GAS PHASE ABSORPTION SPECTROSCOPY OF ${{\rm{C}}}_{60}^{+}$ AND ${{\rm{C}}}_{70}^{+}$ IN A CRYOGENIC ION TRAP: COMPARISON WITH ASTRONOMICAL MEASUREMENTS^*

The coaxial superposition of an ion cloud confined in a linear quadrupole trap and a laser beam provides a well-defined geometry for determining absolute cross-sections for photo-induced processes in ions (Jašík et al. 2015). The intensity of light, I, transmitted through a cell of length l containing molecules with a density n is described by Beer–Lambert's law,

$$\begin{eqnarray}&&I={I}_{0}\mathrm{exp}(-\sigma {nl}),\end{eqnarray} \tag{ 1 }$$

where I₀ is the incident intensity and σ the cross-section for absorbing a photon. Equation (1) also holds for interstellar clouds when $n\;l$ is replaced by the column density, N_C. For example, the relative intensity $I/{I}_{0}=0.91$ for the $9577.5\;{\rm{\mathring{\rm A} }}$ interstellar absorption of ${{\rm{C}}}_{60}^{+}$ was reported by Walker et al. (2015).

In the laboratory experiments the light interacts with a confined ensemble of some thousand ions leading to very small column densities and light attenuation of about $5\;\times \;{10}^{-11}$ in the case of ${{\rm{C}}}_{60}^{+}\quad \mbox{--}\quad {\rm{He}}$ stored in the 22-pole. As a result direct absorption measurements, performed by monitoring the transmitted intensity of light, are difficult. Information on the absolute absorption cross-section comes instead from the fragmentation of complexes, occurring after photon absorption. A unique sensitivity is achieved by counting (almost) all of the mass-selected ions following their extraction from the trap. Under the conditions of the present experiment the quantum yield for dissociation is unity and therefore the photofragmentation and absorption cross-sections are identical.

The probability to hit an ion is proportional to the laser fluence, Φ (number of photons per ${\mathrm{cm}}^{2}$), and the cross-section, σ. Integration over the ion cloud and using the mean fluence, Φ, leads to

$$\begin{eqnarray}&&N({\rm{\Phi }})={N}_{0}\mathrm{exp}(-\sigma {\rm{\Phi }}),\end{eqnarray} \tag{ 2 }$$

where N₀ is the initial number of complexes and $N({\rm{\Phi }})$ those remaining after exposure to the light. The mean value of the fluence is calculated from the measured power of the laser, P, its profile at the location of the trap, and the irradiation time, ${\rm{\Delta }}t$. In the linear quadrupole used the ion cloud is compressed and this enables good superposition with the laser beam, as illustrated in Figure 1.

The number of complexes is measured at several fluencies by varying the laser power or the irradiation time with all other experimental parameters (e.g., geometry, rf amplitude, He density) unchanged. Typical results for the origin bands of the ${{\rm{C}}}_{60}^{+}$ and ${{\rm{C}}}_{70}^{+}$ electronic transitions are shown in Figure 2. The obtained data are fitted to the exponential function

$$\begin{eqnarray}&&N({\rm{\Phi }})={N}_{0}\mathrm{exp}(-{\rm{\Phi }}/{{\rm{\Phi }}}_{0})+{N}_{1}.\end{eqnarray} \tag{ 3 }$$

At high laser fluence, the curves decrease to a common asymptotic value, N₁, which is due to the number of ${}^{13}{{\rm{C}}}_{4}^{12}{{\rm{C}}}_{56}$ (${}^{13}{{\rm{C}}}_{4}^{12}{{\rm{C}}}_{66}$) background ions appearing at $m/z=724\ (844){\rm{u/e}}$. Comparison of Equations (2) and (3) reveals that the derived characteristic fluence, ${{\rm{\Phi }}}_{0}$, can be directly converted into the cross-section, σ,

