Dissociation of Benzene Molecule in a Strong Laser Field (eng)

Dissociation of BenzeneMolecule in a Strong Laser Field M. E. SukharevGeneral Physics Institute ofRAS117942, Moscow, Russia Dissociationof benzene molecule in a strong low-frequency linearly polarized laser field isconsidered theoretically under the conditions of recent experiments. Analogywith the dissociation of diatomic molecules has been found.

The dissociationprobability of benzene molecule has been derived as a function of time. Thethree-photon dissociate process is shown to be realized in experiments. 1. Introduction.The number ofarticles devoted to the interaction of molecules with a strong laser fieldincreased considerably in recent years. The main featuresof interaction between diatomic molecules and a laser radiation were consideredin a great number of experimental 1-5 and theoretical 6-9 papers.

Classicaland quantum investigations of spatial alignment of diatomic molecules and theirmolecular ions in a strong laser field, as well as ionization and dissociationof these molecules and their molecular ions account for physical pictures ofall processes.However, whenconsidering complex organic molecules, we observe physical phenomena to bericher, and they are not thoroughly investigated. Most of results obtained for diatomic molecules can be generalized

to themulti-atomic molecules. This short paper contains the results of theoreticalderivations for dissociation of benzene molecule C6H6 inthe field of linearly polarized Ti Sapphire laser. Data were taken fromexperimental results by Chin s group, Ref. 4 . We use the atomic system of units throughout the paper.2. Theoreticalapproach.Let us consider thebenzene molecule

C6H6in the field of Ti Sapphire laser with the wavelength l 400 nm, pulse length t 300 fs and maximumintensity Imax 2 1014 W cm2.Accordingto Ref. 4 first electron is ejected from this neutral molecule and then thedissociation of C6H6 -ion occurs.The most probable channel for decay of this ion is theseparation into the equal parts Of course, there is anotherchannel for decay of C6H6 -ion which includesthe 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 ionconsidered in Ref. 2 . Indeed, the model scheme of energy levels for C6H6 -ion see Ref. 4 reminds the modelscheme of energy levels for H2 2 containing only two low-lying electronic levels 1sg even and 1su odd .

Therefore we consider the dissociationprocess of C6H6 -ion analogously to that for H2 -ion see Fig. 1 . The benzene molecular ion has the large reduced mass with respectto division into equal parts. Hence, its wave function is well localized inspace see Fig. 2 and therefore we can apply classical mechanics fordescription of the dissociation process 1 . However, the solution of Newtonequation with the effective potential see below does not produce anydissociation,

since laser pulse length is too small for such large inertialsystem. In addition to, effective potential barrier exists during the wholelaser pulse and tunneling of the molecular fragment is impossible due to itslarge mass see Fig. 2 . Thus, we should solve the dissociation problem in theframes of quantum mechanics. The groundeven electronic term of C6H6 -ion is presentedhere in the form of the well-known

Morse potential with parameters b 2k and De 6.2эВ, where k is approximated by the elastic constant of C-C coupling in the C6H6-moleculeand De is the dissociation potential for the C2-molecule. The interaction of the molecular ion with the laserfield is given by expression see. Ref. 9 Where the strength envelope ofthe laser radiation is chosen in the simple Gaussian form F t F0exp -t2 2t2 and R internuclear separation between thefragments

C3H3 and C3H3,w is the laserfrequency and t is the laser pulselength. The value frac12 sinwt frac12 takes into accountthe repulsion between theinvolved ground even electronic term and the first excited odd repulsiveelectronic term. Thus, the Hamiltonian of the concerned systemis The kineticenergy operator being of the formWhere Re is theequilibrium internuclear separation. When calculating we make use of

Re 1.39A. The time dependent Schrodinger equationwith Hamiltonian 3 has been solvednumerically by the split-operatormethod. The wave functionhas been derived by the iteration procedure according to formulaThe initial wave function Y R,0 was chosen asthe solution of the unperturbed problem for a particle in the ground state ofMorse potential. The dissociation probability has been derived as a function of time according to formula

W t lt Y R,0 Y R,t gt 2 . In Fig. 3envelope of laser pulse is depicted and the dissociation probability W t isshown in Fig. 3. Results.The quantity W t is seen from Fig. 4 increase exponentially withtime 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 atunneling of a fragment through the effective potential barrier see Fi. 2 .

Indeed, the tunnelingprobability is on the order of magnitude ofWhere Veff issubstituted for maximum value of the field strength and the integral is derived over theclassically forbidden region under the effective potential barrier. Thetunneling effect is seen to be negligibly small due to large reduced mass ofthe molecular fragment m gt gt 1. The Keldysh parameter g w 2mE 1 2 F gt gt 1.

Thus, the dissociation is the pure multiphotonprocess. The frequency of laser field is w 2.7 эВ, while thedissociation potential is De 6eV. Hence, three-photon process ofdissociation takes place. The dissociation rate of three-photon process isproportional to m-1 2. The totaldissociation probability is obtained by means of multiplying of this rate bythe pulse length

t. Therefore theprobability of three-photon process can be large, unlike the tunnelingprobability. This is the explanation of large dissociation probability W 0.11 obtained inthe calculations.4. Conclusions. Derivations given above ofdissociation of benzene molecule show that approximately 11 of all C3H3 -ionsdecay on fragments C3H3 and C3H3 under the conditions of

Ref. 4 . The absorption of three photons occurs inthis process. Author is grateful to N. B.Delone, V. P. Krainov, M. V. Fedorov and S. P. Goreslavsky for stimulatingdiscussions of this problem. This work was supported by Russian FoundationInvestigations grant N 96-02-18299 .References1. Peter Dietrich, DonnaT.

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E. Sukharev, V. P. Krainov, JETP, 113,No2, 573, 1998. M. E. Sukharev, V. P. Krainov, JOSA B, in press.Figure captionsFig. 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 benzenemolecular ion c as functions

of the nuclear separation R a.u. between thefragments C3H3 and C3H3 .Fig. 3. Envelope of laserpulse as a function of time fs .Fig. 4. The dissociation probability of benzene molecular ionC6H6 as a function of time fs . Fig. 1 Morse potential a a.u effective potential for max. field b a.u , c b a square of the wave function of the groundstate for benzene molecular ion c R, a.u.

Fig. 2t, fsFig. 3 b W t t, fsFig. 4