Single-photon hot electron ionization of C 70 Åke Andersson1Luca Schio2Robert Richter3Michele Alagia2Stefano Stranges2 4Piero Ferrari5Klavs Hansen6 7and Vitali Zhaunerchyk1y

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Single-photon hot electron ionization of C70

Åke Andersson,1Luca Schio,2Robert Richter,3Michele Alagia,2Stefano

Stranges,2, 4 Piero Ferrari,5Klavs Hansen,6, 7, ∗and Vitali Zhaunerchyk1, †

1Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden

2IOM-CNR Tasc, SS-14, Km 163.5 Area Science Park, Basovizza, 34149 Trieste, Italy

3Elettra - Sincrotrone Trieste, Area Science Park, 34149 Basovizza, Trieste, Italy

4Dipartimento di Chimica e Tecnologie del Farmaco, Universitá Roma La Sapienza, Roma 00185, Italy Sapienza

5Quantum Solid-State Physics, Department of Physics and Astronomy, KU Leuven, 3001 Leuven, Belgium

6Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province

and School of Physical Science and Technology, Lanzhou University, Lanzhou, Gansu 730000, China

7Center for Joint Quantum Studies and Department of Physics,

School of Science, Tianjin University, 92 Weijin Road, Tianjin 300072, China

Gas phase C70 molecules have been ionized with single photons of energies between 16 eV and 70 eV and

the electron spectra measured with velocity map imaging in coincidence with the ions. The doubly ionized and

unfragmented species was present at photon energies of 22 eV and up, and triply charged ions from 55 eV. The

low kinetic energy parts of the spectra are explained with thermal emission of transient hot electrons. Deviations

at high photon energies are used to determine a value for the initial electron equilibration time. We propose a

generally applicable mechanism, named Resonance Ionization Shadowing, for the creation of hot electrons by

absorption of above-threshold energy photons.

INTRODUCTION

The large separation in time scales for electronic and vibra-

tional motion of the nuclei opens the possibility of an inter-

mediate phase of transiently hot electrons in molecules and

clusters. If present, this phase will exist between the time of

the initial excitation of the electrons and the dissipation of the

energy into vibrational motion. It tends to be manifested par-

ticularly clearly in ﬁnite systems, but has also been invoked in

the description of the two-temperature model of solid surfaces

exposed to short laser pulses [1].

In gas phase context it was introduced as the explanation of

the Penning ionization yields of C60 and C70 in Ref. [2]. Soon

after it was observed also to be present in C60 upon excitation

with multiple low energy photons from laser pulses of dura-

tion around 100 fs [3]. Subsequently, the phenomenon suc-

cessfully explained ionization of sodium clusters with short

pulse laser light [4–6]. Following this development, it has

been seen for a number of different systems excited with short

laser pulses, including C70 [7] and a number of PAH (poly-

cyclic aromatic) molecules [8].

The dynamics of multi-electron excited states involved in

the phenomenon has been considered theoretically with dif-

ferent approaches in Refs. [9–11], in addition to the more

phenomenological models used to summarize the experimen-

tal results. An integral part of this modeling when applied

to molecules or clusters is the dissipation of the incoherent

electronic excitation energy in the hot electron phase into the

vibrational modes of the molecule. This coupling has been

described in terms of a simple exponential decay of the ex-

citation energy, involving a single parameter of dimension

time, aptly named the coupling time. For some of the gas

phase molecules studied, a proxy for this electron-phonon dis-

sipation time has been measured by pump-probe experiments

[6, 12]. In other cases it has been ﬁtted from ion yield curves

for different clusters [13]. The values found range from a few

hundred femtoseconds to a few picoseconds. The fastest dis-

sipation occurs for C60, with a time constant of 240 fs [13],

and the slowest are the picosecond or longer times for sodium

clusters [5]. With reservation for the still limited number of

systems studied at this point, the data point to a dependence

of the coupling time that correlates positively with the aver-

age vibrational period, as given by the vibrational frequencies

of C60 [14] and the bulk Debye temperature for sodium [5],

although data from condensed phase nanoparticles show dif-

ferent trends [15]. Those data pertain to much lower tempera-

tures than relevant here, though.

The correlation seen in gas phase particles suggests a dis-

sipation mechanism based on internal conversion, i.e. with

similarities to the energy dissipation in molecules after ab-

sorption of single photons. Experiments performed on thin

ﬁlms of C70 have shown a very brief time window for equili-

bration, undetermined but below the pulse duration of 165 fs

used in the experiments in Ref. [16]. Unfortunately it is not

clear from these experiments if this time scale refers to the

initial intra-electron equilibration or to the electron-phonon

coupling time.

The initial electron equilibration in the creation of the hot

electron phase has received much less attention experimen-

tally than the ﬁnal, dissipation stage. It is clearly a subject

of interest for the possibility of single-photon ionization of

larger classes of molecules. The observation of such single-

photon hot electron ionization, already observed for C60 [17],

opens the possibility for studies of the mechanisms of absorp-

tion and initial dissipation of the energy. In addition to the

general relevance for delineating the boundaries of the mech-

anism, single-photon excitation is also of interest in astrophys-

ical context because molecular ions play an important role in

the interstellar chemistry [18], and in particular for fullerenes

because they have been identiﬁed in the interstellar medium.

arXiv:2210.05458v1 [physics.atom-ph] 11 Oct 2022

The experiments reported here on C70 were motivated by the

above questions. As an aside we mention that single-photon

processes come with the additional and very attractive feature

that they eliminate the uncertainty in energy that accompa-

nies multi-photon processes previously used for studies of the

subject. The experiments will also allow a test of the inter-

pretation of the previous results on C60 in Ref. [17], using a

molecule with almost equally well characterized and similar

but still different properties.