$$\begin{eqnarray}&&\sigma =1/{{\rm{\Phi }}}_{0}.\end{eqnarray} \tag{ 4 }$$

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The most reliable cross-sections were obtained using a laser profile with a flat top of diameter $3.2\;{\rm{mm}}$, an irradiation time of $12\;{\rm{ms}}$, and powers of a few mW or even lower for ${{\rm{C}}}_{60}^{+}$. The characteristic fluence for the ${{\rm{C}}}_{60}^{+}\quad \mbox{--}\quad {\rm{He}}$ origin band at $9577.5\;{\rm{\mathring{\rm A} }}$ is determined to be ${{\rm{\Phi }}}_{0}=45\;\mu {\rm{J}}\;{{\rm{cm}}}^{-2}$ which corresponds to an absorption cross-section of $(4.6\;\pm \;0.2)\times \;{10}^{-15}\;{{\rm{cm}}}^{2}$, where the indicated error is the statistical uncertainty. After taking into account the larger systematic uncertainties of the experiment (laser power 5%, mean area 30%, irradiation time 20%, reproducibility of the laser-ion cloud overlap 30%, background N₁ 10%) the cross-sections are determined to be

$$\begin{eqnarray*}\sigma ({{\rm{C}}}_{60}^{+},9577.5\;{\rm{\mathring{\rm A} }}) & = & (5\;\pm \;2)\times \;{10}^{-15}\;{{\rm{cm}}}^{2}\\ \sigma ({{\rm{C}}}_{70}^{+},7959.2\;{\rm{\mathring{\rm A} }}) & = & (7\;\pm \;3)\times \;{10}^{-18}\;{{\rm{cm}}}^{2}.\end{eqnarray*}$$

The ${{\rm{C}}}_{60}^{+}$ absorption spectrum, measured via the fragmentation of ${{\rm{C}}}_{60}^{+}\quad \mbox{--}\quad {\rm{He}}$ in the region $9000\quad \mbox{--}\quad 9700\;{\rm{\mathring{\rm A} }}$, is presented in Figure 3. Measurements of the origin band for ${{\rm{C}}}_{60}^{+}\quad \mbox{--}\quad {{\rm{He}}}_{2}$ indicate that the perturbation on the electronic transition due to the presence of the weakly bound helium atom is very small, $\lt 0.2\;{\rm{\mathring{\rm A} }}$, such that the spectrum may be considered as that of ${{\rm{C}}}_{60}^{+}$ for comparison with astronomical data (Campbell et al. 2015). The individual bands have been fitted with Gaussian functions, following the typical evaluation of astronomical data, giving the parameters listed in Tables 1 and 2.

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Table 1.  Laboratory and Interstellar ${{\rm{C}}}_{60}^{+}$ Bands^a

Laboratory			Interstellar
${\lambda }_{c}/$Å	FWHM/Å	${\sigma }_{{\rm{rel}}}$ b	${\lambda }_{c}$ c/Å	FWHM/Å	Depth/%	Source
$9632.7\;\pm \;0.1$	$2.2\;\pm \;0.2$	0.8	$9632.6\;\pm \;0.2$	$3.0\;\pm \;0.2$	⋯d	Jenniskens et al. (1997)
$9577.5\;\pm \;0.1$	$2.5\;\pm \;0.2$	1	$9577.4\;\pm \;0.02$	$3.3\;\pm \;0.04$	$9.1\;\pm \;0.05$	Walker et al. (2015)
$9428.5\;\pm \;0.1$	$2.4\;\pm \;0.1$	0.3	$9428.4\;\pm \;0.1$	$3.2\;\pm \;0.1$	⋯e	Walker et al. (2015)
$9365.9\;\pm \;0.1$	$2.4\;\pm \;0.1$	0.2	$9365.7\;\pm \;0.02$	$2.5\;\pm \;0.04$	$2.4\;\pm \;0.03$	Walker et al. (2015)
$9349.1\;\pm \;0.1$	$2.3\;\pm \;0.2$	0.07	$9348.5\;\pm \;0.13$	$1.4\;\pm \;0.2$	$0.5\;\pm \;0.08$	This work

Notes.

^aCentral (air) wavelengths (${\lambda }_{c}$), depths and FWHM from Gaussian fits to the lab and astronomical bands. The quoted errors for the astronomical data from Walker et al. (2015) and this work are merely from the Gaussian fits but the systematic uncertainties are certainly larger. ^bRelative cross section. ^cCorrected by −12 km s⁻¹ for the interstellar K line off-set for $\mathrm{HD}\;183143$. ^dA gap in the spectral coverage containing the laboratory absorption at $9632.7\;{\rm{\mathring{\rm A} }}$ prevented detection of the interstellar band in observations toward $\mathrm{HD}\;183143$ (Walker et al. 2015). This DIB has been reported several times previously (see, for example, Foing & Ehrenfreund 1994, 1997). ^eA stellar emission feature at $9429\;{\rm{\mathring{\rm A} }}$ prevented detection of the laboratory absorption at $9428.5\;{\rm{\mathring{\rm A} }}$ in observations toward $\mathrm{HD}\;183143$. The band has been detected in the spectrum of $\mathrm{HD}\;169454$ (Walker et al. 2015).

