  Polyatomic cations $^{87}$Rb$_M^+$ ($M$ = 2, 3,$\ldots$) have been produced
by cascade two-body ion-atom reactive collisions in the two-step CW-laser
photoionization of laser-cooled $^{87}$Rb atoms and accumulated in the ion
trap. Using resonant-excitation mass spectrometry and resonant
excitation-assisted time-of-flight mass spectrometry, we directly observed and
distinguished the charged reaction products. We experimentally verified the
cascade generation and cascade dissociation of $^{87}$Rb$_M^+$. The populations
of $^{87}$Rb$_M^+$ are quantitatively investigated by solving the rate
equations. The $^{87}$Rb$^+$-$^{87}$Rb reaction rate coefficient was derived as
9.10$\times10^{-11}$ cm$^3$/s accordingly. The methods developed here for
assembling and detecting homonuclear polyatomic cations can be applied to any
experiment in ion-atom hybrid traps. The present study lays the foundation for
exploring atomically precise metal clusters and physics from few- to many-body
perspective.
