We study the solutions of a modified version of the isothermal Lane-Emden equation, which incorporates the effect of the (owtwards directed) radiation pressure resulting from photoionizations. These solutions are relevant for HIT regions around a cluster with over approximate to 500 O stars, which can photoionize gas out to approximate to 200 root 10 cm(-3)/n(0) pc (where n(0) is the central gas density), where the effects of the self-gravity and the radiation pressure become important. We find that the solutions have a transition from a gravity dominated regime (in which the solutions converge at large radii to the non-singular, isothermal sphere solution) to a radiation pressure dominated regime (in which the density diverges at a finite radius) for central HIT region densities above n(crit) = 100 cm(-3). We argue that the high central density, radiation pressure dominated solutions will not occur in most astrophysically relevant situations, because of the absence of a possible confining environment with a high enough pressure.