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Inspection of the relative attenuation scale of Figure 3 reveals that the electronic transition of ${{\rm{C}}}_{60}^{+}$ is dominated by the two strong bands at $9632.7\;{\rm{\mathring{\rm A} }}$ and $9577.5\;{\rm{\mathring{\rm A} }}$ which were first identified in diffuse interstellar clouds by Foing & Ehrenfreund (1994). The next two bands to shorter wavelength, at $9428.5\;{\rm{\mathring{\rm A} }}$ and $9365.9\;{\rm{\mathring{\rm A} }}$, are more than a factor of 3 weaker than the $9577.5\;{\rm{\mathring{\rm A} }}$ band but have still been detected as DIBs in the interstellar spectrum of $\mathrm{HD}\;183143$ and $\mathrm{HD}\;169454$, as reported by Walker et al. (2015).

The next laboratory absorption to shorter wavelength is at $9349.1\;{\rm{\mathring{\rm A} }}$ with an intensity of only around 7% of the strong band at $9577.5\;{\rm{\mathring{\rm A} }}$. A DIB matching the characteristics of this weak laboratory feature is reported here in observations toward $\mathrm{HD}\;183143$. The astronomical and laboratory spectra are compared in Figure 4. For the purpose of Table 1, the interstellar spectrum in the region covering the laboratory absorption at $9349.1\;{\rm{\mathring{\rm A} }}$ has been fit with two Gaussians due to the overlap of the ${{\rm{C}}}_{60}^{+}$ band with a nearby interstellar feature of similar magnitude (Figure 4). As a result, in addition to having a depth of less than 1%, the presence of the companion DIB contributes to uncertainty in the listed position and width. It should be noted that the errors for the astronomical data are from the Gaussian fit but the actual uncertainty is certainly larger.

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The laboratory ${{\rm{C}}}_{60}^{+}$ spectrum shown in the upper panel of Figure 3 has a complicated pattern of weaker transitions toward shorter wavelengths, reflecting the vibronic and Jahn–Teller couplings present. In order to determine the wavelengths of the weak bands in this region, the spectrum was recorded in the nonlinear regime using higher laser fluence. This leads to an experimentally observed broadening of the bands (Campbell et al. 2015). Thus the values listed in Table 2 should be considered as upper limits to the natural width.

Table 2.  Laboratory ${{\rm{C}}}_{60}^{+}$ Bands^a

${\lambda }_{{\rm{c}}}$ b/Å	FWHMc/Å	${\sigma }_{\mathrm{rel}}$ d	${\lambda }_{{\rm{c}}}$ b/Å	FWHMc/Å	${\sigma }_{\mathrm{rel}}$ d
9259.6	2.7	0.03	9140.2	2.0	0.01
9253.8	2.3	0.01	9128.0	3.0	0.01
9222.7	2.7	0.02	9118.7	2.3	0.02
9212.6	2.1	0.02	9097.1	2.2	0.01
9200.5	3.7	0.03	9084.3	2.5	0.01
9155.1	1.9	0.01	9081.4	2.5	0.01
9150.3	2.6	0.02	⋯	⋯	⋯

Notes.

^aWavelengths in air, ${\lambda }_{c}$, and FWHM determined by Gaussian fits to the laboratory spectrum of ${{\rm{C}}}_{60}^{+}$ shown in the upper panel of Figure 2. ${\sigma }_{\mathrm{rel}}$ are relative to $9577.5\;{\rm{\mathring{\rm A} }}$ (see Table 1), weak absorptions with ${\sigma }_{\mathrm{rel}}\;\leqslant \;0.01$ are not included. ^bBand positions are given with an uncertainty of ±0.2 Å. ^c ${\sigma }_{\mathrm{rel}}$ are listed with an estimated uncertainty of around 20%. ^dFWHM should be considered as an upper limit (see text).

