Partial wave channels

The formal basis employed in the K-matrix calculation includes the relevant partial wave channel (pwc) subspaces plus a "localized channel" (/c) of discrete functions. These last are usual Cl states and their inelusion in the basis allows to efficiently reproduce the autoionizing states and the eorrelation effects. 

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]

The resonance width Ts is expressed by the Wigner s threshold rule. In the case of isolated O2, the resonance state O2 (X ITg, v = 4) can couple with only one electronic partial wave with an angular momentum 1 = 2. In the case of vdW molecules, intermolecular interaction may couple with additional partial waves such as p-wave and s-wave with low energy. If a third-body molecule distorts the orbital of O2 (X ITg), new attachment channels can open with lower angular momentum of electrons and the resonance width may increase. 

The paper by Jungen and Atabek [10] also contains a sketch of the extension of the theory to include additional purely electronic interactions, such as the mixing of different partial waves l by the nonspherical field of the molecular core and/or interactions with core-excited Rydberg channels. This was not implemented at the time, however. 

In 2p photoionization in magnesium the partial cross section o2p is large compared to o3s and photoionization channel will be small. (In contrast, the effect of 2p photoionization on the 3s and 2s channels can be expected to be significant.) More important here is the continuum mixing of Fig. 5.10(a) with es and ed partial waves. Since Dd is larger than DS, it is essentially the Dd -amplitude which modifies the Ds -amplitude. This can be verified from Table 5.1 by comparing the RRPA results with those of the HFf P) calculation DS is increased while Dd remains nearly the same. 

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. 

Here we have summed the partial-wave series whose terms are represented by (7.139). The first term of (7.159) is the polarisation potential due to the discrete part Q of Q space. The second term is due to the ionisation space Q, and T( )(q, q)) is the exact solution of the Schrodinger equation for an ionised channel. 

The TK code is the most time-consuming part, because it has to be run for each J value (typically from 0 to 30). The time per partial wave varies from 30 sec. for J = 0 (310 channels) to 6 hours for J = 30 (4721 channels) for each energy, with a sustained performance of 7 Gflops. 

The following restrictions have been found to the application of coupled-channel calculations for the computation of pulsed-laser ionization. The dipole approximation restricts the photon energy to < 1 keV in the current treatment. This, however, does not pose a strict condition since a partial-wave expansion of the laser field may be used, similar to as in the case of screened Coulomb potentials. In comparison to ion/atom collisions, typical photon/atom interaction times are extremely long. An upper limit of the pulse width AZp = 100 fs at intermediate laser-power densities follows from the numerically restricted density of continuum states. 

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