Perturbation Theory and the Nuclear Many Body Problem by Kailash Kumar

Author:Kailash Kumar
Language: eng
Format: epub
Publisher: Dover Publications, Inc.
Published: 2017-04-04T04:00:00+00:00

where

On expanding the new propagator in the powers of

one gets

Now in second order if we have

we have not only the diagram of Fig. 26a, but also all the higher diagrams (up to infinite order) of the type shown Figs. 26b-d… These should therefore be omitted when we come to calculate higher orders with the propagator 1/b instead of 1/a. The propagator used in practical applications of the Brueckner method is the following

Fig. 26. Diagrams summed by a propagator modification.

where

The difference now is that at each vertex we have a t-interaction rather than a v-interaction but with the restriction that the state of the particle in the Fermi sea is not changed.

In considering examples of diagrams summed by this modification, recall that the second order v-term is included in the first order t-term together with other, higher order v-terms. Consider the diagrams starting from the third order shown in Fig. 27a. The present propagator 1/e then sums up the diagrams (which are themselves sums of many diagrams) of the type shown in Fig. 27b. The propagator modification is sometimes represented by changing the thickness or doubling the particle-hole lines.

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