ХИМИЧЕСКАЯ ФИЗИКА, 2004, том 23, № 2, с. 53-60
ЭЛЕМЕНТАРНЫЕ ^^^^^^^^^^
ФИЗИКО-ХИМИЧЕСКИЕ ПРОЦЕССЫ
УДК 539.194.196
DISSOCIATIVE RECOMBINATION OF SLOW ELECTRONS WITH MOLECULAR OXYGEN IONS IN THE INTENSIVE LASER FIELD
© 2004 г. G. V. Golubkov*, M. G. Golubkov*, R. J. Buenker**
*N.N. Semenov Institute of Chemical Physics RAS, Moscow, Russia **Bergische Universitaet GH Wuppertal, Germany Received 16.11.2002
The low-temperature reaction e- + O+ —► O(^) + O(3P) in the field of monochromatic laser radiation with the frequency range 13000-25000 cm-1 is studied. We take into account the direct and resonance nonradiative
3 _
transitions, free-bound radiative transitions into field-induced predissociative n1pnu( ~Lu) Rydberg - states, and bound-bound dipole-allowed transitions from intermediate Rydberg states into Schumann-Runge continuum
3 _
mixed with the low-lying 3pnu( Xu) Rydberg state. The analysis is performed in terms of the multichannel
quantum defect theory (MQDT) using the stationary formalism of the radiative collision matrix. The calculations of wavefunctions and adiabatic terms of the system are carried out. The dependences of the reaction cross section on the incident electron energy, the external electromagnetic field strength and frequency, as well as the angle between the directions of the electron beam and the electric vector for linearly polarized radiation are calculated. The cross section is shown to increase by several orders of magnitude for a certain choice of these parameters, suggesting the possible laser stimulation of this reaction.
1. INTRODUCTION
The dissociative recombination (DR) reaction between slow electrons e- and molecular ions XY+,
e- + XY+ —- X + Y*, (1)
plays an important role in the processes that take place in the Earth's ionosphere and upper atmosphere and is the subject of intensive experimental and theoretical studies [1-3]. Investigation of this reaction in an external electromagnetic field is also of great importance both in the theory of radiative collisions and in developing laser stimulation methods for elementary processes involving atoms and molecules [4]. The reaction (1) with participation of oxygen molecular ions is of particular interest of investigators since it is responsible for the green airglow (caused by the 1S to 1D transition at 5577 A) in Earth atmosphere and has been proposed as one of several nonthermal mechanisms for the disappearance of water from Martian surface [5, 6].
Under the condition (h = me = e = 1)
pf vf < 1, p = j2Ee, (2)
(p is the incident electron momentum; f and of are the electromagnetic field amplitude and frequency, respectively), the vibration amplitude of the electron is much smaller than its wavelength and the external field does not affect the electron motion; i.e. it has a certain energy Ee. If the field does not produce any dipole-allowed transitions in an isolated XY+ ion, then it acts most effectively on the states formed at an intermediate stage of a process, because the field action on the (electron +
+ target) system here is possible only if the latter has internal structure [7]. For positive molecular ions, this structure is related to the formation of an intermediate XY** complex. Under the condition (2), the electromagnetic field effect must show up during the formation of this complex, when the electron motion is a multichannel one. Note that the problem of a strong electromagnetic field effect on the intermediate complex differs from conventional nonstationary problems of the theory of laser interaction with atoms and molecules [8-10]. The difference lies in the fact that the time when the intermediate complex emerges cannot be determined (under quantum conditions) and that the study needs to be carried out in the coupling of closed channels with continua.
It should be explained what the strong laser radiation is. We have in mind an external field that is weak compared to the intra-atomic field (e.g., the field strength for the ground atomic state of hydrogen is fa ~ ~ 5 ■ 109 V/cm, which corresponds to a radiation Ia ~ ~ 3.2 ■ 1016 W/cm2) but strongly couples intermediate Rydberg states, which are steady (or quasi-steady) in its absence. In that case, the coupling coefficients prove to be large and perturbation theory is inapplicable.
An additional constraint on the external field strength,
fD < 1 (3)
where D is the transition dipole moment, allows us to restrict our analysis to the following two types of transitions when describing reaction (1): a nonradiative (k = 0) and an induced (k = 1) transition with the radia-
tion of a single photon. The index k denotes the change in the number of photons in the system.
The reaction e- + O+ + kay with quantum yield of
metastable atoms O(D) in the visible spectrum region passes in the following way
e-(lA) + O+(2ng, v = 0)
^ [O2**(Hkf nu(vk)) ~ O*(B3XU)] ^ (4a) —- O(3P) + O(D), e-(lA) + O+(v = 0
— [O*2(nolAg(v > 1)) O*(B3XU)] ^ (4b) —► O (3P) + O (1D).
