Abstract
The energy spectrum of elementary excitations in liquid $^{4}\mathrm{He}$ is studied using the Brillouin-Wigner (BW) perturbation formalism in conjunction with the method of correlated basis functions. Phonon functions and interaction matrix elements associated with three- and four-phonon vertices are derived. Iteration of the BW energy series is carried out by including: (i) two one-ring types of second-order energy corrections evaluated with the inclusion of the leading correction to the convolution approximation for the three-particle distribution function, and (ii) six two-ring types of second-, third-, and fourth-order perturbation energies obtained with the use of the convolution approximations for the three- and four-particle distribution functions. The entire formulation is developed in terms of the liquid-structure function generated by the optimum Bijl-Dingle-Jastrow type of trial wave function. The resulting energy spectrum is found to agree with experimental results more closely than many earlier theoretical calculations.
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