Specific Heat of the Many-Boson Gas

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Abstract
It is shown that the simple Hartree-Fock approximation to the free energy of a many-boson gas changes the Bose-Einstein condensation from a third- to a second-order transition. A term is added to the energy of the interaction system which is proportional to the specific heat of the ideal gas system. Quantitative estimates of the effect for liquid helium give an order of magnitude about 5 times too high, which shows the importance of the effect and the necessity for screening it out.