Abstract
It is argued that the wave function representing an excitation in liquid helium should be nearly of the form , where is the ground-state wave function, is some function of position, and the sum is taken over each atom . In the variational principle this trial function minimizes the energy if , the energy value being , where is the structure factor of the liquid for neutron scattering. For small , rises linearly (phonons). For larger , has a maximum which makes a ring in the diffraction pattern and a minimum in the vs curve. Near the minimum, behaves as , 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 atoms in , the 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.
- Received 11 January 1954
DOI:https://doi.org/10.1103/PhysRev.94.262
©1954 American Physical Society