First, I would like to thank the organizers.
Maybe you'll notice that all three organizers
have a name which starts with S. So it's a triple S.
So some of you might have heard about the intermolecular
or interatomic columbic decay, which is, I will explain it
a little later, is a mode of relaxation of excited systems
in environment.
And I would like to, we started exploring it
by free electron lasers.
Of course, we are theoreticians.
So when I say exploring, it's still on the paper, on paper.
And an idea behind it, which actually
was pointed out by the referee, is
that one can learn from it also that how energy,
because in a free electron laser you deposit a lot of energy
into one site, an atom or a small molecule,
how the energy can be dissipated to the environment.
And so this is an issue here.
Let me see.
I have to switch it on.
Yeah, so let me start with explaining
what we know about an isolated system
before I go to a system in an environment.
And of course, I will concentrate on an excited ion.
But in principle, it doesn't matter
whether you have an ion, a neutral system, whatever.
But I would like to be specific.
And if you have an excited ion and you remove a,
let's say the ion is created by removing a core electron,
we all know there is Auger decay.
I'm not talking about very heavy elements
where you have x-ray emission and who
knows what kind of cascades.
I want to keep it short.
So you have an Auger decay.
So one electron falls into the vacancy, closes the vacancy,
fills the vacancy, and another one flies out.
And this has a wide range of applications,
analytical applications.
And it's a very fast process, one of the fastest processes.
We know femtosecond even into the sub-femtosecond regime.
And if we remove an valence electron,
here I separate them into outer valence and inner valence,
then you usually have radiative decay in an atom
or a small system.
So an electron falls in here and a photon is emitted.
And this we all know, but it's a relatively slow process.
So it's best, so to say, nanoseconds.
And what happened if this isolated system has now
a partner, let's say a neighbor or is in an environment.
I will speak about more neighbors later.
Then you have what we call ICD, so the intermolecular
or interatomic, if these are atoms, columbic decay.
So it's a long range correlation effect.
And what happens if I remove here an inner valence
in the system now, this could only,
if it was isolated, as we show, it can only decay
by emitting a photon.
But having a neighbor, now the energy
can be transferred to the neighbor,
and you can kick out an electron from the neighbor.
So you have two ions at the end.
You started with one ion, and you have a neighboring ion.
And then you have a coulomb explosion.
These two will just fly apart, and this
gives additional damage to the system.
Now we'll come back later a little.
I'll give some examples before I go to the free electron laser.
So it's quite a general phenomenon.
It's found in many systems, and not only for ions, of course,
and in hydrogen bonded systems.
van der Waals clusters recently in helium-2.
It's a wonderful measurement by the donor group in Frankfurt.
And now we started studying what happens in quantum dots.
You also see that there is ICD.
It's usually ultra-fast.
It's femtosecond regime.
And very important, it becomes faster the more neighbors
you have.
So if you have many neighbors, it can be very, very fast.
I'll show an example later.
And what is relevant for us in the last years,
it became more and more clear to us
that the low-energy electrons produced by ICDs,
this ICD electron, which is kicked out here
after transfer of energy from the initially excited system
to the neighbor, they are very slow.
So they have energies between 0 and 10 eV or something like that.
We'll see an example.
And importantly, it has been noticed about a decade ago.
It has been noticed that the damage done
to biological systems is not by the photons,
but by the slow electrons produced.
And this produces slow electrons automatically
at the site where you create the ion.
Excuse me?
Yes?
Why isn't the logic process possible in this configuration?
Why can't the second upper electron be expelled?
There is not enough energy.
No, that's all.
OK, because it's more strongly bound,
because it's an ion.
Ah, you mean, no, not only.
Yeah, first of all, the energy is shifted.
It's an ion.
And second, the neighbor can be any,
the same kind or one which is easier to ionize.
It depends.
But it's correct.
It's an ion.
So to take out the first electron of helium is 24.
The second is 50-something.
Yeah, yeah, all right.
So I'll give you two examples only.
I would like to start with water,
because there are recent measurements on ICD in water.
There are a number of papers now, experimental.
I will discuss only two.
The point is that ICD in water tells you,
and water is only present in biological systems,
for example, that ICD will be important
in biological systems.
And of course, water is the first example
which was measured, which is beyond rare gases, which
that's why it's important.
Now, I will discuss briefly two measurements, two papers,
by the Derna Group, which I mentioned already.
It's a water dimer, so they have electron-ion coincidence
experiments on the dimer.
And it's very important that they are also
in parallel measurements on larger water clusters, where
they have developed a new method to identify ICD,
because you have to be sure that it's not something else.
And it's important, because even if it is, so to say,
operative in a dimer, it doesn't mean
that in a big system, exactly the same stuff happens.
