Microscopic approach to the response of−43He mixtures

Abstract

Correlated-basis-function perturbation theory is used to evaluate the zero-temperature response S(q,) of 3 He mixtures for inelastic neutron scattering, at momentum transfers q ranging from 1.1 to 1.8 Å Ϫ1 . We adopt a Jastrow correlated ground state and a basis of correlated particle-hole and phonon states. We insert correlated one-particle-one-hole and one-and two-phonon states to compute the second-order response. The decay of the one-phonon states into two-phonon states is accounted for in the boson-boson approximation. The full response is split into three partial components S ␣␤ (q,), each of them showing a particle-hole bump and a one phonon, ␦-shaped peak, which stays separated from the multiphonon background. The cross term S 34 (q,) results to be of comparable importance to S 33 (q,) in the particle-hole sector and to S 44 (q,) in the phonon one. Once the response has been convoluted with the experimental broadening, the computed scattering function is in semiquantitative agreement with recent experimental measurements.

Model boson-fermion mixture within the self-consistent-field approximation

“…7 we compare the calculated peak positions of the total dynamic structure factor with the experimental data of Hilton et al 17 and Fåk et al 18 Both the 3 He and 4 He excitation energies are reasonably well described by the present approach for q Շ1.5 Å Ϫ1 . Similar level of agreement with the experimental data was also obtained by Fabrocini et al 12 in their correlated basis function approach, and by Weyrauch and Szprynger 25 in their polarization potential based calculation. We note that it is somewhat surprising to find agreement with experimental data since the bare mass is used in the 3 He response function 3 0 (q,).…”

“…These results are in very good qualitative agreement with those of more sophisticated theoretical calculations. [11][12][13] Once the parameters V 0 g ␣␤ (a 0 ) are known we immediately obtain the resulting effective interactions V ␣␤ eff (q) within our model. Figure 3 displays the effective interactions between the 3 He and 4 He atoms for two different 3 He concentrations at n/n 0 ϭ0.8.…”

“…We can examine the present relatively simple model as applied to liquid 3 He- 4 He mixtures to gain insight in this strongly interacting system. There has been many attempts to understand the ground state energy, correlation functions, collective excitations and singleparticle properties of this novel quantum fluid ranging from phenomenological theories 9,10 to microscopic approaches [11][12][13][14] and Monte Carlo simulations. 15 Neutron scattering [16][17][18][19] and x-ray scattering 20 experiments provide us with the information on ground state correlations.…”

Momentum distributions in3He−4Heliquid mixtures

“…8,9 Also available are variational Monte Carlo ͑VMC͒ calculations 18 with similar correlations of the analytical McMillan type. The studies of the mixture have been recently complemented with variational calculations concerning the energy and stability of the ground state, 19,20 with path-integral Monte Carlo ͑PIMC͒ analysis 21 and with microscopic correlated basis functions estimates of the inelastic neutron-scattering cross sections both at intermediate 22 and high 23 momentum transfers.…”

Learning Many-Body Physics With Adelchi

“…This dependence is important for an understanding of the two branches of the spectrum of elementary excitations of 3 He-4 He mixtures, namely the phonon and roton excitations of the 4 He medium, which are affected very little by the presence of 3 He atoms, and the 3 He quasiparticle excitations characterized by the effective mass studied in the impurity problem. We were then naturally led to investigate the response of 3 He-4 He mixtures [9] in the range of low momentum transfer were the two branches of the response appear well separated in energy.…”