Contents - Max-Planck-Institut für Physik komplexer Systeme

sequential emission shape (SES) of a Coulomb complex,
namely that the photo electron spectrum has a
characteristic plateau (see Fig. 2). It has been observed
in the experiment [6] as well as in simulations [7] but
without an understanding of its origin. For a CC the
plateau can be easily derived: Sequential emission implies
that an electron which leaves the CC of charge Q ′
does not influence the escape of the next electron which
sees a charge Q ′′ = Q ′ + 1. Since its not known from
which position in the CC the electron with final energy
E is released, one has to integrate over all possible initial
positions in the volume V of the CC,
dP/dE(Q ′ ) = V −1
d 3 rδ(E − ǫ − U(r)). (2)
V
The final energy distribution dP/dE is obtained by integrating
over all charges Q ′ in (2),
dP/dE = V −1
Q
0
dQ ′
V
d 3 rδ(E − ǫ − U(r)). (3)
Interchanging the sequence of integration and realizing
that U(r) is linear in Q ′ (see (1)), the emergence of
a plateau for dP/dE is obvious. It is limited to energies
E for which the δ-function in (3) can be fullfilled.
dP/dE
ΛR
e 2
0 ε − 3Qe
2R ε − Qe
R
Figure 2: Analytical electron spectrum dP/dE for a CC with radius
R, charge Q and excess energy ǫ; Λ is a universal constant
Λ = 3 3/2 ln(2 + √ 3) − 6 and e is the elementary charge.
The CC reveals another analytical property: The parameters
involved in photo activation of large systems
are not independent of each other namely the triple
(R,ǫ,T) characterizing a CC of radius R, atomic excess
energy after photoabsorption ǫ and pulse length
T also describes a one-parameter family of CCs with
(η −1 R,ηǫ,η −3/2 T), with η > 0 as illustrated in Fig. 3.
dP/dE [eV -1 ]
8
7
6
5
4
3
2
1
4.5
4
(R [au],ε [eV],T [fs]) =
(52,5,28.28)
3.5
3
(26,10,10)
(13,20,3.54)
0
-120 -100 -80 -60 -40 -20 0 20
0
40 -120 -100 -80 -60 -40 -20 0 20 40
E [eV] E [eV]
2.5
2
1.5
1
0.5
-1 -1 -1
E
ε
Figure 3: Electron spectra dP/dE for different Coulomb complexes
(R, ǫ, T) as given in (a) and related by the scaling parameter η =
1, 2, 1/2; (b) the rescaled spectra η −1 dP(ηE)/dE, after [1].
The double peak structure in Fig. 3 always emerges for
a typical CC with the peak at negative energies representing
the trapped nanoplasma and the peak for
E > 0 but below the photo line at E = ǫ (spike at 10
eV) representing direct escape events.
Understanding experiments with Coulomb Complexes
Thomas Möller and his group at the TU Berlin
performed an experiment with xenon and Argon clusters
under light of 90 eV photon enery at the free electron
laser FLASH in Hamburg with puzzling result: In
general one would expect photo electron signal from a
cluster of atoms at the atomic photo line and red shifted
since electrons ionized later have to overcome the already
existing ion charges upon escape which slows
them down. While this was indeed observed in argon,
xenon clusters exhibit a wing of photo electrons with
energies blue shifted from the atomic line. This wing
grows for increasing intensity.
With the help of the Coulomb complex we could show
that this wing develops for xenon due to the fact that a
large number of photons are activated in a very short
time due to photo absorption close to the giant resonance
frequency xenon (90 eV). This results in energy
changing collisions of the electrons in the continuum
before they leave the CC and therefore to some electrons
which are faster than produced by atomic photo
ionization. If the density of photo activated electrons
is reduced (which can be achieved by either reducing
the laser intensity or using another element with lower
photo cross section, e.g., argon), the blue wing vanishes
and the dynamics approaches the limit of sequential
emission [2]. Indeed, such electrons are already visible
in the typical CC spectrum of Fig. 3 with a small
probability beyond the spike of the atomic photo line
at 10 eV.
US and JMR thank the KITP in Santa Barbara for hospitality
and support of this work.
[1] C. Gnodtke, U. Saalmann, and J.-M. Rost, New Journal of Physics
13, 013028 (2011).
[2] C. Bostedt, H. Thomas, M. Hoener, T. Möller, U. Saalmann, I.
Georgescu, C. Gnodtke, and J.-M. Rost, New Journal of Physics
12, 083004 (2010).
[3] U. Saalmann and J. Rost, Phys. Rev. Lett. 91, (2003).
[4] A. Mikaberidze, U. Saalmann, and J. M. Rost, Phys. Rev. Lett. 102,
128102 (2009).
[5] C. Siedschlag and J. Rost, Phys. Rev. Lett. 93, (2004).
[6] C. Bostedt, H. Thomas, M. Hoener, E. Eremina, T. Fennel, K.-H.
Meiwes-Broer, H. Wabnitz, M. Kuhlmann, E. Plönjes, K. Tiedtke,
R. Treusch, J. Feldhaus, A. R. B. de Castro, and T. Möller, Physical
Review Letters 100, 133401 (2008).
[7] K. Moribayashi, Phys. Rev. A 80, 025403 (2009).
2.1. Photo Activated Coulomb Complexes 43