It could be that there are some other competing processes,
and they are not.
So that's important, too.
And let me see.
And here, I hope you can see, it looks a bit faint to me
from here.
So that's the experiments on the dimer.
So these are coincidence experiments.
And you can also see by integrating
over the other kind of particle.
For example, over the electrons, you
see the kinetic energy released by the two waters.
And here, I should add that the two waters.
So after ICD, you have water plus.
You start with water plus.
An electron moves away from the other water by ICD.
You have two water ions.
And the process seems to be so fast
that the two water ions just fly apart without any time
for proton exchange.
So they measure only two intact H2O pluses,
which is important, too.
And you see the electron distribution.
This you should subtract.
It's due to the photoelectrons.
They chose a singleton wavelength,
which gives you photoelectrons here.
So it goes down like that to about 10 eV or so.
And so you see here that the electrons peak.
They're very slow.
They peak at around 0, and it goes about to 10.
This is a very old calculation by us.
Similar, but it has some more structure.
And now, in the large clusters, this
is a photoelectron experiment.
Those who are used to photoelectron experiments,
they see in this part a normal photoelectron of water.
Even water molecule looks similar.
But you see here, at low energy, a big peak
comes after you ionize the H2O.
So the oxygen 2S electron, that's
the inner valence electron.
If you remove that, this gives rise to slow ICD electrons.
And also here, the distribution of ICD electrons
is between 0 and 10.
Maybe it peaks a little different,
but it's between 0 and 10.
And as I said, this is very relevant
because it was found that it's the slow electrons
by dissociative attachment break the DNA strands,
single-strand breaks, and even double-strand breaks,
which are irreparable, are done by slow electrons.
And here, you have the slow electron produced at the site,
as I said, where you excite.
Now, because of that, we had a look
at building blocks of peptides or biochemically relevant
systems.
There are hydrogen bonds.
And I will not go too much into detail.
So we studied those seven dimers, so always water.
So you can have, for example, let's take here H2S and water.
You can have a place where the water is a electron acceptor
or an electron donor.
So they are a bit different.
But all of them show ICD when you ionize either the oxygen,
sulfur, and nitrogen, and so on.
So all of them, ICD seems to be an open channel.
And ICD and hydrogen bonded systems here is an example.
We calculated all of those.
It's formaldehyde and water, for example.
And you see here the computed ionization.
So like a photoelectron spectrum,
but a computed one at fixed geometry and of this complex.
And you can see that the energies
of the oxygen of water and oxygen of formaldehyde ionization
energy are here.
And the threshold to double ionization,
these are the double ionization potentials.
The threshold is here.
So all these levels, after ionizing
an inner valence electron, removing an inner valence
electron, all these levels are above threshold.
And ICD will take place.
And you will kick out an electron from the neighbor.
And again, the distribution is about up to about 80 V.
So low electrons are produced here.
Now before I go, since our study on ICD
in a free electron laser was done on a neon dimer,
because it's enormous calculations,
we cannot do it yet at all on water or something like that.
I would like to talk about van der Waals class
very, very briefly, and particularly
on the neon dimer, without the free electron laser,
that you see what's going on.
And you see that Robin was very involved in those works.
And here we see the ionization spectrum of a neon atom.
So you remove the 2P electron.
It's about 22 EV.
You remove the neon 2S electron.
It's about 40 ATV, which you need.
And if you ask for, this was your question,
if you ask why there is no OJ, the threshold for single,
the threshold for double ionization.
So it means neon 2 plus is 60.
So about 12 EV are missing.
And it cannot decay by electron emission.
It can only decay by photon emission.
And this takes nanoseconds.
Now if I take a neon dimer, the energies
will not really change, because the two neons
just stand around at some distance over 3 angstrom.
And there is hardly any interaction.
It's a very weak van der Waals interaction.
Now you have, again, the same thresholds, essentially.
So these are the one side where you remove the second electron
from the same neon.
And this is, again, much too high in energy.
But you have the two side threshold, neon plus, neon
plus, which is about 50 EV lower.
And now the channel is open.
Now this level can decay by emitting an electron
from the neighbor.
Then you have neon plus, neon plus.
And you have the Coulomb explosion.
And it was all very nicely measured.
Now what happens if I have more neighbors?
And I mentioned it that it becomes much faster
when you have more neighbors.
In neon dimer, the ICD lifetime.
So if you have a neighbor in equilibrium distance,
the lifetime is about 80 femtoseconds.
In water, by the way, it's about five or six femtoseconds
in that range.
So it's much faster in the hydrogen bonded systems.
But have a look at that.
Let's say I remove from the central neon the 2S electron.
Now I can have ICD to the left.
