Absolute Cooling Rates of Freely Decaying Fullerenes

The cooling rates of ${\mathrm{C}}_{60}^{-}$ have been measured in an electrostatic storage ring between several hundred $\mu \mathrm{s}$ and several tens of ms with one-photon laser excitation. The absolute energy scale is established by the photon energy, and the cooling time interval is derived from the nonexponential decay of the ensemble of hot molecules. The energy decreases due to the combined action of depletion and thermal emission of IR photons with a total energy loss rate that varies inversely proportional to time, $0.9\mathrm{eV}/t$. The radiative component decreases from a few hundred $\mathrm{eV}/\mathrm{s}$ at submillisecond time scales to several tens of $\mathrm{eV}/\mathrm{s}$ at 20 ms and confirms that the crossover from depletion to predominantly radiative cooling occurs around 5 ms. The method is applicable to any large molecule or cluster which decays spontaneously, irrespective of the specific decay channel.

Figure 1

Spectra for photon energies 2.7 eV (top) and 2.0 eV (bottom). The photon absorption probability $p$ (see below) was 4% for both spectra.

Figure 2

Theoretical energy distributions right before and after one photon absorption. The dotted line is the energy distribution at $t=5\mathrm{ms}$ after creation, normalized to unity at low energy. The enhancement of the signal relative to the no-laser signal originates from the hatched area of the $p=20\%$ of the ions that have absorbed one 3 eV photon.

Figure 3

Examples of extrapolation to zero reciprocal intensity, which gives the zero time of the laser enhanced signal, up to the minor corrections mentioned in the text.

Figure 4

Measured absolute cooling rates of ${\mathrm{C}}_{60}^{-}$. The ends of the time intervals are indicated with symbols. Most points are bunched from several close-lying points. Open black circles are total cooling rates. The red triangles are the radiative cooling component calculated by Eq. (9), and blue crosses the depletion cooling rate from Eq. (10). The line is the depletion cooling rate calculated with Eq. (3), fixing the single constant of proportionality required with the short time data. The arrow points to the 5.5 ms, $138\mathrm{eV}/\mathrm{s}$ radiative cooling point modeled from the spontaneous decay curve in 18.