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Optical spectra of two-dimensional transition-metal dichalcogenides (TMDC)are influenced by complex multi-particle excitonic states. Their theoreticalanalysis requires solving the many-body problem, which in most cases, isprohibitively complicated. In this work, we calculate the optical spectra byexact diagonalization of the three-particle Hamiltonian within the Tamm-Dancoffapproximation where the doping effects are accounted for via the Pauli blockingmechanism, modelled by a discretized mesh in the momentum space. Thesingle-particle basis is extracted from the {\it ab initio} calculations.Obtained three-particle eigenstates and the corresponding transition dipolematrix elements are used to calculate the linear absorption spectra as afunction of the doping level. Results for negatively doped MoS$_2$ monolayer(ML) are in an excellent quantitative agreement with the available experimentaldata, validating our approach. The results predict additional spectral featuresdue to the intervalley exciton that is optically dark in an undoped ML but isbrightened by the doping. Our approach can be applied to a plethora of otheratomically thin semiconductors, where the doping induced brightening of themany-particle states is also anticipated.

Three-particle states and brightening of intervalley excitons in a doped MoS$_2$ monolayer