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35
УДК 539.196
Вестник СПбГУ. Сер. 4. 2013. Вып. 4
G. V. Golubkov, M. G. Golubkov, A. Z. Devdariani
QUENCHING OF RYDBERG STATES IN SLOW COLLISIONS WITH NEUTRAL ATOMS AND MOLECULES OF MEDIUM*
Quenching of Rydberg states by the neutral molecules of the medium is of great interest for the chemical physics of the upper atmosphere [1]. During periods of solar activity in the upper atmosphere (extending from 50 to 110 km and higher above the Earth's surface) the microwave radiation (MWR) is formed, whose intensity is much higher than the background ionosphere radiation. This emission is due to radiative transitions between Rydberg states of atoms and molecules that are excited by the action of the incoming radiation and flow of electrons emitted from the ionosphere. The additional background MWR unscathed passes through Earth's atmosphere and is an undesirable factor in the impact on the biosphere [2].
At present it is unclear exactly where the maximum intensity of additional background MWR is formed because at high altitudes (well above 100 km) intensity is low due to the rarefaction of the atmospheric gas, but at the small altitudes (less than or approximately 50 km) surplus excitation quenched efficiently is quenched efficiently owing to the interactions with neutral particles of the medium. On the one hand, this fact is explained by the lack of reliable information about the nature of the atmospheric gas density distribution in the band from 50 to 110 km above the Earth. The density of the medium is known to significantly affect the rate of elementary chemical reactions (dissociation and recombination of electrons and ions, chemi- and Penning ionization, collisional and radiative quenching of excited states, etc.). On the other hand, there is no common understanding of density-dependent mechanisms of formation of the MWR frequency profile. A constructing of the general phenomenon picture requires the determination of the shock and radiation quenching dynamic of highly excited atom and molecule states as a function of the perturbing gas density. To describe the radiation spectrum light in a rarefied gas it can confine taking into account perturbation generated by a neutral particle. In more dense medium it should be considered the effect of a finite number N of randomly moving particles in the volume of the excited atoms or molecules on the optical characteristics of the system (the position and level shifts, wave functions and the corresponding dipole moments).
The most effective quenching process occurs by the interaction of Rydberg particles A** with oxygen molecules through the intermediate ionic complex stage (see Figure)
A**(n) + O2 ^ A+O^s) ^ A**(n') + O2, (n' < n)
where s is the vibrational quantum number. This is due to the fact that the negative ion O^ has a series resonance of vibrationally excited autoionizing levels located on the background of the ionization continuum.
Gennady Valentinovich Golubkov — Professor, Semenov institute of chemical physics RAS, Moscow; e-mail: [email protected]
Maxim Gennadievich Golubkov — Senior Research Fellow, Saint Petersburg State University; e-mail: [email protected]
Alexander Zurabovich Devdariani — Dr. Sci. in physics and mathematics, Herzen University, St. Petersburg; Saint Petersburg State University; e-mail: [email protected]
* По материалам международного семинара «Collisional processes in plasmas and gas laser media», 22—24 апреля 2013 г., физический факультет СПбГУ.
Семинар был проведён при софинансировании фондом «Династия».
© G. V. Golubkov, M. G. Golubkov, A. Z. Devdariani, 2013
Schematic representation of the quenching process of a particle Rydberg A** on the harpoon mechanism
For low-lying electronically excited states the existing quantum chemical methods allow to calculate the required characteristics. But these methods are unsuitable for the case of Rydberg states, and we should use here alternative approaches [3]. The greatest difficulties of describing the collisional quenching of excited states are consisted in the need of correct solving of the dynamic scattering problem. The main processes leading to a decrease in the excitation of reagents are the direct exchange of energy (pulse mechanism) [4] and nonadi-abatic transitions (through intermediate valence or ionic configuration). Their effectiveness is determined by the values of the temperature of free electrons and neutral components of the medium. For fast collisions (when the relative velocity of the colliding particles is much higher than the root-mean-square velocity of the weakly bound electron), the pulse mechanism is dominated.
The second mechanism is more preferable at lower temperatures of the medium (that is usually implemented in the upper atmosphere). In this case, the consideration requires of the preliminary construction of the potential energy surfaces (PES) of interacting particles with the diversity of the pseudocrossing areas which are responsible for the nonadiabatic transitions. The next step is reduced to the calculation of differential and total cross sections for the reaction, which is performed within the semiclassical approach using the idea of moving image points on the various branches of the PES. Then it is necessary to consider a variety of nonadiabatic transitions near the points of quasi-crossings by a successively adding the amplitudes of these transitions with taking into account the phase variations.
