  We theoretically investigate strong-coupling properties of a Bose-Fermi
mixture. In the mass- and population-balanced case, two of the authors have
shown that a strong hetero-pairing interaction in this mixture brings about
coupling phenomena between Fermi atomic excitations and Bose atomic and
composite molecular excitations, that appear as an anomalous multiple peak
structure in the single-particle spectral weight (SW). [D. Kharga, {\it et.
al.}, J. Phys. Soc. Jpn. {\bf 86}, 084301 (2017)]. In this paper, extending
this previous work, we show that, although these many-body phenomena are
sensitive to mass and population imbalances between the Bose and Fermi
components, SW still exhibits the multiple peak structure in a moderately
mass-imbalanced $^{87}$Rb-$^{40}$K and $^{23}$Na-$^{40}$K mixtures. We also
point out that the photoemission spectrum is a useful quantity to observe this
spectral anomaly. Since a real trapped Bose-Fermi mixture is usually
accompanied by mass and (local) population imbalance, our results would
contribute to the study of a strongly interacting Bose-Fermi mixture, under
realistic imbalanced conditions.
