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# Dissociation of Benzene Molecule in a Strong Laser Field \eng\

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**Dissociation of Benzene Molecule in a **

**Strong Laser Field**

M. E. Sukharev

*General
Physics Institute of RAS*

*117942,
**Moscow**,
**Russia*

Dissociation of benzene molecule in a strong low-frequency linearly polarized laser field is considered theoretically under the conditions of recent experiments. Analogy with the dissociation of diatomic molecules has been found. The dissociation probability of benzene molecule has been derived as a function of time. The three-photon dissociate process is shown to be realized in experiments.

Introduction.

The number of articles devoted to the interaction of molecules with a strong laser field increased considerably in recent years. The main features of interaction between diatomic molecules and a laser radiation were considered in a great number of experimental [1-5] and theoretical [6-9] papers. Classical and quantum investigations of spatial alignment of diatomic molecules and their molecular ions in a strong laser field, as well as ionization and dissociation of these molecules and their molecular ions account for physical pictures of all processes.

However, when
considering complex organic molecules, we observe physical phenomena
to be richer, and they are not thoroughly investigated.
Most of results obtained for
diatomic molecules can be generalized to the multi-atomic molecules.
This short paper contains the results of theoretical derivations for
dissociation of benzene molecule C_{6}H_{6}
in the field of linearly polarized Ti:Sapphire laser. Data were taken
from experimental results by Chin’s group, Ref. [4].
We use the atomic system of units throughout the paper.

Theoretical approach.

Let us consider the
benzene molecule C_{6}H_{6
}in the field of
Ti:Sapphire laser with the wavelength
=400
nm, pulse length
=300
fs and maximum intensity
I_{max}=210^{14}
W/cm^{2}.
According to Ref. [4] first
electron is ejected from this neutral molecule and then the
dissociation of C_{6}H_{6}^{+}-ion
occurs.

The most probable channel for decay of this ion is the separation into the equal parts :

Of
course, there is another channel for decay of C_{6}H_{6}^{+}-ion
which includes the ejection of the second electron and subsequent
Coulomb explosion of the C_{6}H_{6}^{++}-ion.
We do not consider the latter process.

The
channel (1) is
seen to be similar to the dissociation of the hydrogen molecular ion
considered in Ref. [2]. Indeed, the model scheme of energy levels for
C_{6}H_{6}^{+}-ion
(see Ref. [4]) reminds
the model scheme of energy levels for H_{2}^{+}
[2] containing only two low-lying electronic levels: 1_{g}
(even) and 1_{u}
(odd).

Therefore we consider
the dissociation process of C_{6}H_{6}^{+}-ion
analogously to that for H_{2}^{+}-ion
(see Fig. 1). The benzene molecular ion has the large reduced mass
with respect to division into equal parts. Hence, its wave function
is well localized in space (see Fig. 2) and therefore we can apply
*classical*
mechanics for description of the dissociation process (1). However,
the solution of Newton equation with the effective potential (see
below) does not produce any dissociation, since laser pulse length is
too small for such large inertial system. In addition to, effective
potential barrier exists during the whole laser pulse and tunneling
of the molecular fragment is impossible due to its large mass ( see
Fig. 2). Thus, we should solve the dissociation problem in the frames
of *quantum*
mechanics.

T

he
ground even electronic term of C_{6}H_{6}^{+}-ion
is presented here in the form of the well-known Morse potential with
parameters =2k
and D_{e}=6.2
эВ, where
k is approximated by the
elastic constant of C-C
coupling in the C_{6}H_{6}-molecule
and D_{e}
is the dissociation potential for the C_{2}-molecule.
The interaction of the
molecular ion with the laser field is given by expression (see. Ref.
[9])

Where
the strength envelope of the laser radiation is chosen in the simple
Gaussian form F(t)=F_{0}exp(-t^{2}/2^{2})
and R internuclear separation between the fragments C_{3}H_{3}^{+}
and C_{3}H_{3},
is the laser frequency and
is the laser pulse length. The valuesint
takes into account the repulsion between
the involved ground even electronic term and the first excited odd
repulsive electronic term.

Thus,
the Hamiltonian of the concerned system is

T

he
kinetic energy operator being of the form

Where
R_{e}
is the equilibrium internuclear separation. When calculating we make
use of R_{e}=1.39
A.

The time dependent
Schrodinger equation with Hamiltonian (3)
has been solved numerically by
the split-operator
method. The
wave function has been derived by the iteration procedure according
to formula

The initial wave function (R,0) was chosen as the solution of the unperturbed problem for a particle in the ground state of Morse potential.

