  The method of collective variables (MCV) has been used to calculate the
logarithm of the He-II ground-state wave function, ln(Psi_0), to an accuracy of
a first correction to the Jastrow function and, in a second approximation, the
wave function Psi_k of the first excited state and the He-II quasiparticle
spectrum. The functions Psi_0 and Psi_k were found as the eigenfunctions of the
N-particle Schro"dinger equation, and the function Psi_0 was connected to the
structure factor of He-II, using the Vakarchuk equation. The model does not
contain any fitting parameter or function. The quasiparticle spectrum
calculated numerically agrees well with the experiment. Our solution improves
the result obtained early by Yukhnovskyi and Vakarchuk.
