Saturation and condensate fraction reduction of cold alpha matter

The ground state energy of ideal α-matter at T=0 is analyzed within the framework of variational theory of Bose quantum liquids. Calculations are done for three local α-α potentials with positive volume integrals and two-body correlation functions obtained from the Pandharipande-Bethe equation. The energy per particle of α matter is evaluated in the cluster expansion formalism up to four-body diagrams, and using the HNC/0 and HNC/4 approximation for a Bose liquid. At low densities the two methods predict similar EOS whereas at higher densities they are sensitively different, the HNC approximation providing saturation at lower density, bellow the saturation value of nuclear matter. Inclusion of higher-order terms in the cluster expansion of the condensate fraction is leading to a stronger depletion of the alpha condensate with the density compared to the two-body approximation prediction.