lower flow velocity than the sound velocity, but this model is useful to illustrate the concept.) Landau also showed that the sound wave and other excitations could equilibrate with one another and flow separately from the rest of the helium-4, which is known as the "condensate". From the momentum and flow velocity of the excitations he could then define a "normal fluid" density, which is zero at zero temperature and increases with temperature. At the so-called Lambda temperature, where the normal fluid density equals the total density, the helium-4 is no longer superfluid. To explain the early specific heat data on superfluid helium-4, Landau posited the existence of a type of excitation he called a "roton", but as better data became available he considered that the "roton" was the same as a high momentum version of sound. The Landau theory does not elaborate on the microscopic structure of the superfluid component of liquid helium. The first attempts to create a microscopic theory of the superfluid component itself were done by London and subsequently, Tisza. Other microscopical models have been proposed by different authors. Their main objective is to derive the form of the inter-particle potential between helium atoms in superfluid state from first principles of quantum mechanics. To date, a number of models of this kind have been proposed, including: models with vortex rings, hard-sphere models, and Gaussian cluster theories. Vortex ring model Landau thought that vorticity entered superfluid helium-4 by vortex sheets, but such sheets have since been shown to be unstable. Lars Onsager and, later independently, Feynman showed that vorticity enters by quantized vortex lines. They also developed the idea of quantum vortex rings. Arie Bijl in the 1940s, and Richard Feynman around 1955, developed microscopic theories for the roton, which was shortly observed with inelastic neutron experiments by Palevsky. Later on, Feynman admitted that his model gives only qualitative agreement with experiment. Hard-sphere models The models are based on the simplified form of the inter-particle potential between helium-4 atoms in the superfluid phase. Namely, the potential is assumed to be of the hard-sphere type. In these models the famous Landau (roton) spectrum of excitations is qualitatively reproduced. Gaussian cluster approach This is a two-scale approach which describes the superfluid component of liquid helium-4. It consists of two nested models linked via parametric space. The short-wavelength part describes the interior structure of the fluid element using a non-perturbative