The problem is greatly simplified if the PES of interacting quantum system near the quasi-crossing areas will be represented in the form of a cone and used additionally the Demkov—Osherov model [5]. In this case, the probability of transition from the initial (i) to the final state (f) can be defined as the product of some set of probabilities of nonadiabatic transitions when moving the representative point is along a given path. Next, you must take into account successively all the possible path of the imaging point and put them together properly. Nevertheless, the procedure for calculating the probability of collisional quenching process is still quite complicated even in this approximation.
To solve this problem you can use the optical potential [6], which allows to take into account successively the totality of the intermediate states in one elementary act of the slow
collision of a Rydberg atom A** with a neutral particle B, and to get rid of these difficulties. Then, for the case ii^2Tm / № "C 1 the amplitude of n.i —► n.f transition takes the form
F(ni^nf) = -±(*i |Vopt|*/>,
where n is the principle quantum number, ^ is the reduced mass of the particles A** and B, TM is the temperature of the medium, ni > nf, (ft = me = e =1). The wave functions of initial (i) and final (f) states are represented as
*i(/)(r, R) = exp(ikR)$„im(r),
where k = a/2|IEu and E& are the relative momentum and kinetic energy of colliding particles; $nlm(r) is the wave function of Rydberg atom A**; R and r are the coordinates of ion A+ and electron measured from the center of atom A; l and m are the angular momentum of an electron and its projection on the axis of quasimolecule A**B. Depending on the total energy E of a nonlocal optical interaction operator is defined as follows
Vopt = Ua+b + Ua+bGa»b [(1 + iKe-b)^1Ke-b] Ga**bUa+b- (1)
Here Ua+b is the local operator defined as [6]
Ua+b(R, R'; r, r') = (2n)6^a+b(^)6(R - R'^ (r)>($nim(r' )|,
nlm
where Ua+b(R) is the potential of A+—B interaction, Ga**b is the Green's operator of the noninteracting A** + B system
kmax
Ga**b(R, R', E) = / Ga»(g-fc2/(2^)sin^rr/^/)]fcrffc, (2)
0
ga** is the Green's operator of the isolated Rydberg atom A**; kmax = \i(E + 1 /R). Note, that for the case expression (2) is real. Operator Ke-B is presented a real e——B scattering matrix built on the standing waves in exp. (1), which consists of two parts [3]
K -K° +V V |cprs)(cprs|
The first part K0_b corresponds to the direct potential scattering. The second term describes the resonant mechanism of inelastic scattering due to transition into an intermediate ionic configuration A+—B-. Operator Ve-b in exp. ((2)) describes a configuration interaction; Er is the energy of electron affinity; Es is the vibrational s-level excitation energy of the ion A+ B-; ^rs is the vibronic wave function for bound states of this ion. In one act of collision the representative point performs multiple virtual transitions between the Rydberg and ionic configurations in the vicinity of the quasi-crossings, which are taken into account consistently in the probability Wif = |f (n ^ nf)|2 by Green's Ga**b operator (see Figure).
The probability of transitions Wif is the result of interference of the amplitudes of the individual for the entire set of such transitions. A remarkable feature of this approach is that
these transitions are consistently taken into account by introducing the interaction operator (1) in which this function is performed by Green's operator (2).
References
1. Golubkov G. V., Golubkov M. G., Manzhelii M. I. Chemical physics of upper atmosphere // Abstracts of III Int. Conf. "Atmosphere, Ionosphere, Safety". Kaliningrad, 2012. P. 23-25.
2. Avakyan S. V. Physics of the solar-terrestrial coupling: results, problems, and new approaches // Geomagn. Aeronomy. 2008. Vol. 48. P. 417-424.
3. Golubkov G. V., Golubkov M. G., Ivanov G. K. Rydberg states of atoms and molecules in a field of neutral particles // The Atmosphere and Ionosphere: Dynamics, Processes and Monitoring / eds V. L. Bychkov, G. V. Golubkov, A. I. Nikitin. New York: Springer, 2010. P. 1-68.
4. Matsuzava M. Theoretical studies of collisions of Rydberg atoms with molecules // Rydberg States of Atoms and Molecules / eds R. F. Stebbings, F. B. Dunning. Cambridge: University Press, 1983. P. 267-292.
5. Demkov Yu. N., Osherov V. I. Stationary and time-dependent quantum problems solved by the contour integral method // Sov. Phys. JETP. 1968. Vol. 26. P. 916-923.
6. Golubkov G. V., Devdariani A. Z., Golubkov M. G. Collision of Rydberg atom A** with atom B in the ground electric state. Optical potential // JETP. 2002. Vol. 95, N 6. P. 987-997.
Статья поступила в редакцию 22 апреля 2013 г.
