Spontaneous decay of small copper-cluster anions ${\mathrm{Cu}}_n{}^{-}$ ($n=3–6$), on long time scales

We have measured the spontaneous neutral particle emission from copper-cluster anions (${\mathrm{Cu}}_n{}^{-}, n=3–6$) stored at cryogenic temperatures in one of the electrostatic ion storage rings of the Double ElectroStatic Ion Ring ExpEriment facility at Stockholm University. The measured rate of emission from the stored ${\mathrm{Cu}}_3{}^{-}$ 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 ${\mathrm{Cu}}_3$ as the excitation energies of the decaying ions approach the electron detachment threshold. The emissions from ${\mathrm{Cu}}_4{}^{-}, {\mathrm{Cu}}_5{}^{-}$, and ${\mathrm{Cu}}_6{}^{-}$ 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 ${\mathrm{Cu}}_6{}^{-}$ ions that were excited by 1.13- or 1.45-eV photons after 46 ms of storage.

Figure 1

One of the DESIREE storage rings with indicated charged and neutral particle trajectories. The ions were injected into the ring using a set of deflector plates. Before the ion bunch has made one turn, the voltage on the deflector was switched to a voltage such that the ion beam was stored in the ring. Neutrals from spontaneously decaying, excited ${\mathrm{Cu}}_n{}^{-}$ clusters with $n=3–6$ or laser-excited ${\mathrm{Cu}}_6{}^{-}$ clusters were detected by a multichannel plate detector at the end of one of the straight sections of the ring. The crossed laser beam, used for experiments with ${\mathrm{Cu}}_6{}^{-}$, is indicated.

Figure 2

Rates of neutral particles leaving a stored beam of ${\mathrm{Cu}}_3{}^{-}$ ions as functions of the time, $t$, after their production in the ion source. The points are measured values and the blue line is the calculated decay rate $R\left(t\right)$ multiplied by $t^{0.67}$ as discussed in the main text.

Figure 3

Rates of neutral particles leaving a stored beam of ${\mathrm{Cu}}_4{}^{-}$. Two quenched power-law decays are needed to fit the data. The blue line is the fit with Eq. (5), and the thin black lines are the individual contributions from the two terms in the same equation. The shortest times are excluded from the analysis for both components because the detector is saturated during the first few turns in the ring. The dotted line is the simulated decay rate without radiative cooling for a single population, calculated analogously to the line in the ${\mathrm{Cu}}_3{}^{-}$ frame. The parameters for the fits are given in Table 1.

Figure 4

Rates of neutral particles leaving a stored beam of ${\mathrm{Cu}}_5{}^{-}$ ions. The lines are analogous to the ones for Fig. 3. The parameters for the fits are given in Table 1.

Figure 5

Rates of neutral particles leaving a stored beam of ${\mathrm{Cu}}_6{}^{-}$ ions. The lines are analogous to the ones for Fig. 3. The parameters for the fits are given in Table 1.

Figure 6

Calculated relative excitation energies (black lines) for two ${\mathrm{Cu}}_3{}^{-}$ (upper panel) and three ${\mathrm{Cu}}_4{}^{-}$ (lower panel) conformers in their lowest vibrational states as functions of $J(J+1)$ where $J$ is the rotational angular momentum quantum number. The corresponding electron detachment limits (full gray lines) and the lowest-energy fragmentation channels (dash-dotted lines) are also indicated. There are progressions of vibrational states (not indicated) from the lowest state (black lines) of each conformation, reaching into the continuum beyond the corresponding detachment limit. No states exist below the lowest black line in each plot (the yrast line). Ions in excited states that are below both the lowest-energy detachment limit and the lowest dissociation limit are bound and cannot produce neutrals. The rotational barrier heights for the fragmentation channels increase with $J$ and the dash-dotted lines should in principle have small nonzero slopes. We have calculated this effect for the dissociating ${\mathrm{Cu}}_3{}^{-}$ clusters, but the effect is not visible on the scale shown here (the same is expected to be true for ${\mathrm{Cu}}_4{}^{-}$).

Figure 7

A double-logarithmic plot of the photoinduced decay of ${\mathrm{Cu}}_6{}^{-}$ at the two wavelengths 850 nm (blue circles) and 1100 nm (red crosses). The time unit is the revolution period for the ${\mathrm{Cu}}_6{}^{-}$ ions in the ring which is $\sim 120\mu \mathrm{s}$. The straight lines are power-law fits. For comparison, an exponential decay with the lifetime of one period is plotted (curved line).