Double-pole approximation

Table 10 Transition Frequencies and Oscillator Strengths (OS) Calculated Using the Double-Pole Approximation (DPA) for the Lowest...

The appearance of a double pole is not a serious problem, because we can make the approximations... 

The title of this subsection refers to a recent paper by Kylstra and Joachain investigating double poles of the S matrix [25]. Their paper is based on the time-dependent Lippmann-Schwinger equation. Since the Hamiltonian is periodic in time the use of the Floquet theorem permits one to apply the time-independent theory of scattering. As in Ref. [25] we consider two quasi bound states (n = 2). Instead of starting from an Hamiltonian periodic in time (semi-classical approximation) we use a time-independent model. The laser field is assumed to be quantized and as a result the total Hamiltonian describing the atom in the laser field is time-independent (see chapter VI of Ref. [13]) Our aim is twofold To reproduce the results of Ref. [25] and, more generally, to illustrate the relevance of simple models to describe collision... 

The Brueckner-reference method discussed in Section 5.2 and the cc-pvqz basis set without g functions were applied to the vertical ionization energies of ozone [27]. Errors in the results of Table IV lie between 0.07 and 0.17 eV pole strengths (P) displayed beside the ionization energies are approximately equal to 0.9. Examination of cluster amplitudes amd elements of U vectors for each ionization energy reveals the reasons for the success of the present calculations. The cluster operator amplitude for the double excitation to 2bj from la is approximately 0.19. For each final state, the most important operator pertains to an occupied spin-orbital in the reference determinant, but there are significant coefficients for 2h-p operators. For the A2 case, a balanced description of ground state correlation requires inclusion of a 2p-h operator as well. The 2bi orbital s creation or annihilation operator is present in each of the 2h-p and 2p-h operators listed in Table IV. Pole strengths are approximately equal to the square of the principal h operator coefiScient and contributions by other h operators are relatively small. 

The structure of the p-p propagator is very similar to that of G. This popagator describes the simultaneous annihilation of two electrons from the system as well as the simultaneous attachment of two electrons to the system. In particular, the pole positions of the first and second part of FI represent double ionization potentials (DIP) and double attachment energies. DIPs, EAs, and IPs are, of course, important quantities of electronic systems. But not only the pole positions are related to experiment. The residue amplitudes and contain relevant information on the single and double ionization and attachment (or scattering) processes. For instance, the partial-channel photoionization cross section for production of molecular ions in the nth state reads in the sudden approximation ... 

An electrical signal is generated by an RF tone-burst source. In the beginning, a Colpitts oscillator, or the like, was used as the RF tone-burst source. Nowadays, however, burst waves are gated out from continuous waves by a single pole double throw switch for frequency stability. The output (i.e., voltage) of the source is approximately 10 V... 

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