Variational calculations of the excited states of liquidHe4

Abstract

Approximate wave functions of the form $\mathcal{G}\Phi \left(n\right(\overrightarrow{\mathrm{k}}\left)\right)$, where $\mathcal{G}$ is a correlation operator that contains two-body, three-body, and momentum-dependent correlations, and $\Phi \left(n\right(\overrightarrow{\mathrm{k}}\left)\right)$ is a noninteracting-Bose-gas wave function with occupation numbers $n\left(\overrightarrow{\mathrm{k}}\right)$, are used to calculate the energies of excited states of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The energy expectation values are calculated by generalizing the Fermi hypernetted-chain methods. The single-quasiparticle excitation spectrum provides stringent tests for the correlation operator $\mathcal{G}$. The calculated phonon, maxon spectra are not in good agreement with the experimental results presumably because of the truncations in the large-distance behavior of the two-body correlations in the $\mathcal{G}$. The results obtained for the roton energies are in good agreement with the experiments over the range of liquid-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ density.