Vacancy excitation spectrum in solid 4He and longitudinal phonons

The first microscopic ab initio calculation of the excitation spectrum of a vacancy in solid 4He is reported. The energy-wave vector dispersion relation has been obtained at melting density within a development of the shadow wave function variational technique. The calculation of the excitation spectrum of a vacancy gives a bandwidth which ranges from 6 to 10 K in the hcp solid 4He, depending on the particular direction of the wave vector of the excitation. The effective mass of the vacancy turns out to be about 0.35 4He masses. We have also computed the spectrum of longitudinal phonons and we find rather good agreement with recent experimental results.