Atomic Theory of the Two-Fluid Model of Liquid Helium

It is argued that the wave function representing an excitation in liquid helium should be nearly of the form i^f (r₈), where is the ground-state wave function, f (r) is some function of position, and the sum is taken over each atom i. In the variational principle this trial function minimizes the energy if f (r) =exp (ik), the energy value being E (k) ={^2k^2}2mS (k), where S (k) is the structure factor of the liquid for neutron scattering. For small k, E rises linearly (phonons). For larger k, S (k) has a maximum which makes a ring in the diffraction pattern and a minimum in the E (k) vs k curve. Near the minimum, E (k) behaves as +{^2 (k-{k₀) }^2}2, which form Landau found agrees with the data on specific heat. The theoretical value of is twice too high, however, indicating need of a better trial function. Excitations near the minimum are shown to behave in all essential ways like the rotons postulated by Landau. The thermodynamic and hydrodynamic equations of the two-fluid model are discussed from this view. The view is not adequate to deal with the details of the transition and with problems of critical flow velocity. In a dilute solution of He^3 atoms in He^4, the He^3 should move essentially as free particles but of higher effective mass. This mass is calculated, in an appendix, to be about six atomic mass units.