body Tight-Binding models reported earlier (Staszewska, G.; Staszewski, P.; Schultz, N. E.; Truhlar, D. Phys. Rev. B 2005, 71, 045423). The method is illustrated for clusters and nanoparticles containing aluminum.

Energy‐adapted basis sets for quantal scattering calculations

A simple technique for energy adapting translational basis functions for quantal scattering calculations is proposed. It is demonstrated to reduce the required number of basis functions by up to a factor of 5 for a test case.

Effective exchange potentials for electronically inelastic scattering

We propose new methods for solving the electron scattering close coupling equations employing equivalent local exchange potentials in place of the continuum‐multiconfiguration‐Hartree–Fock‐type exchange kernels. The local exchange potentials are Hermitian. They have the correct symmetry for any symmetries of excited electronic states included in the close coupling expansion, and they have the same limit at very high energy as previously employed exchange potentials. Comparison of numerical calculations employing the new exchange potentials with the results obtained with the standard nonlocal exchange kernels shows that the new exchange potentials are more accurate than the local exchange approximations previously available for electronically inelastic scattering. We anticipate that the new approximations will be most useful for intermediate‐energy electronically inelastic electron–molecule scattering.

A coherent state undergoing a continuous nondemolition observation

Abstract It is shown that there exists a continuous nondemolition observation (in Belavkins sense) preserving a coherent state of an open harmonic oscillator. The condition for such measurement, requiring a joint observation of position and momentum, is given.

Transient Effects for Continuously Observed Quantum Particle

Transient phenomena that occur when a free quantum particle undergoes a continuous nondemolition observation of its position are discussed. Independently of a particular case of observation (specified by particle mass, the strength of coupling, and the value of initial dispersion of the Gaussian wave packet) the dispersion of the posterior Guassian wave packet always decreases in the beginning of observation, then (after some time) takes the form of oscillations decaying to the asymptotic value (ħ/2mλ)1/2. We say that the quantum particle is frightened when observation begins, then it is trembling, and finally relaxes. The discussion is preceded by a brief presentation of basic ideas of the theory of continuous in time quantum measurements.