Summary
The technique of the double time-temperature Green functions is applied to study the excitation spectrum and the dynamical correlations of a mixed system of interacting bosons and fermions. The previously found (6) dispersion laws for the excitation spectra are reobtained, and the approximations involved are discussed. The Van Hove-Placzek method for calculating the cross-sections for scattering of particles (or photons) from a system of atoms is applied, and the pertinent correlation functions are calculated from the respective Green functions. The nonresonant and the resonant scatterings are discussed. As a numerical example the scattering of photons from a homogeneous (dilute) mixture of liquid4He+liquid3He at a very low temperature is discussed. In particular, a modified Brueckner-Sawada pseudopotential is applied. The spectra for small momentum transfersq exhibit two peaks: one of the collective fermion-phonon resonance, the second of the « zero sound » character.
Riassunto
Si applica la tecnica delle funzioni di Green a due punti, allo studio dello spettro di eccitazione, e delle correlazioni dinamiche, di un sistema misto di bosoni e fermioni interagenti. Si ottengono (6) le relazioni di dispersione per gli spettri d’eccitazione e si discutono le approssimazioni fatte. Si applica il metodo di Van Hove-Placzek per calcolare le sezioni d’urto di diffusione di particelle (o fotoni) da un sistema di atomi. Si derivano le funzioni di correlazione dalle corrispondenti funzioni di Green. Come esempio numerico si calcola la diffusione di fotoni da parte di un miscuglio omogeneo di3He-4He a bassissima temperatura. Si fanno i calcoli sia con un pseudopotenziale costante che con uno del tipo Brueckner-Sawada. Lo spettro per piccoli impulsi trasferiti ha due picchi: uno relativo alla risonanza collettiva fermione-bosone, l’altro ha carattere di suono zero.
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The numerical examples of Figs. 1–4 of ref. (6)
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Savoia, M., Bortolani, V. & Sawicki, J. Double time-temperature Green functions for an interacting mixed system of bosons and fermions. Nuovo Cim 35, 36–53 (1965). https://doi.org/10.1007/BF02734823
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DOI: https://doi.org/10.1007/BF02734823