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In a recent paper (Dai & Lu 1999), we have proposed a simple model in whichthe steepening in the light curve of the R-band afterglow of the gamma-rayburst (GRB) 990123 is caused by the adiabatic shock which has evolved from anultrarelativistic phase to a nonrelativistic phase in a dense medium. We findthat such a model is quite consistent with observations if the medium densityis about $3\times 10^6 {\rm cm}^{-3}$. Here we discuss this model in moredetails. In particular, we investigate the effects of synchrotron selfabsorption and energy injection. A shock in a dense medium becomesnonrelativistic rapidly after a short relativistic phase. The afterglow fromthe shock at the nonrelativistic stage decays more rapidly than at therelativistic stage. Since some models for GRB energy sources predict that astrongly magnetic millisecond pulsar may be born during the formation of GRB,we discuss the effect of such a pulsar on the evolution of the nonrelativisticshock through magnetic dipole radiation. We find that after the energy whichthe shock obtains from the pulsar is much more than the initial energy of theshock, the afterglow decay will flatten significantly. When the pulsar energyinput effect disappears, the decay will steepen again. These features are inexcellent agreement with the afterglows of GRB 980519, GRB 990510 and GRB980326. Furthermore, our model fits very well all the observational data of GRB980519 including the last two detections.Comment: 21 pages, LaTeX, accepted for publication in ApJ, one paragraph adde

Environment and Energy Injection Effects in Gamma‐Ray Burst Afterglows