We have measured the spontaneous neutral particle emission from copper cluster anions (Cu$_n^-$, $n=3-6$) stored at cryogenic temperatures in one of the electrostatic ion storage rings of the DESIREE (Double ElectroStatic Ion Ring ExpEriment) facility at Stockholm University. The measured rate of emission from the stored Cu$_3^-$ ions follows a single power law decay for about 1 ms but then decreases much more rapidly with time. The latter behavior may be due to a decrease in the density of available final states in Cu$_3$ as the excitation energies of the decaying ions approach the electron detachment threshold. The emissions from Cu$_4^-$, Cu$_5^-$ and Cu$_6^-$ are well-described by sums of two power laws that are quenched by radiative cooling of the stored ions with characteristic times between a few and hundreds of milliseconds. We relate these two-component behaviors to populations of stored ions with higher and lower angular momenta. In a separate experiment, we studied the laser-induced decay of Cu$_6^-$ ions that were excited by 1.13 eV or 1.45 eV photons after 46 milliseconds of storage.
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