Crossed ladder diagram

The details of a very similar calculation of the ladder and crossed ladder diagrams for n = 2 excited states of helium, which differs only in angular momentum factors, can be found in Ref. [31]. The technique used is that of a Wick rotation, in which the transformation z iu is carried out and the to> integration carried out numerically. In the present case, while this basic approach is used, significant complications from the photon cuts are encountered, which requires the use of a somewhat complicated contour integration. The results of a rather involved calculation are tabulated as 2 in Tables 2 and 3. 

Figure 14. Ladder eind crossed ladder diagrams for second-order correlation energies.

It can be seen that the ladder diagram has the same electron-electron term as -ED iaci its positron-positron term has an opposite sign. Moreover, electron-positron terms, which come from the crossed ladder diagram only, are very different from those in and... 

Polyacrylonitrile (PAN) is the most common precursor used to make carbon fibers. A flow diagram showing the steps involved in making PAN-based carbon fiber is shown in Fig. 8.3. The PAN precursor has a flexible polymer chain structure like any other polymer, but it has an all carbon backbone chain that contains polar nitrile groups, as shown in Fig. 8.4. During the stabilization treatment, the PAN precursor fiber is heated to 200-220 C, under tension. When this is done oxygen is absorbed, and it serves to cross-link the chains the fibers turn black, and a stable ladder structure is formed. A ladder polymer is a rigid... 

---