Modified Born series

Comparison of the inequalities (9.147) and (9.169) clearly demonstrates that the accuracy of the Born approximation depends only on the order N, while the accuracy of QL approximation of the same order can be increased by a proper selection of A. This circumstance makes the QL approximation a more efficient tool for EM modeling than a conventional or modified Born series. 

Now we can start iterations by the modified Born series with a quasi-analytical approximation for the anomalous field ... 

We have noticed that the background of the modified Born approximation and the new first order QL approximation is the same. The main difference is that in the case of the Born approximation the starting point (zero order approximation) for the iteration process is the zero anomalous field, while in the QL approach we start with the anomalous field proportional to the background field. In principle we can extend our approach to computing all iterations bj (9.149). In this case we will obtain a complete analog of the Born series. For example, the second order QL approximation is equal to... 

From the last formula we can see that higher order QL approximations are more accurate than the modified Born approximation of the higher order because they take into account an additional term in the series. 

As we turn up the interaction, EIMP becomes important. We must certainly modify our treatment of the K-shell electron and treat its excitation to all orders in the Born series. However, now we have to worry about the role that the other electrons play. Should we not introduce Pauli blocking operators in the Bom series Now we can make a hole in the L-shell, should we not allow this as a possible final state for the K-shell electron The answer to these questions is yes, if we wish to calculate exdusive cross sections, in perturbation theory. However it is not necessary to use many-electron perturbation theory, and we are only interested in an inclusive cross section. 

The goddess of learning is fabled to have sprung full-grown from the brain of Zeus, but it is seldom that a scientific conception is born in its final form, or owns a single parent. More often it is the product of a series of minds, each in turn modifying the ideas of those that came before, and providing material for those that come after. The electron is no exception. 

Taking into account formula (9.145), we can obtain the following expression for the modified A-th order Born approximation as the sum of N terms of the Born (or Neumann) series, which helps to understand better the internal structure of the new series ... 

Malaria is a vector-borne infectious disease caused by protozoan parasites. Human malaria is usually caused by the infection of Plasmodium falciparum, P. malariae, P. ovale, and P. vivax (Mendis et al, 2001). It is widespread in tropical and subtropical regions, including Asia, Africa, and parts of the Americas. Each year there are about 350-500 million cases of malaria, and more than 1 million people die (CDC, 2009). A series of gossypol derivatives with modified aldehydic groups and hydroxyl groups (Figs. 6.10 and 6.11) have been shown to inhibit the growth of P. falciparum (Razakantoanina et al, 2000 Royer et al, 1986). Table 6.3... 

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