Excitation Spectrum for a Bose Gas with Repulsive Core and Attractive Well

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Abstract
The correct qualitative features of the helium II elementary excitation spectrum are derived microscopically for a realistic interparticle potential using a form of pair Hamiltonian. The strong repulsive core is included by using reaction matrix elements in the Hamiltonian, and the attractive well is successfully included by assuming a generalized Bose-Einstein condensation. The pair Hamiltonian is diagonalized by the thermodynamically equivalent Hamiltonian method of Wentzel. Numerical solution of the equations yields spectra with phonon and roton regions. Since the energies in the spectrum are too high when the Yntema-Schneider potential is used, another potential is constructed which still fits the second-virial-coefficient data and gives better results. Spectra calculated for a series of attractive well strengths show the effect of weaker wells.