Pole strength

Pol-papier, -reagenipapler, n. Elec.) pole paper, -platte, /, Elec.) pole plate, pole piece. -Starke,/, pole strength. 

For F , still the most difficult case, the pole strength is 0.90. The 2p orbital in the reference determinant dominates the normalized DO with a coefficient of 0.9997. In the U vector of equation 17, the lpp 2pa3 2p0 contribution ss 0.1. 

Similar results follow for the remaining anions with eight valence electrons. Pole strengths are between 0.88 and 0.90 for NHj, SH and PHJ A somewhat larger value, 0.95, obtains for Cl . For NHj and PHJ, there are 2h-p U elements for both finad states with absolute values between 0.1 and 0.2. The operators in question have the form a a t,aan6i0 or aJjj a 6,Qamoi/J> where n and m are labels for occupied orbitals and t is an unoccupied orbital label. 

For diatomics with ten valence electrons, pole strengths lie between 0.86 and 0.89. DOs are dominated by a single occupied orbital in all cases. In the normalized DO for the state of AlO, there are other contributions with coefficients near 0.02. For the states of BO and AlO, certain operators have U elements that are approximately 0.1. Recent experimental work has produced a revised figure, 2.508 0.008 eV, for the electron affinity of BO [42] and the entry in Table III is in excellent agreement. Similar agreement occurs for the electron affinities of CN, AlO and AIS. 

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 ionization process can be described as a one-particle event, when only one term dominates in summation (3), yielding a pole strength close unity. In this case, 1 - Fu gives an estimate of the fraction of photoemission intensity dispersed in many-body effects. On the contrary, small pole strengths are indicative (18-20) of a breakdown of the one-particle picture of ionization. 

The pole strength profiles obtained in the outer valence region of the 1,3-trans butadiene, 1,3,5-trans hexatriene and 1,3,5,7-trans octatetraene compounds relate also typically to that found (10) with low-gap hydrogen chains. They nicely reflect the competition for intensity between the main and the correlation i.e. satellite) bands in that region. In both cases, the less energetic (HOMO LUMO (10,12)... 

Very similarly, higher-order processes can be shown to yield a size-consistent redistribution of the intensity of shake-up states among themselves, via multiple 2h-lp/2h-lp interactions. Any restriction on this balance will therefore yield a size-inconsistent description of correlation bands, which will tend to vanish with increasing system size (11). A nice example is provided here, with the necessary introduction of a lower limit on pole strengths in the block-Davidson diagonalization procedure. 

The differential cross section is then proportional to the spectroscopic factor (or pole strength) ... 

In the Hartree-Fock, frozen-orbital case, Pp acquires its maximum value, unity. Final states with large correlation effects are characterized by low pole strengths. Transition intensities, such as those in Eq. (2.7), are proportional to Pp. 

For normalized Hartree-Fock orbitals, the pole strength reads... 

First-row transition metals. These metals present formidable challenges for quantum chemistry. With the energies of the d orbitals being so close to those of the v orbitals for these atoms, the possibility of final states with low pole strengths cannot be ignored. In addition, the middle transition metals are generally difficult to describe with singledeterminant methods and require a more advanced approach for a proper description. 

The pole strength is a useful diagnostic criterion of problematic cases. Close agreement with experiment in the presence of a pole strength that is less than 0.80 is likely to be the result of a fortuitous cancellation of errors. 

Hence the process is the first known process that deliberately and interactively alters the pole strengths of the poles of a permanent magnet, utilizing... 

This is a very important result. It states that both dipole amplitudes from the RRPA calculation are modified by a common factor that reflects the influences of electron correlations in the initial and final ionic states which are beyond mean-field electron-electron interactions. The A0a0 2-value is called the spectroscopic factor (or the quasi-particle strength or the pole strength or the renormalization factor) and describes the weight given to the improved 2p photoionization cross section as compared to a calculation which does not include these specific electron correlations. The remaining intensity is transferred to satellite processes... 

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