Theory of binary boson solutions

The theory of binary boson solutions is derived by an extension of the paired-phonon analysis previously applied to liquid ⁴He. The results include expressions for an approximate ground state energy and wavefunction. the latter is composed of a product of a Jastrow factor and the correlation function employed in a correlated basis. The excited state energies are expressed in terms of a two-branch excitation spectrum, which is the generalization of the Bijl-Feynman excitation spectrum to a two-component system. A powerful variational principle satisfied by the optimum ground state solution of the paired-phonon analysis is derived. Techniques are discussed for calculating an interaction function which is necessary to obtain the optimum ground state. Finally, we speculate about the nature of long-range correlations in the results based upon the quantization of density fluctuations and the previous results of the paired-phonon analysis of liquid ⁴He.