Quantum SU(2$\mathrm{\mid }$1) supersymmetric Calogero-Moser spinning systems

$\mathrm{S}\mathrm{U}(2\mathrm{\mid }1)$ supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an $\mathcal{N}=4$ supersymmetrization of the quantum ${\rm U}(2)$ spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra $\widehat{su}(2\mathrm{\mid }1)$. The full system admits an $\mathrm{S}\mathrm{U}(2\mathrm{\mid }1)$ covariant separation into the center-of-mass sector and the quotient. We derive explicit expressions for the classical and quantum ${\rm SU}(2|1)$ generators in both sectors as well as for the total system, and we determine the relevant energy spectra, degeneracies, and the sets of physical states.