Fraction of stars f_merger that merge with the central star in a cluster with a total stellar mass of M_stars = 10⁴ M_⊙, a virial radius of R_v = 0.14 pc, and an external potential with a mass of M_ext = M_stars after 1 Myr (left panel), 2 Myr (middle panel), and 10 Myr (right panel) for different combinations of the number of stars N and the stellar radius R_star calculated using our model presented in Eq. (8). We can see that when the collisions are maintained for short periods of time, that is, 1 Myr, an object that is not so massive with ∼f_mergerM_stars = 0.1 × 10⁴ M_⊙ = 1000 M_⊙ is formed in the cluster center only when N is very small (given that t_delay becomes larger than the integration time for large N) or when R_star is large. If the time limit is 2 Myr (middle panel), we expect that clusters with a small N experience core collapse and form a massive central star. However, if the number of stars is large and R_star is also large, given the higher velocity of the stars in those clusters compared to clusters without the external potential, there is a larger probability for hyperbolic mergers to occur before core collapse, which we see on the right-hand side of middle panel. If the time limit is long, that is, 10 Myr, most of the clusters form stars with ∼0.3−0.4 M_stars = 3000−4000 M_⊙ and even 0.7 M_stars = 7000 M_⊙ if N is large enough.