It means energy will be transferred to the left
and kick out the electron.
Since they don't really interact,
the neutral species don't really interact.
It means that you have, again, about 80 femtoseconds,
like in the dimer.
But the energy can be transferred as well to the right
and kick out an electron from there.
And it's the same probability.
So you have twice the probability.
You will have about half the lifetime.
So it will be already 40.
And when you arrive here, when this
is a natural next neighbors of a neon in, let's say,
in a big neon cluster or in a neon solid,
you have 12 neighbors.
The lifetime will be just a few femtoseconds.
This was measured.
So you can, in principle, see that more neighbors, even
neon becomes a bomb.
It's comparable to the OJ of an inner core in those systems.
Here you see the plot.
This is the decay width or rate as a function of neon atoms
in this cluster.
So it's 0, of course, if you have neon alone.
It will only be by photo emission.
And then it really goes linearly.
And then it even goes faster due to some collective effects,
which I will not talk about.
And if you look at the lifetime, it's about 80 femtoseconds.
And it goes down to just a few femtoseconds
if you take the full next shell into account.
Now I go to actually the title of my talk.
So we thought about what to do if you have a free electron
laser at your disposal, sufficient intensity,
and also, of course, that you also
have the frequencies we need.
So here is a cartoon and the scheme.
So if you ionize, let's say we have a free electron laser pulse
coming, it has sufficiently many photons.
So first, if you ionize one of the outer electrons,
and if the energy of this pulse fits into an excitation of,
let's say, an inner valence up, so you're now
created by the second photon, a hole in the shell,
inner valence shell, where you can have ICD.
Now there will be ICD.
It will fall back.
The energy will be transferred to the neighbor,
kick out an electron there.
Then you have neon plus, neon plus, like in the usual ICD.
And you will have a coulomb, a coulomb explosion.
And you can measure, for example,
if this is a neon dimer, you could measure the neon plus
yield, and if possible, also the electron distribution
of all the electrons.
Because one should not forget that the same pulse could also
one photon ionize one neon and one, let's say, the other neon.
Then you'll also have neon plus, neon plus
by a different mechanism.
And I'll show you the competition and interference.
If the pulse is coherent, then you really
have interference of these two processes.
And the interference is enormous.
And this surprised me, actually, and I would like to discuss now.
So to go into some details, not too many,
these are the potential, the computed potential energy
curves of all the involved states.
So this is neon dimer ground state.
This is a very different scale.
So it's very, very shallow.
The minimum is about 3.1 eV, angstrom.
Sorry, I'm too much into the energy business, seems.
And here, in the first photon, you ionize.
Here, we chose a photon of about that energy.
And I'll give you more details later.
So the first photon ionizes, like I said, one neon.
You see, neon plus 2p minus 1.
And there are four states there.
So all four states can be ionized.
Then the second photon takes you to the neon plus 2s minus 1,
where the hole is now in the 2s shell.
And you have two states there.
And this can now decay to the final states,
neon plus, neon plus, which are essentially
one over r in atomic units.
Very steep curves compared to those.
So you can decay and emit an electron of this small energy.
You see, it's small energies.
The ICD electrons have relatively small energy.
Now, let me first show you what happens at relatively low
intensity.
So this is intensity in units of 10 to the 10 watts
per centimeter square.
So like we said, we need, at that photon energy of about 27,
we need two photons at least.
So you see, indeed, essentially a quadratic
at low intensity, a quadratic behavior.
So these are the calculated points.
So up to here about it's really nicely quadratic.
And if we want to compare it with something
would be more standard.
So we take, let's say, twice the frequency, the same intensity,
twice the frequency, and the same pulse
of 60 femtoseconds in this case.
And then you find much less ICD.
Here it's essentially still only ICD.
At these intensities, you find much less.
So it means a two-photon process triggers much more ICDs
than a single-photon process, which is nice.
Already at relatively low intensity, you see here,
this intensity is quite low.
And it's still quite more pronounced.
Now here you see the electron spectra, a different pulse
duration and intensities.
So we have two pulses.
I think here this was 60 femtoseconds and 30
and different intensities, the peak intensities.
But let's concentrate on one.
You cannot follow so fast all the details, of course.
But here we see the fraction after the pulse is over,
the fraction of neutrals, dimers which have survived,
and the fraction of single ions which, so to say, survived.
All others are neon plus pairs.
So it means it's either ICD or direct ionization
of the two neons.
So the total yield of these neon plus or electrons,
in coincidence, doesn't matter, are the red curves.
And ICD alone are the black curves.
You see it here.
It's even here.
I'm standing two neons, so I didn't really find it.
So ICD are the broken black curves.
And the total yield of neon plus ions or electrons,
emitted electrons in coincidence are the red curves.
