Molar volume and expansion coefficient of liquid He3

cussed by I)rever and others. The purpose of t,his article is to discuss this idea wit,hin the framework of a classical, generally covariant field theory. The usual electromagnetic field equat,ions are modified so that, t,he value of the fine structure constant which one would determine from a local experiment is given by a scalar gravitational field. Wit,h these modified equations, a field t,heory of gravity, in which the motion of free test particles is consistent with the observed st,ructure independence of gravitational acceleration may be constructed in a straightforward way. However, it is shown that t,his theory must be ruled out, by the experimental observations of spatial isotropy. Molar ~durne and Expansion Coejicient of Liyuid He3. EUGENE C. KERR AND R. TIEAN T~nr,on. University of California, Los Alamos Scientific Laboratory, Los Alamos, New Mexico. IXrect measurement,s of the molar volume of liquid He3 under its own vapor pressure have been made over the temperature range, 0.16% to 1.8%. Espansion coefficient values (a”), derived from comput,er analysis of over one hundred direct observations, range from zero at 0°K to a minimum of -0.0104°K-1 at O.l94”K, again to zero at 0.502%, and at higher temperatures increase monotonically. These results are in semiquantitat,ive agreement with the theory of L. Goldstein. Comparisons are made wit,h the results of several indirect determinations of the expansion coefficients. (‘omplex Yukaum Poter&als. R. W. LARUNER, Physics Ijepartment, Columbia University, New York, New York. An investigation is made of a variant of the Yukawa potential for which the scattering amplitude may have no more analyticity in moment,um transfer than the Lehmann ellipse. A representation, t.he generalization of the Mandelstam representation to this case, is written down, and unitarity used t,o determine the spectral function. Green’s WARREN

Funvtions H.

for CHESTON.

Fermion School

Systems ,with Pairing of Physics, University

Correlations. of Minnesota,

H. Minneapolis,

I)ONAI,D

KOBE

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Minne-

sota. The Bogoliubov-Valatin canomical transformation is used to t,ransform the Hamiltonian for a system of interacting fermions, to that for a syst,em of quasi particles in which an import,ant part of the pairing interaction has been absorbed intothe freequasi particle. Field theoretic Green’s functions, which do not in general conserve the number of quasi particles, are introduced to treat t,he interaction between the quasi particles. These Green’s functions are shown to satisfy an infinite set of coupled integral equations, which can be conveniently represent,ed graphically. The infinite set of equations cm be terminated by neglecting the interact,ion Hamiltonian above some arbitrarily chosen equation. The Green’s function equat,ions are then solved in the special case where the sum of quasi particles created and annihilated is four, neglecting self-energy terms, and using a pairing plus Coulomb interA secular equation for t,he energy action of the type important in superconductivity. cigenvalues is obtained which is examined for t,he cases of no pairing interaction and no Coulomb interaction. When t,he Coulomb interaction alone is present the secular equation becomes that obtained by Sawada et al. for plasmons. When the pairing interaction alone is present,, the energy spectrum for excitons, bound pairs of quasi particles, is obtained. It is shown that one of the excitons is a phonon.