Parameters of the Gaussian fit to the number of mergers with the central star for simulations of clusters with an external potential. The data points were obtained after the fit to the combined data of six simulations. Upper panel: values of the normalization factor A_ext for different values of N and R_star along with our model from Eq. (8). These data points show that the number of mergers increases with both N and R_star as expected. Middle panel: different values of t_delay, ext in addition to the different values of N and R_star along with the fitting function presented in Eq. (14). These points show that t_delay, ext decreases with R_star, but it increases with N. Additionally, these values are larger than the values of t_delay for clusters without an external potential (see Fig. 11). Lower panel: values of t_{duration, ext} along with the fitting function from Eq. (15). We clearly see a positive correlation with N and a negative correlation with R_star.