'\ 13' CA01 2003, 16-20 September 2003, Alushta. Crimea, Ukralne 1'

INFLUENCE OF THE SQUEEZED VIBRATIONAL STATES ON NONRADIATIVE TRANSITIONS IN THE EXCIMER MOLECULES IN

INTENSIVE LASER FIELD

E.P. Sineavsky, E.Yu. Kanarovsky

Institute ofilpplied Physics, Academy of Sciences of Moldova 5, Academic str., MD-2028, Kishinev, Republic of Moldova

tel. : (003732) -738092, E-mail: arusanov@,mail.ru

SUMMARY

For investigation of the nonradiative transitions in excimers we used the adiabatic approximation. The adiabatic potential of the excited electron-vibrational state (1) has the

minimum on the normal coordinate U, = - W q + E,, and the adiabatic potential of the

ground electron-vibrational state (0) of excimer molecule is presented as the repulsive potential U, = Qq. The electron-vibrational system in model of two electron terms it is

convenient to describe applying the Fermi's operators U , i' according to expressions [I]:

1 2 2

2

Y.

U = 10) (11 , a+ = I]} (01 , a+Q + UU+ = 1. Here 10) , 11) are the wave functions of the ground and the excited states of the electron subsystem.

The Hamiltonian of the researched electron-vibrational system in the representation of the secondary quantization has the kind

H(t ) = H,(t) + w , (1)

1 Ho(t) = Eoa'a + *U( b'b + X) + [ v, ( b + b+ ) - -( b + b+ )" uu+ - hw 4

- Fo (d,au' + d,u'a)cosQot

w =[&,a + &p+](b + b')

, and b+(b) are the operators of creation (annihilation) of 2w

vibrations with energy hw, and so is the electron energy, count off from the ground electron-vibrational state. The last addend in (1) describes the interaction of an electron

with a laser radiation of frequency a and intensity F,; do, d, are the diagonal'matrix elements of the operators of own electrical dipole moments of the ground and the excited electronic states, accordingly. The operator Wof electron-vibrational interaction is mixing the electronic states and is generating nonradiative transitions [2].

0-7803-7948-9/03/$17.00 02003 IEEE

CAOL 2003, 16-20 September 2003. Alushta. Crimea, Ukraine 14 1

The probability of the nonradiative transition in the lowest order on interaction w is calculated with using the standard methods of the theory of multiphonon transitions [2 ] . In result, accounting the natural case Ut -+ a,, Qt + a, [3] for the equilibrium vibrational states the desired probability of the nonradiative transitions becomes:

exp{-ur2[1-;]+ (1 + N)e" - N

Following notations here are entered:

2 v 2 a, =

1 A 0

2

Where 3?, ( p ) is the Bessel's function of real argument p = -[( F,d,) - (Fad,)],

(3)

At creation of the excimt'r molecules, for example by a supershort laser pulse [4], in the excited electron-vibrational state the squeezed vibrational states [5] (i.e. a packet of stationary states of harmonic oscillator) are formed. In this case the probability of the nonradiative ,transition with using the matrix of density for squeezed Bose's states [6] is defined by'expression (for simplicity it is considered the coherent phonc

. . .. 0 . . ~ . . . " . .~ ,. . _. --

In the considered case the parameter IpI > 1. One is connected to a position of a minimum of an adiabatic potential of dimer, from which the excited state (excimer) is

formed [7]. Let's remark, that the appearance of the damping of Gauss's type e-aor-under the integral is connected to the transition of electron on the repulsive potential. Thus the availability in (4) Bessel's functions under the integral on T actually describes the noiii-adiative transitions with emission of phonons with the subsequent tunneling on the repulsive potential.

. It is possible to execute integrating on r in (3), (4) approximately for the case of

strong electron - phonon coupling a, > 1 and - E, >> 1 (it is typical for the excimer Aw

\ 15 CAOL 2003, 16-20 September 2003, Alushta, Crimea, Ukraine ,’

molecules in which one the broad unstructured bands of luminescence in high frequency area of the spectrum are watched) In outcome the probability of a nonradiative transition (3) in absence of a Iaser radiation ( p = 0 ) can be written to the kind:

2% . 2 A, =- 3 h o

In an intensive laser radiation field the probability of the nonradiative transitions with account of first photon quasi-level ( n = 1 ), which determines the basic contribution to the investigated transitions, according to (3) is described by the expression:

I

2(&, - tzn) 2 A, =

3Am

Let’s remark, that for the ordinary molecular systems the nonradiative transitions at strong electron-phonon coupling are determined by the energy of activation A . This A is noticeably less, than for the considered excimer molecule ( A << Ao). Consequently, the nonradiative multiphonon decay of excimer is low-probability. In the laser radiation field

(exponential) increase of the nonradiative decay of excimer. the energy. of activation can become less A,, which has the result in thelessential >

Accordingly, the ignition of the nonradiative transitions occurs at:

Thus, even at the moderate intensity of the laser radiation.

ACKNOWLEDGMENTS

The investigation is executed at financial support INTAS (N 99-01495)

REFERENCES

1 . Mollow B.R., Phys. Rev. 1969, v.188, p.1969. 2. Kovarsky V.A., i2ftrltiqucmttim Transitions, “Shtiintsa”, Kishinev, 1974, p.228. 3. Belousov A.V., Kovarsky V.A., Sineavsky E.P., Optical properties of the rnolectilar system in low~freqziency laser ~ucliationjelcl, “Shtiintsa”, Kishinev, 1989, p. 128. 4. Datsyuk V.K., Izmailov I.A., Kochelap V.A., Physics-Uspekhi 1998, v.41, (4), p.379. 5 . Janszky J., A.P., Vinogradov An.V., Kobayashi T.,Chem.Phys.Lett.l993,~.213,p.386. 6. Kim M.S., F.A.M. de Oliveira, Knight P.L., Phys. Rev. A 1989, v.40, (5) , p.2494. 7 . FainV.M., J. Chem. Phys. 1976, v.65,p.1854.