Pseudostates

A partial acknowledgment of the influence of higher discrete and continuum states, not included within the wavefunction expansion, is to add, to the tmncated set of basis states, functions of the fomi T p(r)<6p(r) where dip is not an eigenfiinction of the internal Flamiltonian but is chosen so as to represent some appropriate average of bound and continuum states. These pseudostates can provide fiill polarization distortion to die target by incident electrons and allows flux to be transferred from the the open channels included in the tmncated set. 

PG Muijselaar, HA Claessens, CA Cramers. Characterization of pseudostation-ary phases in micellar electrokinetic chromatography by applying linear solvation-energy relationships and retention indexes. Anal. Chem. 69 1184—1191... 

Fig. 2.47 Pseudostable perforated layer structure, observed following a quench from the lam to hex phase using a multimode analysis of the time-dependent Ginzburg-Landau equation, within the single-wavenumber approximation (Qi and Wang 1997). This structure results from the superposition of six BCC-type wavevectors.

Levy P.J. Herley, Effects of Radiation on the Thermal Decomposition Induction Period in Ammonium Perchlorate and other Pseudostable Materials , JChemPhys 75, 191 (1971) 209) V.V. Boldyrev, Radiolysis of Crystalline... 

Fig. 5.1. Cross sections for the excitation of atomic hydrogen obtained using the coupled-state approximation with 30 hydrogen states and pseudostates plus three positronium states (a) 1S-2S (b) 1S-2P (Kernoghan et al., 1996).

R. Santra, J.M. Shainline, Chris H. Greene, Siegert pseudostates Completeness and time evolution, Phys. Rev. A 71 (2005) 032703/1. 

The B-spline K-matrix method follows the close-coupling prescription a complete set of stationary eigenfunctions of the Hamiltonian in the continuum is approximated with a linear combination of partial wave channels (PWCs) [Pg.286]

However, to obtain results with good accuracy, it is also necessary to include a pseudostate (or localized) channel, which accounts for those closed channels that have not been included, as well as for the multiple ionization channels, since the set of single-ionization PWCs alone would be incomplete. The localized channel may comprise a large number of normalized many-electron functions /, built from localized orbitals... 

P.J. Marchalant, K. Bartschat, R-matrix with pseudostates calculation for single and double ionization of helium by photon impact, Phys. Rev. A 56 (1997) 1697-1700. 

His early work on atomic and molecular properties and dispersion energies involved the development and application of ab initio pseudostate techniques for the reliable evaluation of atomic and molecular multipolar properties and dispersion energies for small species.216 This was followed by the development and application of practical constrained dipole oscillator strength (DOSD) techniques, based on a combination of experimental and theoretical input, for the reliable evaluation (errors < 1-2%) of the dominant dipolar... 

Many pharmaceutical preparations contain multiple components with a wide array of physico-chemical properties. Although CZE is a very effective means of separation for ionic species, an additional selectivity factor is required to discriminate neutral analytes in CE. Terabe first introduced the concept of micellar electrokinetic capillary chromatography (MEKC) in which ionic surfactants were included in the running buffer at a concentration above the critical micelle concentration (CMC) [17], Micelles, which have hydrophobic interiors and anionic exteriors, serve as a pseudostation-ary phase, which is pumped electrophoretically. Separations are based on the differential association of analytes with the micelle. Interactions between the analyte and micelles may be due to any one or a combination of the following electrostatic interactions, hydrogen bonding, and/or hydro-phobic interactions. The applicability of MEKC is limited in some cases to small molecules and peptides due to the physical size of macromolecules... 

Since only a relatively small number of coupled equations can be solved in practice, the target states p must be selected carefully. Virtual target excitation into the ionization continuum must be approximated by inclusion of closed-channel pseudostates that cannot be target eigenstates but have the character of wave packets in the continuum. Target polarization response is treated by including polarization pseudostates y(P). 

Table (8.1) shows results of test calculations of e-He partial wave phase shifts, compared with earlier variational calculations [383], The polarization pseudostate was approximated here for He by variational scaling of the well-known hydrogen pseudostate [76]. The present method is no more difficult to implement for polarization response (SEP) than it is for static exchange (SE). 

This work introduced the concept of a vibronic R-matrix, defined on a hypersurface in the joint coordinate space of electrons and intemuclear coordinates. In considering the vibronic problem, it is assumed that a matrix representation of the Schrodinger equation for N+1 electrons has been partitioned to produce an equivalent set of multichannel one-electron equations coupled by a matrix array of nonlocal optical potential operators [270], In the body-fixed reference frame, partial wave functions in the separate channels have the form p(q xN)YL(0, radial channel orbital function i/(q r) and antisymmetrized in the electronic coordinates. Here 0 is a fixed-nuclei A-electron target state or pseudostate and Y] is a spherical harmonic function. Both and i r are parametric functions of the intemuclear coordinate q. It is assumed that the target states 0 for each value of q diagonalize the A-electron Hamiltonian matrix and are orthonormal. 

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