The
dissociation probability has been derived as a function of time
according to formula W(t)=<(R,0)(R,t)>^{2}
. In Fig. 3 envelope of laser pulse is depicted and the dissociation
probability W(t) is shown in Fig. 4.

Results.

The quantity W(t)
is seen from Fig. 4 increase
exponentially with time and it is equal to 0.11 after the end of
laser pulse. It
should be noted that the
dissociation process can not be considered as a tunneling of a
fragment through the effective potential barrier (see Fi. 2). Indeed,
the t

unneling
probability is on the order of magnitude of

Where
V_{eff}
is substituted for maximum value of the field strength
and the integral is derived
over the classically forbidden region under the effective potential
barrier. The tunneling effect is seen to be negligibly small due to
large reduced mass of the molecular fragment 1.
The Keldysh parameter
=(2E)^{1/2}/F>>1.
Thus, the dissociation is the
pure multiphoton process. The frequency of laser field is
2.7 эВ, while the
dissociation potential is D_{e}=6
eV.
Hence, *three-photon*
process of dissociation takes place. The dissociation rate of
three-photon process is proportional to ^{-1/2}.
The total dissociation probability is obtained by means of
multiplying of this rate by the pulse length .
Therefore the probability of three-photon process can be large,
unlike the tunneling probability. This is the explanation of large
dissociation probability W0.11
obtained in the calculations.

Conclusions.

Derivations given above
of dissociation of benzene molecule show that approximately
11
of all
C_{3}H_{3}^{+}-ions
decay on fragments C_{3}H_{3}
and C_{3}H_{3}^{+}
under the conditions of Ref. [4]. The absorption of three photons
occurs in this process.

Author is grateful to N. B. Delone, V. P. Krainov, M. V. Fedorov and S. P. Goreslavsky for stimulating discussions of this problem. This work was supported by Russian Foundation Investigations (grant N 96-02-18299).

References

Peter Dietrich, Donna T. Strickland, Michel Laberge and Paul B. Corkum, Phys. Rev. A,

**47**, N3, 2305 (1993). M. Ivanov, T. Siedeman, P. Corkum, Phys. Rev. A,**54**, N2, 1541 (1996).F. A. Ilkov, T. D. G. Walsh, S. Turgeon and S. L. Chin, Phys. Rev. A,

**51**, N4, R2695 (1995). F. A. Ilkov, T. D. G. Walsh, S. Turgeon and S. L. Chin, Chem. Phys. Lett**247**(1995).S. L. Chin, Y. Liang, J. E. Decker, F. A. Ilkov, M. V. Amosov, J. Phys. B: At. Mol. Opt. Phys.

**25**(1992), L249.A. Talebpour, S. Larochelle and S. L. Chin, in press.

D. Normand, S. Dobosz, M. Lezius, P. D’Oliveira and M. Schmidt: in

*Multiphoton Processes*, 1996, Conf., Garmish-Partenkirchen, Germany, Inst. Phys. Ser. No 154 (IOPP, Bristol 1997), p. 287.A. Giusti-Suzor, F. H. Mies, L. F. DiMauro, E. Charon and B. Yang, J. Phys. B: At. Mol. Opt. Phys.

**28**(1995) 309-339.P. Dietrich, M. Yu. Ivanov, F. A. Ilkov and P. B. Corkum, Phys. Rev. Lett.

**76**, 1996.S. Chelkowski, Tao Zuo, A. D. Bandrauk, Phys. Rev. A,

**46**, N9, R5342 (1992)M. E. Sukharev, V. P. Krainov, JETP,

**83**, 457,1996. M. E. Sukharev, V. P. Krainov, Laser Physics,**7**, No3, 803, 1997. M. E. Sukharev, V. P. Krainov, JETP,**113**, No2, 573, 1998. M. E. Sukharev, V. P. Krainov, JOSA B, in press.

Figure captions

Fig.
1. Scheme of dissociation for
benzene molecular ion C_{6}H_{6}^{+}.

Fig.
2. The Morse potential (a), the effective potential (b) for maximum
value of the field strength (a.u.), and the square of the wave
function of the ground state for benzene molecular ion (c) as
functions of the nuclear separation R (a.u.) between the fragments
C_{3}H_{3}
and C_{3}H_{3}^{+}.

Fig. 3. Envelope of laser pulse as a function of time (fs).

Fig.
4. The dissociation
probability of benzene molecular ion C_{6}H_{6}^{+}
as a function of time (fs).

Fig. 1

Morse potential (a) (a.u.),

effective potential for max. field (b) (a.u),

a

b

c

square of the wave function of the ground state for benzene molecular ion (c)R, a.u.

Fig. 2

t

,
fs

Fig. 3

b

W

(t)

t, fs

Fig. 4

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