An explanation of the second branch excitations observed in superfluid 4He

An attempt has been made to explain the second branch of excitations observed by Cowley and Woods in the recent neutron scattering experiments from superfluid 4He by evaluating the two phonon contribution, X2(vector k,ω), of the dynamic structure function. The theory gives a good fit with the intensity distribution curve of the scattered neutrons in the deep inelastic scattering region. Using a model short range potential, it is shown that for Bose systems like superfluid 4He, the dominant contribution to X2(vector k, ω) in the limit of small momentum and large energy transfer is of the order (ksup(2)/ωsup(5/2)) as against the result (ksup(4)/ωsup(7/2)), obtained in earlier theories. An interesting feature of the present theory is that it is able to reproduce a peak in the intensity versus ω curve for k=0.8 Asup(-1) around ω approximately equal to 22.1deg K which is close to the value of ω a.oproximately equal to 24.5deg K at the position of the experimentally observed second peak. (author)