Phonon frequencies of caesium and metallic hydrogen

The logarithmic plots of measured frequencies for different phonon wave vectors, q, with their atomic numbers, N, are found to give a straight line fit. The relation between the frequency v_N(q) and the atomic number may be approximated by v_N(q) = N^-mC(q,ε{lunate}), where m is found to be a constant equal to 0.75 and C(q,ε{lunate}) is a constant depending on phonon wave-vector and polarization ε{lunate}. This relationship has been used to predict the phonon frequencies of caesium and metallic hydrogen.