Long-wavelength behavior of the optimal HNC/0 solution for the ground state: III. Two-body correlation factor for symmetric films of liquid4He atT=0 K

The set of Euler-Lagrange equations for the ground state of a symmetric film of liquid 4 He at T= 0 K is solved. The optimal two-body correlation factor is determined by applying a recently proposed finite-difference relaxation method to equations formulated within the framework of the paired-phonon analysis. A relationship between the two-body correlation factor at the center of the film and that corresponding to bulk liquid is suggested. Numerical results for a «rather» thick film supported by an external potential are reported. A good overall agreement between results for non-uniform and uniform systems is found at the middle of the film