Feynman, R. P. (1954) Atomic theory of the twofluid model of liquid helium. Physical Review, 94 (2). pp. 262277. ISSN 0031899X. http://resolver.caltech.edu/CaltechAUTHORS:FEYpr54a

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Abstract
It is argued that the wave function representing an excitation in liquid helium should be nearly of the form Σif(ri)φ, where φ is the groundstate 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·r), the energy value being E(k)=2k2/2mS(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 Δ+2(kk0)2/2μ, which form Landau found agrees with the data on specific heat. The theoretical value of Δ 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 twofluid model are discussed from this view. The view is not adequate to deal with the details of the λ transition and with problems of critical flow velocity. In a dilute solution of He3 atoms in He4, the He3 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.
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Additional Information:  ©1954 The American Physical Society. Received 11 January 1954. The author has profited from conversations with R. F. Christy and with Michael Cohen. 
Record Number:  CaltechAUTHORS:FEYpr54a 
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:FEYpr54a 
Alternative URL:  http://dx.doi.org/10.1103/PhysRev.94.262 
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  3539 
Collection:  CaltechAUTHORS 
Deposited By:  Tony Diaz 
Deposited On:  13 Jun 2006 
Last Modified:  26 Dec 2012 08:54 
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