By J. G. Zabolitzky (auth.), J. W. Negele, Erich Vogt (eds.)
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In that case, the free Fermi gas kinetic energy is the only place where the determinant is differentiate which can be done trivially, however. It is necessary in this approach to select a specific approximation to the three-body distribution function entering prominently into the kinetic energy expression. It is found(28) that, very much like the situation with Bosons discussed above, there does not exist a solution to the Euler-Lagrange equation if ohe employs the superposition approximation. Using the convolution approximation a solution exists and similar results as with the Jackson-Feenberg energy functional are obtained.
19). The JF energies corresponding to the optimum correlation factor are shown in Fig. IC-opt in HNC approximation. (37) It is seen that the energy is lowered by 1/2 to 10 K in the high-density region, as one would expect from using an improved wave function. 2. Figure 22 shows the experimental energy as a function of density at the bottom. All the previously discussed variational results are much too high in energy, even those using the optimum Jastrow wave function. Therefore, either the Hamiltonian or the Jastrow ansatz must be inappropriate for the liquid 4He problem.
20) to the exact Euler-Lagrange equation is very reasonable and takes into account properly the many-body correlations via the parameter A.. Another remarkable fact is that in spite of the difference exhibited in the figure the energies are very much alike. This again illustrates the point made for bosons. An important feature of approximate variational calculations is that the validity of the approximation scheme depends on the variational wave function used, in our case on the correlation factor.