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We report formulas for the joint moments of the determinantal products(det{rho})^k (det{rho^PT})^K (k=0, 1, 2,...,N; K = 0, 1, 2, 3, 4) ofHilbert-Schmidt (HS) probability distributions over the two-rebit and (K = 0,1) two-qubit density matrices rho. Here PT denotes the partial transpositionoperation of quantum-information-theoretic importance. Each formula is theproduct of the expression for the moments of (det{rho})^k,k=0,1,2,...,N--already known from work of Cappellini, Sommers and Zyczkowski(Phys. Rev. A 74, 062322 (1996))--and an adjustment factor. The factor is abiproper rational function, with its numerators and denominators both being 3K-degree polynomials in k. We infer the structure that the denominators followfor arbitrary K in both the two-rebit and two-qubit cases, and the sixleading-order coefficients of k of the numerators in the two-rebit scenario..We also commence an analogous investigation of generic rebit-retrit andqubit-qutrit systems. This research was motivated, in part, by the objective ofusing the computed moments to well reconstruct the associated HS probabilities(for which we present plots) over the two determinants, and to ascertain--atleast to high accuracy--the associated (separability) probabilities of"philosophical, practical and physical" interest that (det{rho^PT})>0.

Joint Hilbert-Schmidt Determinantal Moments of Product Form for the Two-Rebit and Two-Qubit and Higher-Dimensional Quantum Systems