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The equivalent width (EW) of the $9577.5\;{\rm{\mathring{\rm A} }}$ ${{\rm{C}}}_{60}^{+}$ DIB is around $300\;{\rm{m\mathring{\rm A} }}$ (Walker et al. 2015). The relative intensities of these weak ${{\rm{C}}}_{60}^{+}$ laboratory bands (Figure 3, upper panel) indicates that the corresponding DIBs would have EWs in the range of just a few ${\rm{m}}\mathring{\rm A}$ and therefore be difficult to detect. After correction for telluric lines, the signal-to-noise ratio (S/N) for the $\mathrm{HD}\;183143$ spectra in the region of $9577\;{\rm{\mathring{\rm A} }}$ is 300 per pixel or 1500 per Å. For a band with a $2.5\;{\rm{\mathring{\rm A} }}$ FWHM this gives a 3σ EW detection limit of $3\;{\rm{m\mathring{\rm A} }}$.

The gas phase absorption cross-section and astronomical observations can be used to determine the column density of ${{\rm{C}}}_{60}^{+}$ in diffuse clouds directly. The column density is given by $\mathrm{ln}({I}_{0}/I)/\sigma$, where I represents the intensity of the light transmitted by the interstellar cloud. Walker et al. (2015) reported $I/{I}_{0}=0.91$ for the $9577.5\;{\rm{\mathring{\rm A} }}$ band of ${{\rm{C}}}_{60}^{+}$ following observations toward the reddened star $\mathrm{HD}\;183143$. Together with the measured cross-section of $(5\;\pm \;2)\times \;{10}^{-15}\;{{\rm{cm}}}^{2}$ this leads to a column density of $(2\;\pm \;0.8)\times \;{10}^{13}\;{{\rm{cm}}}^{-2}$.

The ${{\rm{C}}}_{70}^{+}$ absorption spectrum, measured via the fragmentation of ${{\rm{C}}}_{70}^{+}\quad \mbox{--}\quad {\rm{He}}$ in the region 7000–8000 Å, is shown in Figure 5. The individual bands have been fitted with Gaussian functions giving the wavelengths and FWHMs listed in Table 3. The weaker bands have been evaluated in the linear regime (attenuation $\lt 20\%$). The stronger absorption bands of ${{\rm{C}}}_{70}^{+}$ may be partly saturation broadened in addition to their natural width. The electronic transition has been previously assigned as ${}^{2}{E}_{1}^{\prime }\leftarrow \;X{}^{2}{E}_{1}^{\prime\prime }$ in ${{\rm{D}}}_{5h}$ symmetry (Fulara et al. 1993).

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Table 3.  Laboratory ${{\rm{C}}}_{70}^{+}$ Bands^a

${\lambda }_{{\rm{c}}}$ b/Å	FWHMd/Å	${\sigma }_{\mathrm{rel}}$ c	${\lambda }_{{\rm{c}}}$ b/Å	FWHMd/Å	${\sigma }_{\mathrm{rel}}$ c
7959.2	8.0	0.4	7685.8	2.3	0.3
7857.6	4.9	0.1	7670.7	5.0	0.7
7843.1	10.0	0.2	7632.6	10.0	1.0
7821.3	10.6	0.2	7582.3	8.6	0.8
7811.9	8.0	0.6	7558.4	5.4	0.6
7777.2	3.8	0.1	7538.7	7.4	0.8
7766.4	5.7	0.1	7518.0	2.4	0.4
7750.0	3.5	0.2	7501.6	9.3	1.0
7728.1	2.9	0.2	7470.2	6.9	0.6
7713.3	5.2	0.2	7372.8	7.3	0.9
7701.9	9.3	0.1	⋯	⋯	⋯

Notes.

^aWavelengths in air, ${\lambda }_{c}$, and FWHM determined by Gaussian fits to the laboratory spectrum of ${{\rm{C}}}_{70}^{+}$ shown in Figure 5. ^bBand positions are given with an uncertainty of $\pm 1\;{\rm{\mathring{\rm A} }}$. ^c ${\sigma }_{\mathrm{rel}}$ are quoted with an estimated uncertainty of around 20%. ^dFWHM should be considered as an upper limit (see text).

