: Молекула бензола в сильном лазерном поле
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 lowfrequency 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 threephoton 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 [15] and theoretical [69] 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 multiatomic
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.
2. Theoretical approach.
Let us consider the benzene molecule C_{6}H_{6} in the field of
Ti:Sapphire laser with the wavelength l=400 nm, pulse length t=300 fs and
maximum intensity I_{max}=2´10^{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
lowlying electronic levels: 1s_{g} (even) and 1s_{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.
The ground even electronic term of C_{6}H_{6}^{+}ion is
presented here in the form of the wellknown Morse potential with parameters
b=2k and D_{e}=6.2 эВ, where k is approximated by the elastic constant
of CC 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}/2t^{2}) and R
internuclear separation between the fragments C_{3}H_{3}^{+}
and C_{3}H_{3}, 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
The 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 splitoperator 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, threephoton
process of dissociation takes place. The dissociation rate of threephoton
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 threephoton 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 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 960218299).
References
1. 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).
2. 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).
3. S. L. Chin, Y. Liang, J. E. Decker, F. A. Ilkov, M. V. Amosov, J. Phys.
B: At. Mol. Opt. Phys. 25 (1992), L249.
4. A. Talebpour, S. Larochelle and S. L. Chin, in press.
5. D. Normand, S. Dobosz, M. Lezius, P. D’Oliveira and M. Schmidt: in
Multiphoton Processes, 1996, Conf., GarmishPartenkirchen, Germany, Inst.
Phys. Ser. No 154 (IOPP, Bristol 1997), p. 287.
6. A. GiustiSuzor, F. H. Mies, L. F. DiMauro, E. Charon and B. Yang, J.
Phys. B: At. Mol. Opt. Phys. 28 (1995) 309339.
7. P. Dietrich, M. Yu. Ivanov, F. A. Ilkov and P. B. Corkum, Phys. Rev.
Lett. 76, 1996.
8. S. Chelkowski, Tao Zuo, A. D. Bandrauk, Phys. Rev. A, 46, N9,
R5342 (1992)
9. 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),
square of the wave function of the ground state for benzene molecular
ion (c)
R, a.u.
Fig. 2
t, fs
Fig. 3
W(t)
t, fs
Fig. 4
