Corrections core polarization

As previously done [11], we have employed two differents forms of the transition operator, Q(r) = r, and a core-polarization corrected expression [12], given by ... 

In order to explicitly account for core-polarization effects in the calculation of oscillator strengths, a corrected transition operator is frequently employed in our calculations,... 

There has been some success in developing effective interactions for finite nuclei using realistic two-body interacti n3. Much of this work has been done on the lighter nuclei. Kuo and Brown [KU066] developed a g-matrix interaction for the sd and fp shells. They used the Hamada-Johnson nucleon-nucleon interaction in their calculations with a core polarization correction. This work was extended to the region near Ca and [KU068] and... 

Figure 2a,b. Calculations on 134xe and 130sn showing results with the bare KK potential and the KK with core polarization corrections. Only the positive parity states with even angular momentum are shown. 

In some cases however serious errors can result from the use of such a simple trial wavefunction in Equation 3. The terms in the Be REP are quite similar to those of Li, but the ground state electron distribution is considerably more compact and the correlation correction from the p2 configuration far more important. In Table II we have listed SCF and REP- C energies for the lowest S, P, and states of Be along with e )erimental values (JH) for ocanparison. Numbers in square brackets include core polarization corrections (72)., . ... 

A further reduction of the computational effort in investigations of electronic structure can be achieved by the restriction of the actual quantum chemical calculations to the valence electron system and the implicit inclusion of the influence of the chemically inert atomic cores by means of suitable parametrized effective (core) potentials (ECPs) and, if necessary, effective core polarization potentials (CPPs). Initiated by the pioneering work of Hellmann and Gombas around 1935, the ECP approach developed into two successful branches, i.e. the model potential (MP) and the pseudopotential (PP) techniques. Whereas the former method attempts to maintain the correct radial nodal structure of the atomic valence orbitals, the latter is formally based on the so-called pseudo-orbital transformation and uses valence orbitals with a simplified radial nodal structure, i.e. pseudovalence orbitals. Besides the computational savings due to the elimination of the core electrons, the main interest in standard ECP techniques results from the fact that they offer an efficient and accurate, albeit approximate, way of including implicitly, i.e. via parametrization of the ECPs, the major relativistic effects in formally nonrelativistic valence-only calculations. A number of reviews on ECPs has been published and the reader is referred to them for details (Bala-subramanian 1998 Bardsley 1974 Chelikowsky and Cohen 1992 Christiansen et... 

The parameter Ka — 0.24 — 0.33 is determined from nuclear model calculations [49]. These two interactions can be treated together using (104) with Ka K = Ka — 7C2(k — 1/2)1 K. The resulting spin-dependent correction was evaluated in the Dirac-Fock approximation including weak core-polarization corrections. Combining that calculation with the previous spin-independent result, we obtain... 

What remedies do we have The brute-force device tried in pioneer days, of incorporating core- and core-valence correlation effects into pseudopotentials just by fitting to experimental reference data containing these effects, does not work since the one-electron/one-center PP ansatz is insufficient for this purpose, cf. below. Certainly more reliable is a DFT description of core contributions to correlation effects which is possible with (and actually implied in) the non-linear core corrections discussed in Section 1.4. Another device, which has shown excellent performance in the context of quantum-chemical ab initio calculations180 and has later been adapted to PP work cf. e.g. refs. 139, 181-184), is that of core-polarization potentials (CPP)... 

R1 decays quite well gives reassurance that the less-important RO core polarization is calculated with sufficient precision. The core-polarization correction to M, has a quite small tensor contribution but that for M is comparable to that of the RO matrix elements. We will find in the next section that a weakening of the tensor force results in better agreement with experiment for the RO matrix element. Thus an important question, which will be answered in the next section, is Whether this better agreement for the RO decays is accompanied by a significantly worsening of the previous excellent agreement for R1 decays . 

---