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The origin band of ${{\rm{C}}}_{70}^{+}\quad \mbox{--}\quad {{\rm{He}}}_{2}$ was also recorded to provide information on the perturbation of the electronic transition of ${{\rm{C}}}_{70}^{+}$ due to the presence of the weakly bound helium atom. This yields band maxima ($\sim \pm \;0.4\;{\rm{\mathring{\rm A} }}$) at $7959.2\;{\rm{\mathring{\rm A} }}\;\mathrm{and}\;7958.8\;{\rm{\mathring{\rm A} }}$ for ${{\rm{C}}}_{70}^{+}\quad \mbox{--}\quad {\rm{He}}$ and ${{\rm{C}}}_{70}^{+}\quad \mbox{--}\quad {{\rm{He}}}_{2}$, respectively. Thus, as in the case of ${{\rm{C}}}_{60}^{+}$, the ${{\rm{C}}}_{70}^{+}\quad \mbox{--}\quad {\rm{He}}$ photofragmentation spectrum is, for astrophysical purposes, the laboratory absorption of ${{\rm{C}}}_{70}^{+}$.

The production of ions in the source leads to a huge ${{\rm{C}}}_{60}^{+}$ or ${{\rm{C}}}_{70}^{+}$ rotational angular momentum. However, under the conditions of the experiment, with helium number densities of some ${10}^{15}\;{\mathrm{cm}}^{-3}$, there are millions of collisions prior to the spectroscopic measurement. The mean values of the FWHM given in Tables 2 and 3, are $2.5\;{\rm{\mathring{\rm A} }}$ and $6.5\;{\rm{\mathring{\rm A} }}$ for ${{\rm{C}}}_{60}^{+}$ and ${{\rm{C}}}_{70}^{+}$, respectively, indicating a significant difference between them. The narrowest width measured is $1.9\;{\rm{\mathring{\rm A} }}$ while the broadest reaches $10.6\;{\rm{\mathring{\rm A} }}$. In comparison the rotational envelope is estimated to be $1\;{\rm{\mathring{\rm A} }}$ at the temperature of the trapped ions, indicating that all lines are lifetime broadened due to internal conversion. According to simulations (Edwards & Leach 1993) the rotational profile would exceed 2.5 Å only at temperatures above 30 K. The implication is that for ${{\rm{C}}}_{60}^{+}$ the excited electronic state lifetimes are between 1.2 and $2.3\;{\rm{ps}}$ while for ${{\rm{C}}}_{70}^{+}$ these range from 0.3 to $1.4\;{\rm{ps}}$.

Unlike the absorption spectrum of ${{\rm{C}}}_{60}^{+}$ (Figure 3), in which the two strong origin bands at $9632.7\;{\rm{\mathring{\rm A} }}$ and $9577.5\;{\rm{\mathring{\rm A} }}$ provide a major contribution to the oscillator strength, the system of ${{\rm{C}}}_{70}^{+}$ consists of many overlapping transitions of roughly equal intensity. The origin band at $7959.2\;{\rm{\mathring{\rm A} }}$ is a factor of 2–3 weaker than the strongest absorption at $7632.6\;{\rm{\mathring{\rm A} }}$ (Figure 5). The absorption cross-section at $7959.2\;{\rm{\mathring{\rm A} }}$ is determined to be $(7\;\pm \;3)\times \;{10}^{-18}\;{{\rm{cm}}}^{2}$. Even under the assumption that the column density of ${{\rm{C}}}_{70}^{+}$ is the same as for ${{\rm{C}}}_{60}^{+}$, the expected depth in the astromomical spectrum due to absorption at $7632.6\;{\rm{\mathring{\rm A} }}$ is only 0.04%. For comparison, the strong ${{\rm{C}}}_{60}^{+}$ absorption at $9577.5\;{\rm{\mathring{\rm A} }}$ has a depth of 9.1% in observations toward $\mathrm{HD}\;183143$ (Walker et al. 2015).

None of the the laboratory bands of ${{\rm{C}}}_{70}^{+}$ could be detected in the spectra of HD 183143. The S/N per pixel in the region of $7700\;{\rm{\mathring{\rm A} }}$ was 1100 or 5000 per Å. For a typical band of $8\;{\rm{\mathring{\rm A} }}$ FWHM this sets a 3σ EW detection limit of $2\;{\rm{m\mathring{\rm A} }}$.