By J. G. Zabolitzky (auth.), J. W. Negele, Erich Vogt (eds.)
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Extra resources for Advances in Nuclear Physics
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. , 0'---'0 +3 h Fig. 20. Expansion of the three-body distribution function. Hypernetted-Chain Theory of Matter 29 e----I" I " I " I I Fig. 21. Four-point basic diagram contributing to the three-body radial distribution function. 3) and dropping all terms which violate the diagram rules. 20) tremendously. In FHNC/4 then, there is not only the single additional contribution Fig.
This point will become more clear in the discussion of numerical results below. 2. 15) in order to obtain the energy as functional on the correlation factor alone, E = E[f]. 16) From this equation one could determine the optimum correlation factor giving the lowest energy within the Jastrow function space. One should bear in mind from the very beginning, however, that there will be no unique best solution possible. There exist at least three different versions for the kinetic energy, several different approximations for the three-body radial distribution function, and several different ways of performing partial summations to obtain the two-body distribution function.
There was exactly one diagram involving four points, Fig. 9a, five diagrams involving five points, and so on. This situation is quite different in the fermion case. Not only do we have four different types of elementary diagrams because of exchanges on the two reference points, but also there are different exchanges taking place on the internal points. This leads to a total of 35 numerically different basic diagrams. Figure 13 shows the seven basic diagrams which appear in addition to Fig. 9a if one does not consider bonds of type de.
Advances in Nuclear Physics by J. G. Zabolitzky (auth.), J. W. Negele, Erich Vogt (eds.)