Transverse phonon frequencies in bcc solid 4He

We have computed the excitation spectrum of transverse phonons in bcc solid 4He near the melting density with the shadow wave function technique. The representation of a transverse phonon is obtained by taking the wave vector of the excitation operator (a density fluctuation written in terms of the shadow variables) as a combination of a reciprocal lattice vector and a wave vector orthogonal to ; in this way one is able to compute almost pure transverse phonon excitation energies when is not too large. The computed transverse phonon frequencies are in good agreement with recent experimental results.