And you see in the beginning, as it
means at low intensity of about 5 to 10 to the power of 11,
it's essentially only ICD.
Then you start to see also direct ionization
of the two neons.
And of course, the higher you go,
you will see more and more ionization of the two neons.
But there is enormous interference here.
So it's misleading to think that the difference
is due to direct ionization.
I thought so in the beginning.
And then we looked at it, and we were very surprised.
So here you see a breakup of the contributions.
In one case, this is 30 femtosecond and this intensity.
And you see about 50% of the neutrons have survived the pulse.
So it's not a very strong pulse.
So ICD alone is a broken curve.
Then the total is red, as before.
And if you calculate only the direct,
you don't allow for ICD.
And you calculate only the direct ionization
of the two neons by two photons, so to say, or by the pulse,
you get this blue broken curve.
So it's not at all the difference here, of course.
So most of it is really a question of interference
to get the total.
And now I address a last point concerning these results,
is how to measure the ICD alone.
This is a calculation.
We can, of course, calculate ICD alone.
But we would like to know how to measure it.
Now ICD in the neon dimer would take about 80 femtosecond.
So if the pulse is shorter, like 30 femtoseconds,
then of course when most of the ICD
happens after the pulse is over.
So the direct ionization of the two neons
is only during the pulse.
So if we measure, so to say, the total yield after a long time,
or the total yield up to 30 femtoseconds,
let's say, then the pulse is over.
And we subtract.
So this is measured the total yield up to 30 femtoseconds.
And if you subtract, you get a green curve.
And the calculated ICD alone is a broken curve here.
So of course you could take even a shorter pulse
and get better agreement.
But this is just to show that you can play also
and learn about the times of the processes by such measurements.
And now I didn't tell you anything about theory.
And I will not tell you much, because my time is probably
how much time do I have?
I still have time.
Perhaps it's still something like this.
Oh, great.
I will be finished even before, I guess.
So now the calculation are rather involved,
because what one does not realize
is that in a laser field, if you have a resonant,
for example, if you excite, for example, of the 2s electron
up to the 2p, you have two levels, these two levels.
I mean, this is quite general.
These two levels, if you have a resonant frequency,
the potential curves will cross.
And at this crossing, if you take the rotational angle,
rotational will mean the angle between the polarization
of the light and the axis of the molecule,
is now a dynamical variable and not fixed.
So if you fix it, you lose most of the information.
If you take it as a dynamical variable,
you will find that there is a conical intersection
between the two surfaces.
And those who have ever heard about conical intersections,
they know that at conical intersections,
the non-ideabatic effects are maximal.
So you have a very strong mixing of the two electronic states
and of the vibration coordinate r and of the rotation.
So even if you start with j equals 0,
afterwards you will have j up to 30, 40, whatever you like,
after the process, because of this very strong
non-ideabatic mixture.
Now, in our case, it's even a little more complicated,
because we have decay.
This would be the case for stationary states.
But if you have decay, the surfaces
will become complex because of the decay time, or decay rate,
which you have.
And then instead of a conical intersection,
one has something which, a long time ago actually,
I called doubly intersecting complex energy surfaces.
Because there are two intersections
where both the real part and the imaginary part
of the surfaces, these are real cases,
intersect at two points in the coordinate space.
And the coordinates here are r and theta,
so the rotational angle and the vibrational.
And also, these two points, the non-ideabatic coupling
are singular, like in the conical intersection.
And the effect on this coupling is enormous.
We see it also in this neon dimer
when we compute the spectra, or the process,
we see in the wave function that the wave function becomes
very, very mixed and totally non-ideabatic.
So this plays a role, and you don't see too much.
I will not go into detail here.
You have to build some wave packet which
has everything, the rotation, the vibration, the coupling,
of course, to the field, and so on,
and ionization probabilities by the photons
of the high intensity.
And finally, let me summarize what
we saw in the last part of the talk.
That ICD is enhanced by two-photon absorption
is more efficient than one-photon absorption
of double frequency, of sufficient frequency
to ionize directly the decaying state.
Then, of course, we have a sequential two-photon absorption
by the two neon atoms, and they strongly interfere.
So we have a strong interference.
And you can also measure the different parts
of the spectrum, for example, different contribution,
for example, ICD, by doing time-dependent measurements.
So you measure up to some time.
And by subtraction, I showed you, you can determine the ICD.
And of course, I have to thank many, many people
over the years.
The list is not complete because it's full.
Sorry.
But we have quite many people who worked.
The field did not emerge by itself.
Many people contributed, and I'm very thankful for that.
And we have also collaboration with Nimod, Francesco,
and some experimental groups.
And thank you for your attention.