Here nk and vk are the principal and vibrational quantum numbers (value vk >1 for k = 0 and vk = 0 for k = 1), l and A are the electron orbital angular momentum and its projection onto the molecular axis, respectively. The electron energy is assumed to be low and lies within the range 0 < Ee < a, where a is the ion vibration frequency. Therefore, we neglect bound-bound dipoleal-lowed transitions from the intermediate n0lAg resonance Rydberg states to the n1pnu( 3XU) predissociation states, since their contribution relative to the leading n0pnu series turns out to be small [11].
In the visible spectrum region the reaction (4) can pass by three basic mechanisms. The first one (M1) is significant in the whole frequency range lying above low bound of the visible spectrum (=13000 cm-1). It is responsible for the direct and resonant radiation's transition
(k = 0) into Schumann-Runge continuum (B 3XU), i.e.
pn ^ np%u(% vo=1) — B3XU, k = 0. (5) Second (M2) is responsible for free-bound radiation transitions (k = 1) into predissociative Rydberg n1pnu( 3XU) states in the frequency region [12]
23000 < ay < 25000 cm1.
The transition scheme for all allowed ingoing lA channels of electron takes the form
sa
d c dn dS
•3 p nu( % v 1 = 0 ) ^ B%, k =1. (6)
It includes the bound-bound dipole-allowed transitions from Rydberg states of intermediate complex into Schu-
nann-Runge continuum and to low-lying 3pnu( 3XU ) predissociative Rydberg state [13]. The corresponding transition scheme is as follows
nscg ( 3nr v 0 = 1)
ndcg ( 3ng, v 0 = 1) B3xu
nd%g ( 3Xg, v 0 = 1) _3 p Ku( v 1 = 1 )_
ndSg( ng, v 0 = 1)
The third mechanism (M3) is the most effective in the frequency region
22000 < ay < 23000 cm1.
(7)
k = 1
where the intermediate Rydberg states of O2 molecule are in the left side and possible Schunann-Runge continuum states are in the right side of Eq. (7).
In the case of v1 = 1 the mixing between nscg and ndog (owing to interaction with dissociative 13ng and 23ng states) can be neglected [14], since the corresponding potential curves cross the ion potential curve in the vicinity of left and right turn points of v = 3 vi-bronic state and the configuration interaction is weak [1]. On account of the reason we neglect the direct transitions into dissociative 23ng state which correlates with the quantum yields of the reaction (4) at the infinity.
The present paper is concerned with the investigation of reaction (4) in the frequency region 13000 < oy < < 25000 cm-1, where the processes (4a), (4b) are well-separated and weakly overlapped. The analysis is performed in terms of MQDT using the stationary formalism of the radiative collision matrix [7]. The stationary approach is valid if the laser-pulse duration is much longer than the time scales of intermolecular transitions in the intermediate complex. For example, the predissociation time scales for a highly excited XY** molecule are of the order of ^ 10-11 s. The intensity of typical tunable lasers widely used in various photoprocesses ranges from 1012 to 1014 W/cm2, the pulse duration is x ^ 10-8 s, and the pulse repetition period is Ax ^ 10-3 s. The broadening through saturation and the rotational broadening here do not exceed 10-1 cm-1, while the Doppler broadening is eliminated in a standard way by means of light-beam splitting [15]. Since the accuracy of measuring the energy dependence of the cross sections for reaction (1) does not exceed AE ^ 10-3 eV, the spread in external-radiation frequency oy in the pulse may be disregarded, assuming the radiation to be monochromatic.
Taking into account the above constraints, we analyzed the dependences of the cross section for reaction (4) on the external field frequency and strength, as well as on the angle between the directions of the electron beam and the electric field of linearly polarized laser radiation.
2. INTEGRAL VARIANT OF MQDT
Assuming the external electromagnetic field to be classical (taking the average number of photons to be large, N0 > 1), we will describe the interaction of the XY+ + e- system with this field by a time-periodic dependence,
u f = 2 Vf cos œ ft, Vf =
f
Df
V
Under condition (2) the analysis can be carried out in the framework of the stationary MQDT, in which the field is taken into account by introducing quasi-energetic states and related new channels of motion [7]. The subsequent analysis is based on information about adiabatic terms of the intermediate Rydberg complex XY**. We will also deal with the rotationally adiabatic spectral range Bn3 < 1 (B is rotational ion constant and n is the principal quantum number of the Rydberg level), where the molecular axis during the collision is assumed to be fixed and the analysis is carried out in the coordinate system associated with the molecule. We determine the zero Hamiltonian H0 on a Coulomb basis in such a way that all interactions in the isolated (diabatic) X + Y* configuration are exactly taken into account. I
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