| Summary: | $q$-deformed oscillators and the $q$-Bose gas model enable effective description of the observed non-Bose type behavior of the intercept (''strength'') $lambda^{(2)}equiv C^{(2)}(K,K)-1$ of two-particle correlation function $C^{(2)}(p_1,p_2)$ of identical pions produced in heavy-ion collisions. Three- and $n$-particle correlation functions of pions (or kaons) encode more information on the nature of the emitting sources in such experiments. And so, the $q$-Bose gas model was further developed: the intercepts of $n$-th order correlators of $q$-bosons and the $n$-particle correlation intercepts within the $q,p$-Bose gas model have been obtained, the result useful for quantum optics, too. Here we present the combined analysis of two-and three-pion correlation intercepts for the $q$-Bose gas model and its $q,p$-extension, and confront with empirical data (from CERN SPS and STAR/RHIC) on pion correlations. Similar to explicit dependence of $lambda^{(2)}$ on mean momenta of particles (pions, kaons) found earlier, here we explore the peculiar behavior, versus mean momentum, of the 3-particle correlation intercept $lambda^{(3)}(K)$. The whole approach implies complete chaoticity of sources, unlike other joint descriptions of two- and three-pion correlations using two phenomenological parameters (e.g., core-halo fraction pluspartial coherence of sources).
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