Variational calculation of excited-state properties of a He-3 impurity in superfluid He-4

We report a variational Monte Carlo calculation with shadow wave function of the excited-state properties at T=0 K for a system composed by one He-3 atom in superfluid He-4. Explicit nonperturbative backflow contributions are used both for the collective He-4 excitation and for the impurity He-3 excitation. The impurity and the collective excitation states have been orthogonalized and diagonalization of the Hamiltonian has been obtained directly through the Monte Carlo calculation. This process has strong effect on some of the expectation values for the observables of the system. Energy, effective mass, and strength of the single excitation peak of the impurity are computed. Above q approximate to 0.5 Angstrom(-1) the effective mass increases significantly with q but this increase is not as large as deduced from experiment. The strength of the single excitation peak in the dynamical structure factor for the He-3 impurity atom is strongly reduced by an interference contribution due to He-4 atoms and the resulting strength is now in good agreement with experiment. The importance of the coupling between He-3 and He-4 suggests the need for a reanalysis of the experimental data. [S0163-1829(99)00829-2].