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The formation of vortex rings in negatively buoyant starting jets has been studied numerically for different values of the Richardson number, R-i, covering the range of weak to moderate buoyancy effects (0 <= R-i <= 0.20). Two different regimes have been identified in the vortex formation and the transition between them takes place at R-i approximate to 0.03. The vorticity distribution inside the vortex ring after pinching off from the trailing stem as well as the total amount of circulation it encloses (characterized by the formation number, F) show different behaviours with the Richardson number in the two regimes. The differences are associated with the different mechanisms by which the head vortex absorbs the circulation injected by the starting jet. While secondary vortices are engulfed by the leading vortex before separating from the trailing jet in the weak buoyancy effects regime (0 < Ri < 0.03), this phenomenon is not observed in the moderate buoyancy effects regime (0.03 < R-i < 0.2). Moreover it is shown that the formation number of a negatively buoyant vortex ring can be determined by considering that its dynamics are similar to that of a neutrally buoyant vortex but propagating with velocity corresponding to the negatively buoyant one. Based on this simple idea, a phenomenological model is presented to describe quantitatively the evolution of the formation number with the Richardson number, F(Ri), obtained numerically. In addition, the limitations of different vortex identification methods used to evaluate the vortex properties in buoyant flows are discussed.