The clearest experimental signature for these purposes re-

mains the emission of electrons that are thermalized to the

very high energies which characterize the hot electron phase.

The emission of electrons that can be unambiguously assigned

as hot electrons occurs between the initial excitation and the

dissipation of energy into the vibrational motion. These dis-

tributions are unique to hot electron emission, and have the

added experimental convenience that the spectra do not need

to be measured time-resolved. However, ionization may also

occur both before and after the creation of the hot electron

phase. Either by direct ionization, which may remove enough

energy by the departing electron to preempt the creation of the

hot electron phase, or by thermionic emission after dissipation

of the energy into the predominantly vibrational excitations of

the equilibrium state.

The form of the thermal electron spectra is shaped by a

number of factors [19]. One is the product of the emitted elec-

trons’ phase space and a ﬂux factor in the form of the speed

of the emitted electrons. These combine to give a factor pro-

portional to the kinetic energy of the channel. A second factor

is the cross section for the inverse (attachment) reaction. The

third and last factor is the ratio of the level densities of the

product and emitting molecules [13]. These factors enter the

expression for the electron kinetic energy-resolved rate con-

stants, which is identical to the one for the usual thermionic

emission apart from the different level densities that describe

the emitting systems in the two situations. The phase space

and the speed factors combine to give the electron kinetic en-

ergy to the power one. For neutral or positively charged emit-

ters the cross section of the inverse process of absorption is

basically that of a Coulomb potential. In a classical calcu-

lation, which will be used here, it is proportional to the re-

ciprocal of the electron energy, plus a constant (see ref. [13]

for details). The ratio of level densities acts as an effective

Boltzmann factor. The net result is that for neutral and posi-

tively charged emitters, the energy distributions calculated un-

der these assumptions resemble Boltzmann factors with the

effective temperatures given by the product microcanonical

electron temperature, as discussed in [20]. For more informa-

tion on the derivation of the expression, please see Ref. [21].

The very good consistency of several different experimentally

measured quantities with the predictions derived from this de-

scription reported in [13] constitute a strong support of the

modeling.

In addition to the Boltzmann-like shape of the spectrum,

there are several other features that makes it distinct from the

spectra originating either from direct ionization or from ther-

mal emission from completely equilibrated molecules, known

as thermionic emission. A necessary feature of the spectra is

that the velocity distributions of the emitted electrons must be

spherically symmetric. This is a property shared with elec-

trons emitted into single particle s-states, and for a single-

photon excitation this could explain this symmetry, albeit not

the Boltzmann shape. However, the energies of such electrons

and indeed all electrons emitted from single-particle states

move in parallel with the photon energy and will therefore

have a different photon energy dependence than the hot elec-

tron spectra. Measurements at a few different photon energies

are therefore sufﬁcient to distinguish an origin of the relevant

low energy part of the spectra as thermal or as emitted in a

direct process.

A third possible origin of electrons, besides the hot electron

emission and the direct ionization, is a regular thermionic pro-

cess. There are two important differences between this type of

process and hot electron emission. One is the effective tem-

perature of the Boltzmann distribution. A standard thermionic

emission process comes with an internal energy which ren-

ders the effective (microcanonical) temperature much lower

than the hot electron emission. For fullerenes, for example,

the thermionic emission temperature has been ﬁtted to values

around 3500 K from electron spectra measured with the ve-

locity map imaging (VMI) technique also used in this work

[22]. Although this is a very high temperature in many con-

nections, the very fast emission required for the hot electron

system requires much higher temperatures, on the order of 1

eV (= 11605 K) and higher [13]. The ﬁtted temperature for

the one photon hot electron ionization of C60 reported in [17]

reached 1.6 eV, for example.

The other difference to hot electron ionization is the much

longer time scale on which thermionic emission can be ob-

served. Hot electron emission is limited to picosecond or sub-

picosecond time scales. Thermionic emission, in contrast,

will, for low excitation energies, extend to time scales that

under some conditions can be detected as a several microsec-

ond long tail on the mass peak in time-of-ﬂight mass spectra

[23] As a secondary signature, thermionic emission from neu-

tral and cationic fullerenes is usually observed together with

a substantial amount of fragmentation. Their absence here

is only corroborative for the absence of thermionic emission,

though.

For the doubly ionized species observed in the experiments

here, two other possible channels should be considered. One

is the direct double electron ionization. The electrons asso-

ciated with prompt double ionization are characterized by a

U-shaped electron kinetic energy distribution [24]. The steep-

ness of these distributions depend on the relation between

photon energy and the double ionization potential values.

Another possible channel is the emission of a second elec-

tron by regular thermionic emission. This process would oc-

cur after the excitation energy has been dissipated into the pre-

dominantly vibrationally excited equilibrium state. However,

this is ruled out for two reasons. One is that the competing C2

loss channel would dominate over thermionic emission by a

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Single-photonhotelectronionizationofC70ÅkeAndersson,1LucaSchio,2RobertRichter,3MicheleAlagia,2StefanoStranges,2,4PieroFerrari,5KlavsHansen,6,7,andVitaliZhaunerchyk1,y1DepartmentofPhysics,UniversityofGothenburg,41296Gothenburg,Sweden2IOM-CNRTasc,SS-14,Km163.5AreaSciencePark,Basovizza,34149Trieste,It...

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Single-photon hot electron ionization of C 70 Åke Andersson1Luca Schio2Robert Richter3Michele Alagia2Stefano Stranges2 4Piero Ferrari5Klavs Hansen6 7and Vitali Zhaunerchyk1y

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