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Multiparticle distributions and intercepts of $r$-particle correlation functions in the symmetric Tamm-Dancoff type $q$-Bose gas model

Symmetric Tamm-Dancoff (STD) type $q$-deformed quantum oscillators are used as the base for constructing the respective STD type $q$-Bose gas model. In this letter, within the STD $q$-deformed Bose gas model we derive explicit analytic expressions for the $r$-particle momentum distribution functions, and for the (momentum) correlation function intercepts of 2nd, 3rd, and any $r$th order. Besides, we obtain large-momentum asymptotic formulas for the $r$th order intercepts which show dependence on the $q$-parameter only. The obtained formulas provide new example, in addition to already known two cases, of exact results for $r$-particle distributions and the correlation function intercepts in deformed analogs of Bose gas model.