Bound-continuum interactions

Fig. 20.1 A three channel, three limit problem. Three levels of the ion, shown by the bold lines, have Rydberg series converging to them from below and continua above them. The interactions between the series are shown by the horizontal arrows. Bound-continuum interactions are shown by single headed arrows while bound interactions are shown by...

Here, we confine the discussion to cases that can be reduced to one dimension. As far as bound-continuum interactions are concerned, we restrict ourselves to weak interactions. This condition is mostly fulfilled for... 

Briefly, XANES is associated with the excitation process of a core electron to bound and quasibound states, where the bound states interacting with the continuum are located below the ionization threshold (vacuum level) and the quasibound states interacting with the continuum are located above or near the threshold. Thus, XANES contains information about the electronic state of the x-ray absorbing atom and the local surrounding structure. However, as stated above, unhke EXAES, since the excitation process essentially involves multielectron and multiple scattering interactions, interpretation of XANES data is substantially more complicated than that of EXAFS data. 

The vibrational part of the H matrix elements is much easier to calculate than the electronic one. Methods for such calculations are described in Section 5.1 for bound bound interactions and in Section 7.6 for bound continuum vibrational interactions. 

So far, the combination of a large susceptibility with a wide region of wavelength tunability over the ionization continuum seems to be unique to magnesium vapor. Two factors are important. First, there is constructive interference in the bound-continuum matrix elements, which reflect the continuum electronic structure. Second, configuration interaction with the even parity doubly excited np series brings extra two-photon transition... 

Assuming that we have a situation in which bound states interact with continuum states, we define, according to this approach, two Hermitian projection operators Q and P, satisfying the equalities... 

Paschual-Ahuir J L, E Silla, J Tomasi and R Bonaccorsi 1987. Electrostatic Interaction of a Solute with a Continuum. Improved Description of the Cavity and of the Surface Cavity Bound Charge Distribution. Journal of Computational Chemistry 8 778-787. 

One thus identifies the adiabatic states of 9.33, with the 0 ) bound states of a Q space within the PT projection formalism given in Section 9.2 these state become resonances, since they are superpositions of the I q) and IA2) states, which interact with continuum states c,E 1) in the P space. Following Section 9.2, it follows that the E - QhQ matrix in such a case of two overlapping resonances case is given by... 

Welsh suggested correctly that similar transitions take place even if the molecular pair is not bound. The energy of relative motion of the pair is a continuum. Its width is of the order of the thermal energy, Efree 3kT/2. Radiative transitions between free states occur (marked free-free in the figure) which are quite diffuse, reflecting the short lifetime of the supermolecule. In dense gases, such diffuse collision-induced transitions are often found at the various rotovibrational transition frequencies, or at sums or differences of these, even if these are dipole forbidden in the individual molecules. The dipole that interacts with the radiation field arises primarily by polarization of the collisional partner in the quadrupole field of one molecule the free-free and bound-bound transitions originate from the same basic induction mechanism. 

Dimers. It is well known that H2 pairs form bound states which are called van der Waals molecules. The discussions above based on the isotropic interaction approximation have shown that for the (H2)2 dimer a single vibrational state, the ground state (n = 0), exists which has two rotational levels f = 0 and 1). If the van der Waals molecule rotates faster ( > 1), centrifugal forces tear the molecule apart so that bound states no longer exist. However, two prominent predissociating states exist which may be considered rotational dimer states in the continuum (/ = 2 and 3). The effect of the anisotropy of the interaction is to split these levels into a number of sublevels. 

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