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

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.

1.  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 C₆H₆ 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.

2.  Theoretical approach.

Let us consider
the benzene molecule C₆H₆ in the field of
Ti:Sapphire laser with the wavelength l=400 nm,
pulse length t=300 fs and maximum
intensity I_max=2´10¹⁴
W/cm².
According to Ref. [4] first
electron is ejected from this neutral molecule and then the dissociation of C₆H₆⁺-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 C₆H₆⁺-ion which includes the ejection
of the second electron and subsequent Coulomb explosion of the C₆H₆⁺⁺-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 C₆H₆⁺-ion
(see Ref. [4]) reminds the model scheme of energy levels
for H₂⁺ [2] containing only two
low-lying electronic levels: 1s_g (even) and 1s_u
(odd).

         Therefore we consider the
dissociation process of C₆H₆⁺-ion analogously
to that for H₂⁺-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.

Where the strength envelope of the laser
radiation is chosen in the simple Gaussian form F(t)=F₀exp(-t²/2t²)  and R internuclear separation between the fragments
C₃H₃⁺ and C₃H₃, w is the laser frequency and t
is the laser pulse length. The value½sinwt½ 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

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 Y(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)=|<Y(R,0)|Y(R,t)>|² . In Fig. 3 envelope of laser pulse is depicted and
the dissociation probability W(t) is shown in Fig. 4.

3.  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

tunneling 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 m>>1. The
Keldysh parameter g=w(2mE)^1/2/F>>1. Thus,
the dissociation is the pure multiphoton process. The frequency of laser field
is w µ 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 m^-1/2. The total dissociation probability is obtained by
means of multiplying of this rate by the pulse length t. Therefore the probability of three-photon process
can be large, unlike the tunneling probability. This is the explanation of
large dissociation probability W»0.11
obtained in the calculations.

4.  Conclusions.

     Derivations
given above of dissociation of benzene molecule show that approximately 11% of all
C₃H₃⁺-ions
decay on fragments C₃H₃ and C₃H₃⁺
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

1.   
Peter Dietrich, Donna
T. Strickland, Michel Laberge and Paul B. Corkum, Phys. Rev. A, 47, N3,
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2.   
F. A. Ilkov, T. D. G.
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3.   
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4.   
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9.   
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Figure captions

Fig. 1. Scheme of dissociation for benzene
molecular ion C₆H₆⁺.

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 C₃H₃
and C₃H₃⁺.

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

Fig. 4. The dissociation probability of benzene
molecular ion C₆H₆⁺ as a function of time (fs).

Fig. 1

  Morse potential (a) (a.u.),

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

R, a.u.

Fig. 2

t, fs

Fig. 3

W(t)

t, fs

Fig. 4