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The concept of \textit{optical} exciton - a photo-excited bound electron-holepair within a crystal - is routinely used to interpret and model a wealth ofexcited-state phenomena in semiconductors. Beside originating sub-band gapsignatures in optical spectra, optical excitons have also been predicted tocondensate, diffuse, recombine, relax. However, all these phenomena are rootedon a theoretical definition of the excitonic state based on the followingsimple picture: "excitons" are actual particles that both appear as peaks inthe linear absorption spectrum and also behave as well-defined quasiparticles.In this paper we show, instead, that the electron-phonon interaction decomposesthe initial optical excitons into \textit{elemental} excitons, the latter beinga different kind of bound electron-hole pairs lacking the effect caused by theinduced, classical, electric field. This is demonstrated within a many-bodyperturbation theory approach starting from the interacting electronicHamiltonian including both electron-phonon and electron-hole interactions. Wethen apply the results on two realistic systems, monolayer MoS$_2$ (where thelowest-bound exciton is optically inactive) and monolayer MoSe$_2$ (where it isoptically active), using first-principles methods to compute the exciton-phononcoupling matrix elements. Among the consequences of optical-elementaldecomposition, we point to a homogeneous broadening of absorption peaksoccurring even for the lowest-bound optical exciton, we demonstrate this bycomputing exciton-phonon transition rates. More generally, our findings suggestthat the optical excitons gradually lose their initial structure and evolve aselemental excitons. These states can be regarded as the real intrinsicexcitations of the interacting system, the ones that survive when the externalperturbation and the induced electric fields have vanished.

Exciton-phonon interaction calls for a revision of the "exciton" concept