Download e-book for iPad: Advances in Nuclear Physics by J. G. Zabolitzky (auth.), J. W. Negele, Erich Vogt (eds.)

By J. G. Zabolitzky (auth.), J. W. Negele, Erich Vogt (eds.)

ISBN-10: 1461398894

ISBN-13: 9781461398899

ISBN-10: 1461398916

ISBN-13: 9781461398912

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Example text

The sequential relation is not satisfied but the error will be smaller than in the superposition approximation because of the inclusion of diagram Fig. 20e. Terms e to h can be gathered together to yield a single correction to the superposition approximation, Fig. 21. The ordering principle in the expansion of g3 again is seen to be the connectiVity of the diagrams involved. 20) is not valid since g(r) contains exchanges of the particles involved. Products of g(r) would involve then an exchange of one particle with two others at the same time, which is clearly impossible and violates the diagram rules.

Making use of the Fourier transform of Eq. , the sum is equal to zero. In the volume integral, the elementary diagram is not small! Figure 14 exhibits a strong cancellation within the quantity Xee of Eq. 4) between the Eee and other-noneIementary-contributions. It is only one example of a quite general property: There is strong cancellation between diagrams involving a fixed number, n, of dynamical correlation lines, her), and an arbitrary number of statistical correlation lines, I"(k pr), valid to all orders n.

2. Bose Homework Problem In order to compare different many-body theories, a so-called "homework problem" has been posed. 9 f-1. Table II shows various energies as function of density for this potential. 20) with d = 2ro. It is seen that the HNC approximation does much better here. The difference between the PB and JF energies remains quite small up to very high densities. In a HNCj4 calculation the difference is further reduced. lting from the optimum two-body correlation factor in HNC. The energy is lowered only insignificantly.

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Advances in Nuclear Physics by J. G. Zabolitzky (auth.), J. W. Negele, Erich Vogt (eds.)

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