Hole lines

In the Brueckner-Hartree-Fock (BHF) approximation, the Brueckner-Bethe-Goldstone (BBG) hole-line expansion is truncated at the two-hole-line level [5]. The short-range NN repulsion is treated by a resummation of the particle-particle ladder diagrams into a n effect vc i n tcract ion or G-matrix. Self-consistency is required at the level of the BHF single-particle spectrum eBHF(k),... 

In the standard choice BHF the self-consistency requirement (5) is restricted to hole states (k < kF, the Fermi momentum) only, while the free spectrum is kept for particle states k > kF- The resulting gap in the s.p. spectrum at k = kF is avoided in the continuous-choice BHF (ccBHF), where Eq. (5) is used for both hole and particle states. The continuous choice for the s.p. spectrum is closer in spirit to many-body Green s function perturbation theory (see below). Moreover, recent results indicate [6, 7] that the contribution of higher-order terms in the hole-line expansion is considerably smaller if the continuous choice is used. 

Figure 1. Comparison of BHF two hole-line (lines) and three hole-line (markers) results for symmetric nuclear matter (left plot) and pure neutron matter (right plot), using continuous and gap choice for the single-particle potentials.

Figure 5 illustrates the interaction of these different levels. Based on Reason s model, it explains that there are a number of significant and inherent risks in the system, and when the holes line up, an incident or accident can occur. 

The sign of the total expression corresponding to the pertinent Goldstone diagram is given by (—l),+ i where l is the number of closed loops and h is the number of hole lines. 

Figure 1 Diagram elements (a) one-electron operator, (b) two-electron operator, (c) particle line, (d) hole line...

Figure 1 Some basic components of coupled cluster diagrams (a) hole lines ...

Label all directed lines with appropriate indices. By the convention we have used so far, hole lines would be labeled with i, j, k, I,. .. and particle lines with a, b, c, d,. . . . Therefore, for the diagram abovewe label the... 

Therefore, the two energy diagrams are equivalent, because the two hole lines and the two particle lines from the T2 diagram both connect to the same diagram fragment ... 

Unlike the diagram in Eq. [165], this diagram contains a pair of equivalent vertices since both Tj fragments are connected to the same interaction line in exactly the same manner (each by a hole line and a particle line), a prefactor of Vi is multiplied into the final expression. Generally speaking, if there are n equivalent vertices in the diagram, they contribute a prefactor of Hn to the final expression. 

However, the first two of these fragments can connect to the T diagram in only one index—via either a single hole line or particle line—thus leaving an additional line extending below the Tj interaction line in the final diagram, for example,... 

The 514-inch floppy disks are made from a polyester disk coated with iron oxide and a flexible outer covering. The disk has a large hole in the center, called the drive hole, that is used by the motor in the disk drive to spin the disk. In addition, there is also a 114-inch oval window cut into the case to allow the read/write heads access to the disk media. A small round hole cut into the disk shell next to the drive hole lines up with an even smaller hole cut into the disk media. When this smaller hole spins past the slightly larger hole in the shell, it allows a light to shine all the way through the disk system. In this way, the floppy drive can tell how fast the disk is rotating by how many times in a second that hole appears. 

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