気態および液態ヘリウムのクラスター理論^*I

抄録

The properties of liquid in thermal equilibrium at low temperatures are investigated on the basis of orthodox quantum statistical mechanics. In this paper (part I), assuming the computability of the momentum operators with the potential energy and taking into account the effect of Bose statistics through a set of symmetric wave functions, we define the composite cluster integrals and obtain the Ursell expansion of the partition function, where the composite cluster is a group of atoms which are bound not only by f-bonds due to the interatomic potentials but also by g-bonds due to the Bose apparent attractions or zero-bonds representing the contributions from zero momentum atoms. Next, we constitute the composite frame integrals which mean a kind of generalization of Mayer's irreducible integrals. Then the properties of the composite clusters and frames are discussed, and it is shown that in “small” clusters and “small” frames the contributions from zero bonds are negligible, and then the “large” frame integrals are expanded in a suitable form. In the next paper (part II), using the results obtained in this paper, the phase transitions (the gas-liquid transition and the λ-transition) in He⁴ will be discussed.