Long-Term Monitoring of the Internal Energy Distribution of Isolated Cluster Systems

A method is presented to monitor the internal energy distribution of cluster anions via delayed electron detachment by pulsed photoexcitation and demonstrated on ${\mathrm{Co}}_4^{-}$ in an electrostatic ion beam trap. In a cryogenic operation, we calibrate the detachment delay to internal energy. By laser frequency scans, at room temperature, we reconstruct the time-dependent internal energy distribution of the clusters. The mean energies of ensembles from a cold and a hot ion source both approach thermal equilibrium. Our data yield a radiative emission law and the absorptivity of the cluster for thermal radiation.

Figure 1

(a) ${\mathrm{Co}}_4^{-}$ neutralization rate $R(t)$ (for ions produced by MISS, averaged over $\sim {10}^4$ injections) showing hot-ion relaxation after injection ($t=0$) and peaks induced by laser pulses with $h\nu =1.55\mathrm{eV}$. Inset: schematic of the EIBT with the mirror electrodes, the crossing laser, and the MCP detector. (b) Schematic laser-probing signal with delayed spikes spaced by half the EIBT oscillation period ($T$). (c) Delayed signals $\mathrm{\Sigma }R$ summed over laser-pulse pairs marked in (a). Solid lines: approximate power-law decays (to guide the eye). (d) Probability functions $p(E^{\prime })$ for observing neutrals at the MCP (unit detector response assumed) as functions of the internal energy $E^{\prime }$ after laser excitation [thick solid and dashed curves for the delay time windows marked in (c); thresholds at the detachment energy $E_{\mathrm{EA}}$]. Rectangles: energy windows with the heights marking the averages of $p(E^{\prime })$ in the $E^{\prime }$ intervals.

Figure 2

Normalized yield $Y(h\nu ,t)$ in delay window 1 for the listed photon energies $h\nu$ and a scheme of the IED scan. Data for (a) hot (MISS) and (b) cold (LVAP) ion source, averaged over three consecutive probing times. Legend: values of $h\nu$ and their symbols as used in (a) and (b). (c) Scheme of scanning the IED of stored ions (lower shaded band) by laser excitation at varying $h\nu$ (vertical arrows). A bar just above the detachment energy $E_{\mathrm{EA}}$ shows the sensitive range of the delayed photodetachment signal.

Figure 3

Normalized histograms $N(E)$ from yields $Y(h\nu ,t)$ ($h\nu$ from Fig. 2) for marked probing times, representing IEDs of ions produced with the (a) MISS and (b) LVAP sources. Bin shading encodes $h\nu$. Thin lines: statistical uncertainties of the bin contents. Marks at the top of each panel: histogram averages $\overline{E}$ and their statistical uncertainties. Straight segments connect the data for window 1. Smooth curves: canonical distributions (0.02 eV bins) for harmonic approximation with the respective $\overline{E}$. Dashed: upper probing energy limit.

Figure 4

(a) Average internal energy $\overline{E}$ derived from the measured IEDs for ion sources MISS (triangles) and LVAP (dots) with statistical uncertainties. Full curves: fit using Eq. (1). Horizontal line: ${\overline{E}}_{\mathrm{eq}}$ with the estimated systematic uncertainty. Large symbols and vertical marks: data points for the IEDs of Fig. 3. (b) Average variance between the IED data (bins from window 1) and the canonical energy density averaged over the same bins for ion sources MISS (triangles) and LVAP (dots), averaged over two consecutive probing times.