One introduces a model of the superfluid state of a Bose liquid with repulsion between bosons, in which at $T=0$, along with a weak single-particle Bose-Einstein condensate, there exists an intensive pair coherent condensate, analogous to the Cooper condensate in a Fermi liquid with attraction between fermions. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is solved numerically, and a quasiparticle spectrum is obtained, which is in good agreement with the experimental spectrum of elementary excitations in superfluid ${}^4\mathrm{H}\mathrm{e}$. It is shown that the roton minimum in the spectrum is associated with the negative minimum of the Fourier component of the pair interaction potential.

• Received 8 February 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.075301